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• International Mathematical Olympiad
  ...le (inclusive and integers only). Full credit is only given for complete, correct solutions. Each solution is intended to be in the form of a [[proof writin
  3 KB (490 words) - 03:32, 23 July 2023
• American High School Mathematics Examination
  For every correct answer: 5 points
  3 KB (388 words) - 23:07, 5 February 2024
• AIME Problems and Solutions
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  3 KB (391 words) - 16:00, 21 February 2024
• 2004 AMC 12A Problems
  On the AMC 12, each correct answer is worth <math>6</math> points, each incorrect answer is worth <math
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2003 AMC 12A Problems
  ...ssumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?
  13 KB (1,955 words) - 21:06, 19 August 2023
• 2002 AMC 12A Problems
  ..., and <math>R</math> the area of the red square. Which of the following is correct?
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2003 AMC 12B Problems
  Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch rea
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2005 AMC 12B Problems/Problem 22
  Inductive Step: Suppose the formula is correct for <math>z_k</math>, then ...z|</math>. Therefore, the magnitude of <math>\frac{iz_n}{|z_n|}</math> is always <math>1</math>, meaning that all of the numbers in the sequence <math>z_k</
  4 KB (660 words) - 17:40, 24 January 2021
• 2004 AIME I Problems/Problem 6
  ...4}</math> But, this over-counts since it counts numbers like 0213. We can correct for this over-counting. Lock the first digit as 0 and permute 3 other chose
  3 KB (562 words) - 18:12, 4 March 2022
• 2004 AIME II Problems/Problem 7
  ...clear from the problem setup that <math>0<\theta<\frac\pi2</math>, so the correct value is <math>\tan(\theta)=\frac53</math>. Next, extend rays <math>\overri
  9 KB (1,501 words) - 05:34, 30 October 2023
• 1984 AIME Problems
  ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. Students are not
  6 KB (933 words) - 01:15, 19 June 2022
• 1988 AIME Problems
  ...ailable ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1, 2, 3, 6, 9\}</math> as
  6 KB (902 words) - 08:57, 19 June 2021
• 2002 AIME II Problems
  ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
  7 KB (1,177 words) - 15:42, 11 August 2023
• 1984 AIME Problems/Problem 10
  ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. (Students are no Let Mary's score, number correct, and number wrong be <math>s,c,w</math> respectively. Then
  7 KB (1,163 words) - 23:53, 28 March 2022
• 1988 AIME Problems/Problem 8
  Since this is an AIME problem, there is exactly one correct answer, and thus, exactly one possible value of <math>f(14,52)</math>.
  4 KB (538 words) - 13:24, 12 October 2021
• 1988 AIME Problems/Problem 1
  ...available ten-button lock may be opened by pressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1,2,3,6,9\}</math> as its
  1 KB (181 words) - 18:23, 26 August 2019
• 2006 AMC 10B Problems/Problem 7
  ...As no other option choice fits, <math>\boxed{\textbf{(A)}-x}</math> is the correct solution.
  1 KB (179 words) - 10:33, 19 August 2022
• 1991 AIME Problems/Problem 6
  THIS SOLUTION IS INCORRECT, PLEASE CORRECT IT IF YOU HAVE TIME!
  3 KB (447 words) - 17:02, 24 November 2023
• 1991 AIME Problems/Problem 1
  ...r of <math>11</math> is <math>(5,11)</math>, and checking shows that it is correct.
  4 KB (628 words) - 22:05, 7 June 2021
• 2006 AMC 10B Problems/Problem 25
  ...way to do the problem is by the process of elimination. The only possible correct choices are the highest powers of each prime, <math>2^3=8</math>, <math>3^2
  5 KB (878 words) - 14:39, 3 December 2023
• 2000 AIME I Problems/Problem 15
  ...th> to <math>96</math> alternate in fake-real-fake-real, where we have the correct order of cards once the first <math>96</math> have moved and we can start p ...the spacing of the cards moved, <math>a</math> is an integer such that the correct first card is moved, and <math>k</math> is an integer greater than or equal
  15 KB (2,673 words) - 19:16, 6 January 2024
• 2000 AIME I Problems/Problem 5
  ...ing <math>2</math> and <math>7</math> for <math>w_1</math> does not give a correct product. Thus, <math>\frac{27}{50}</math> must be a reduced form of the ac
  7 KB (1,011 words) - 20:09, 4 January 2024
• 2001 AIME I Problems/Problem 6
  ...ination counts only one of the permutations; we can say that it counts the correct (ascending order) permutation. ...sformations of the problem, a recursion formula can be a robust way to the correct answer.
  11 KB (1,729 words) - 20:50, 28 November 2023
• 2003 AIME II Problems/Problem 13
  ...th> and <math>C</math>. Oh wait they are symmetric. So then if this is the correct answer, why am I wrong, or what happened to that factor of <math>3</math>?"
  15 KB (2,406 words) - 23:56, 23 November 2023
• 2002 AIME II Problems/Problem 10
  ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
  2 KB (336 words) - 19:30, 24 June 2020
• 2000 AIME II Problems/Problem 13
  ...math>, so no real solution exists for <math>x</math>. Thus our solution is correct.
  6 KB (1,060 words) - 17:36, 26 April 2024
• 2005 AMC 10B Problems/Problem 24
  ...math>11</math> while <math>(a-b)</math> is a factor of nine (1 or 9). The correct guesses are <math>a = 6, b = 5</math> causing <math>x = 65, y = 56,</math>
  5 KB (845 words) - 19:23, 17 September 2023
• 2006 AMC 12A Problems/Problem 3
  ...h>, we see <math>6\cdot8=30+18</math>. Therefore, we can see our answer is correct.
  1 KB (155 words) - 17:30, 16 December 2021
• 2006 AMC 12A Problems/Problem 8
  Thus, the correct answer is <math>\boxed{\textbf{(C) }3}.</math> Note to readers: make sure to always read the problem VERY carefully before attempting; it could mean the differ
  3 KB (450 words) - 02:00, 13 January 2024
• 2006 AMC 12A Problems/Problem 9
  ...= 72</math>. 28 is not divisible by 3, so we know that this number is not correct. Moving on to 7, <math>13 \cdot 7 = 91</math>. We know that 9 is a multiple
  3 KB (429 words) - 18:14, 26 September 2020
• Furman University Wylie Mathematics Tournament
  The test is scored as 1 point for each correct answer, 0 points for blank answers, and -.25 for incorrect answers except f
  2 KB (365 words) - 21:21, 18 March 2017
• University of South Carolina High School Math Contest/1993 Exam/Problem 20
  ...lifying of the brackets. Open the brackets and you should notice why it is correct. If you are also wondering whether or not if we got all the sets in the abo
  2 KB (263 words) - 18:13, 19 October 2021
• Pierre de Fermat
  ...rn techniques. However, a flaw was discovered soon after. Wiles managed to correct the proof by October 1994, thus solving the last of Fermat's problems. It i
  5 KB (860 words) - 17:10, 21 March 2023
• P versus NP
  The [[Clay Mathematics Institute]] has offered a USD \$1,000,000 prize for a correct solution, as it has listed it as one of its [[Millennium Problems]].
  6 KB (1,104 words) - 15:11, 25 October 2017
• Congruent (geometry)
  ...given side of <math>A'</math> on the straight line <math>a'</math>, we can always find one and only one point <math>B'</math> so that the segment <math>AB</m Every segment is congruent to itself; that is, we always have
  10 KB (1,655 words) - 21:43, 24 March 2022
• 2005 AMC 10A Problems/Problem 4
  So our correct answer choice is <math>\boxed{\textbf{(B) }\frac{2}{5}x^2}</math>
  2 KB (265 words) - 19:07, 25 December 2022
• Derangement
  ...c{1}{1} + \frac{1}{2} - \frac{1}{6}\right) = 2</math>, which we know to be correct.
  3 KB (473 words) - 12:57, 20 February 2024
• Cobb County Math Meets
  ...ive minute, twenty-five question multiple-choice test worth six points per correct response, and ten ciphering questions. Each ciphering question is worth te
  2 KB (307 words) - 20:25, 12 March 2012
• United States of America Computing Olympiad
  ...s. Every test case has equal weight within the problem. For each test case correct, you receive the points for the test case. Programs get 4 seconds per test Each test case will give feedback on how well your program did. Correct test cases show how much time and memory used. Incorrect test cases are dif
  2 KB (297 words) - 01:41, 21 January 2023
• Cyprus Mathematical Olympiad
  ...ts must answer 30 multiple choice mathematics problems in 60 minutes. Each correct answer gives 4 points, each wrong answer subtracts 1 point and no answer gi
  2 KB (366 words) - 14:26, 4 September 2017
• 1999 AMC 8 Problems/Problem 16
  Altogether, Tori answered <math>7 + 12 + 21 = 40</math> questions correct. ...e needed to answer <math>45 - 40 = 5</math> more questions to pass, so the correct answer is <math>\boxed{(B) 5}</math>
  1 KB (167 words) - 20:30, 11 January 2024
• Special relativity
  ...ciple of Relativity says it is impossible to ascertain that one of them is correct while the other is wrong.
  3 KB (538 words) - 23:39, 2 March 2008
• 2001 AMC 8 Problems
  On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and eac
  13 KB (1,994 words) - 13:04, 18 February 2024
• Georgia Tech High School Math Competition
  ...ng questions, each of which contestants have three minutes to answer. Each correct answer is worth five points. Each team's score is determined by the top fou
  3 KB (475 words) - 21:51, 31 December 2013
• Georgia Junior Varsity State Tournament
  ...twenty-five question multiple-choice test. Four points are given for each correct answer, and 1.1 points are given for each blank answer. On this round a [[
  2 KB (324 words) - 10:23, 24 April 2007
• Vestavia Hills High School Math Tournament
  ...ears. The tests consist of 25 questions which are worth 4 point each for a correct answer, minus 1 point for an incorrect answer. Ciphering rounds- 4 of them,
  1 KB (160 words) - 12:31, 27 December 2006
• GCTM State Math Tournament
  ...ons and five free-response questions; a student's score is five points per correct questions, plus one point per answer left blank; there is no penalty for in
  2 KB (353 words) - 17:02, 7 June 2009
• Georgia Southern Invitational Mathematics Tournament
  ...nior high division; a student's score is forty points plus four points per correct question minus one point per incorrect question. No calculators are permit
  1 KB (154 words) - 09:45, 21 March 2010
• Mock AIME 4 2006-2007 Problems/Problem 10
  ...o we divide the whole sum by 3 and we add or subtract <math>q(n)</math> to correct for the integer based on the modularity of the sum with 3
  4 KB (595 words) - 12:14, 25 November 2023
• 2007 AIME II Problems/Problem 14
  The answer is clearly correct, but the proof has a gap, i.e. there is no reason that <math>f(-2)\neq1</ma
  7 KB (1,335 words) - 17:44, 25 January 2022
• 1989 USAMO Problems/Problem 2
  All possibilities yield a contradiction, so our assumption can not be correct.
  3 KB (438 words) - 01:19, 27 December 2023
• 2007 Cyprus MO/Lyceum/Problems
  ...ac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}</math>, which of the following is correct?
  13 KB (1,990 words) - 08:29, 19 December 2009
• 2007 Cyprus MO/Lyceum/Problem 11
  ...ac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}</math>, which of the following is correct?
  808 bytes (139 words) - 16:56, 6 May 2007
• 2006 Cyprus MO/Lyceum/Problems
  Which of the following is correct, about the graph of <math>f</math>? ...and <math>y=\sqrt[3]{6}-\sqrt[3]{3}</math>, then which of the following is correct?
  11 KB (1,672 words) - 10:56, 27 April 2008
• Polish Mathematical Olympiad
  ...s have three problems to solve in five hours. Students with three to four correct problems are usually invited to the final round, which has the same format
  1 KB (223 words) - 22:34, 2 January 2008
• 2007 AMC 12B Problems/Problem 5
  The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each pro
  864 bytes (121 words) - 10:50, 4 July 2013
• 2006 Cyprus MO/Lyceum/Problem 4
  Which of the following is correct, about the graph of <math>f</math>? From above, <math>\mathrm{(A)}</math> is not correct because the graph does not intersect the x-axis (it is tangent to it).
  1 KB (216 words) - 10:46, 27 April 2008
• 2006 Cyprus MO/Lyceum/Problem 9
  ...and <math>y=\sqrt[3]{6}-\sqrt[3]{3}</math>, then which of the following is correct?
  1 KB (182 words) - 10:40, 27 April 2008
• 2007 AMC 12A Problems/Problem 22
  ...ind out that out of the 9 cases, in 4 the value <math>n_{?}</math> has the correct sum of digits. <br/> ...s of whether the sum carries or not, the modulo 9 of the sum of the digits always increases by <math>1</math>.
  15 KB (2,558 words) - 19:33, 4 February 2024
• PMWC Problems and Solutions
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  924 bytes (121 words) - 00:41, 12 October 2013
• 2007 AMC 12B Problems
  The 2007 AMC 12 contests will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each pro
  12 KB (1,814 words) - 12:58, 19 February 2020
• 2002 AMC 12A Problems/Problem 2
  ...; the number that Cindy started with is <math>3(43)+9=138</math>. Now, the correct result is <math>\frac{138-3}{9}=\frac{135}{9}=15</math>. Our answer is <mat ...ath>. Solve for <math>x</math> gives us <math>x=138</math>. Therefore, the correct result is <math>\frac{138-3}{9}=\frac{135}{9}=\boxed{\textbf{(A) }15}</math
  1 KB (163 words) - 12:46, 8 November 2021
• 1999 AHSME Problems
  Which one of the following must necessarily be correct?
  13 KB (1,945 words) - 18:28, 19 June 2023
• 2004 AMC 12A Problems/Problem 2
  On the AMC 12, each correct answer is worth <math>6</math> points, each incorrect answer is worth <math
  837 bytes (122 words) - 20:14, 3 July 2013
• Ideal gas law
  ...-[[density]], low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the [[van der Waals equation]] is ano
  1 KB (225 words) - 08:59, 11 March 2008
• 2008 AMC 12B Problems/Problem 23
  ...whence we immediately obtain <math>\framebox[1.2\width]{(A)}</math> as the correct answer.
  5 KB (814 words) - 18:02, 17 January 2023
• 2007 AMC 10A Problems/Problem 9
  Therefore the correct answer is <math>\mathrm{(E)}</math>
  2 KB (268 words) - 12:40, 3 June 2021
• 1995 AHSME Problems
  The addition below is incorrect. The display can be made correct by changing one digit <math>d</math>, wherever it occurs, to another digit
  17 KB (2,387 words) - 22:44, 26 May 2021
• 1951 AHSME Problems
  <math> \textbf{(B)}\ \text{In some cases there is more than one correct order in proving certain propositions.} </math> <math> \textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposi
  23 KB (3,641 words) - 22:23, 3 November 2023
• 2002 AMC 12B Problems/Problem 12
  For all integers x, <math>x^2</math> is always a positive integer. So solve for <math>\frac{n}{20-n} = 0</math>, getting < ...hat also yield an integer n value, meaning that there are 4 values, so the correct answer is <math>\boxed{(D)}</math>
  4 KB (579 words) - 05:54, 17 October 2023
• 2004 AMC 12B Problems/Problem 23
  ...e of <math>2004</math>, so there is a very high probability that it is the correct answer.
  3 KB (533 words) - 14:52, 29 October 2023
• 2008 AMC 12B Problems/Problem 22
  Subtracting that from 1 to get the probability she can park, the correct answer is <math>\boxed{E}</math>.
  4 KB (653 words) - 11:06, 15 October 2022
• 2008 AIME I Problems/Problem 6
  ...Indeed, note that <math>a(1,k) = 2^{1-1}(1+2k-2)=2k-1</math>, which is the correct formula for the first row. We claim the result by [[induction]] on <math>n<
  3 KB (509 words) - 17:21, 22 March 2018
• NYSML Problems and Solutions
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  1 KB (115 words) - 13:51, 1 May 2008
• Mathleague.org
  |4 points per correct answer, 0 points per blank answer, -1 points per incorrect answer |1 point per correct answer, 0 points otherwise
  5 KB (801 words) - 12:47, 23 September 2023
• 2003 AMC 12B Problems/Problem 18
  ...<math>a+b+c+d=7+5+11+8=31</math>. <math>\boxed{\textbf{(B)}\ 31}</math> is correct.
  6 KB (914 words) - 11:07, 7 September 2023
• 1995 AHSME Problems/Problem 13
  The addition below is incorrect. The display can be made correct by changing one digit <math>d</math>, wherever it occurs, to another digit ...either a <math>5</math> (no carry) or a <math>6</math> (carry) to create a correct statement.
  1 KB (223 words) - 13:59, 5 July 2013
• Millennium Problems
  ...of them as soon as the mathematical community had pronounced his solution correct. All but one of these problems had been solved by the meeting in 2000, and
  13 KB (1,969 words) - 17:57, 22 February 2024
• 2008 iTest Problems
  Michael plays catcher for his school's baseball team. He has always been a great player behind the plate, but this year as a junior, Michael's Joshua finds an answer which Michael confirms is correct. What is Joshua's correct answer (the units digit of <math>2008^{2008}</math>)?
  71 KB (11,749 words) - 01:31, 2 November 2023
• Asymptote: Macintosh
  ...e are what you really need to compile it - the first 2 are to get into the correct folder), in the terminal, run:
  5 KB (732 words) - 00:47, 13 December 2023
• 2005 AMC 8 Problems
  have divided the number by 2 to get the correct answer. What is the correct
  13 KB (1,821 words) - 22:18, 5 December 2023
• 2003 AMC 12A Problems/Problem 10
  ...ssumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?
  1 KB (213 words) - 10:16, 4 July 2013
• Intermediate Math Open
  ...have given up, they turn them in for 4 more. A scoreboard reports how many correct answers various teams have. There are a total of 36 problems, to be complet
  1 KB (243 words) - 17:53, 1 November 2014
• 2002 AMC 10A Problems
  ...9, but instead, Cindy subtracted 9, then divided by 3, getting 43. If the correct instructions were followed, what would the result be? ..., and <math>R</math> the area of the red square. Which of the following is correct?
  11 KB (1,733 words) - 11:04, 12 October 2021
• 2002 AMC 10A Problems/Problem 2
  ...}5.5) + (\text{a little})</math>, and as all the options are integers, the correct one is <math>\boxed{\textbf{(C) }6}</math>.
  1,017 bytes (138 words) - 12:26, 8 November 2021
• 2002 AMC 12A Problems/Problem 8
  ..., and <math>P</math> the area of the red square. Which of the following is correct?
  2 KB (345 words) - 12:50, 8 November 2021
• 1962 IMO Problems/Problem 3
  ...if he clearly understands what he is doing- just a little mistake) Here is correct soluton:
  3 KB (581 words) - 02:00, 6 May 2023
• 1963 IMO Problems/Problem 4
  Can someone change this answer so it's correct?
  3 KB (415 words) - 00:51, 15 September 2023
• 1998 AHSME Problems/Problem 18
  Clearly, <math>M = A+C \Longrightarrow</math> the correct answer is <math>\mathrm{(A)}</math>. ...math> which is negative. Thus <math>\mathrm{(A)}</math> is indeed the only correct answer.
  1 KB (187 words) - 14:29, 5 July 2013
• 2000 AMC 10 Problems/Problem 5
  Only <math>1</math> quantity changes, so the correct answer is <math>\boxed{\text{B}}</math>.
  1 KB (242 words) - 01:24, 27 July 2023
• 1985 AJHSME Problems/Problem 25
  ...if one of these is correct, then the other option in its pair must also be correct. There can't be 2 answers. So, the only remaining answer choice is <math>\b
  2 KB (300 words) - 09:07, 22 January 2023
• 1986 AJHSME Problems/Problem 23
  This is equal to the area of a small circle, hence the correct answer is <math>\boxed{\text{(B)}\ 1}</math>.
  2 KB (277 words) - 21:32, 3 July 2013
• 1987 AJHSME Problems
  ...sts of <math>20</math> questions. The scoring is <math>+5</math> for each correct answer, <math>-2</math> for each incorrect answer, and <math>0</math> for e
  12 KB (1,568 words) - 09:35, 31 October 2021
• 1987 AJHSME Problems/Problem 3
  &= 1800 & \text{ Thus \boxed{\text{E}} is the correct answer}
  1 KB (138 words) - 01:03, 22 January 2020
• 2004 AMC 12B Problems/Problem 9
  The entire situation is in the picture below. The correct answer is <math>\boxed{\mathrm{(E)}\ (3,2)}</math>.
  955 bytes (149 words) - 19:56, 3 July 2013
• 2004 AMC 12B Problems/Problem 14
  ...th>. So we place bets on <math>\boxed{\mathbf{(D)}240/13} </math> which is correct!
  7 KB (1,083 words) - 22:41, 23 November 2020
• 2009 AMC 12A Problems/Problem 15
  ...w verify which of <math>n=96</math> and <math>n=97</math> will give us the correct imaginary part.
  4 KB (634 words) - 16:34, 3 December 2020
• 2001 AMC 12 Problems/Problem 8
  Therefore the correct answer is <math>\boxed{\textbf{(C)} \text{ A cone with slant height of } 10
  2 KB (279 words) - 00:32, 30 December 2023
• 2001 AMC 12 Problems/Problem 23
  Note: I think this solution is not correct. the products of the roots are integers do not mean the product of the two Note: I believe this solution is correct. We know that the two real solutions are integers and that the final produc
  6 KB (1,035 words) - 09:18, 3 September 2023
• 2001 AMC 12 Problems/Problem 16
  ...hings on all legs is <math>\frac{1}{2^{8}}</math>. Therefore the number of correct permutations must be <math>\boxed{\frac {16!}{2^8}}</math>.
  3 KB (418 words) - 23:48, 3 July 2022
• 2001 AMC 12 Problems/Problem 12
  This is correct.
  7 KB (1,110 words) - 15:20, 30 May 2022
• 2001 AMC 12 Problems/Problem 18
  ...ch puts the center on the wrong side of <math>A</math>, so this is not the correct case.
  5 KB (822 words) - 01:35, 7 February 2024
• 2001 AMC 12 Problems/Problem 20
  ...us <math>D</math> outside the first quadrant, hence the first case is the correct one. As <math>(6,3)</math> is the midpoint of <math>CD</math>, we can compu
  2 KB (238 words) - 11:21, 7 April 2022
• 2009 AMC 10B Problems/Problem 1
  ...or <math>3.00</math> dollars. So, <math>\boxed{\textbf{(B) } 2}</math> is correct.
  4 KB (585 words) - 22:41, 14 September 2021
• 2009 AMC 12B Problems
  ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?
  13 KB (2,030 words) - 03:04, 5 September 2021
• 2009 AMC 12B Problems/Problem 22
  ...general content of this solution, that would be great. If the notation is correct, then just delete this footnote)
  6 KB (1,071 words) - 22:25, 9 October 2021
• 2009 AMC 12B Problems/Problem 10
  ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time? ...or any given hour. Hence the fraction of the day that the clock shows the correct time is <math>\frac 23 \cdot \left(1 - \frac {15}{60}\right) = \frac 23 \cd
  2 KB (372 words) - 17:36, 28 June 2021
• 2009 AMC 10B Problems
  ...ncorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?
  15 KB (2,262 words) - 00:53, 18 June 2021
• 1987 AJHSME Problems/Problem 24
  ...sts of <math>20</math> questions. The scoring is <math>+5</math> for each correct answer, <math>-2</math> for each incorrect answer, and <math>0</math> for e Let <math>c</math> be the number of questions correct, <math>w</math> be the number of questions wrong, and <math>b</math> be the
  2 KB (325 words) - 12:17, 28 July 2020
• API:User::get user name
  echo "I should never be seen since the API sends in correct parameters.<br>\n";
  2 KB (210 words) - 08:37, 17 November 2022
• 2010 AMC 12A Problems/Problem 9
  ...2\times 2</math> cube is included in each of these three cuts. To get the correct result, we can take the sum of the volumes of the three cuts, and subtract
  2 KB (383 words) - 17:42, 28 June 2021
• 2002 AMC 10B Problems/Problem 25
  Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math> We can check that this is the correct answer by having <math>4, 9, 6,</math> and <math>1</math> as our numbers. T
  4 KB (679 words) - 19:11, 17 September 2023
• 2010 AMC 10B Problems
  ...gnored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for <math>a</math>, <m ...multiple choice math contest, students receive <math>4</math> points for a correct answer, <math>0</math> points for an answer left blank, and <math>-1</math>
  12 KB (1,817 words) - 22:44, 22 December 2020
• 2010 AMC 12B Problems
  ...gnored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for <math>a</math>, <m
  12 KB (1,845 words) - 13:00, 19 February 2020
• Ball-and-urn
  ...ou can imagine that any balls in the "repeat" urns are moved on top of the correct balls in the first <math>n</math> urns, moving from left to right. There is
  5 KB (775 words) - 23:53, 13 April 2024
• 2007 AMC 8 Problems/Problem 15
  ...b</math>, adding a positive number (<math>a</math>) to <math>c</math> will always make it greater than <math>b</math>. ...see that <math>3+1>2</math>, so <math>\boxed{\textbf{(A) }a+c<b}</math> is correct.
  1 KB (187 words) - 17:18, 3 November 2023
• 2010 AMC 12B Problems/Problem 5
  ...ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for <math>a</math>, <ma
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• Python reference
  ...cial kind of function called a constructor. The name of the constructor is always the name of the corresponding class. t.right(90) # point in the correct direction
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• 2007 AMC 8 Problems/Problem 20
  We can check each answer choice from left to right to see which one is correct. Suppose the Unicorns played <math>48</math> games in total. Then, after di
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• 1999 AMC 8 Problems/Problem 15
  ...answer is <math>5 \cdot 5 \cdot 4 - 5 \cdot 3 \cdot 4 = 40</math>, and the correct choice is <math>\boxed{D}</math> ...s. So, <math>100-60=\boxed{40}</math> ADDITIONAL plates can be made.So the correct choice is <math>\boxed{D}</math>
  3 KB (516 words) - 14:50, 21 December 2022
• 2005 CEMC Gauss (Grade 7) Problems/Problem 2a
  Calculating, <math>0.8 - 0.07 = 0.80 - 0.07 = 0.73</math> The correct answer is <math>\boxed E</math>.
  347 bytes (43 words) - 23:04, 1 January 2020
• 2010 AMC 10B Problems/Problem 15
  ...multiple choice math contest, students receive <math>4</math> points for a correct answer, <math>0</math> points for an answer left blank, and <math>-1</math>
  1 KB (210 words) - 02:44, 26 September 2020
• 1958 AHSME Problems
  ...ath> dollars and <math> x</math> cents, the incorrect amount exceeding the correct amount by <math> \$17.82</math>. Then: \textbf{(D)}\ \text{the incorrect amount can equal twice the correct amount}\qquad \\
  25 KB (3,872 words) - 14:21, 20 February 2020
• 2011 AMC 10A Problems/Problem 19
  ...=25</math>. This time, <math>p^2+300=22^2+300=784=28^2</math>. This is the correct pair. Now, we find the percent increase from <math>22^2=484</math> to <math ...iffer by <math>300</math>, and we can confirm that <math>484</math> is the correct starting number by noting that <math>484+150=634=25^2+9</math>. Thus, the a
  3 KB (545 words) - 20:54, 21 August 2023
• 2011 AMC 10A Problems/Problem 23
  ...mod {729}</math> and less than <math>1,000</math> is <math>365</math>, the correct answer is <math> \boxed{365\ \mathbf{(C)}} </math>.
  6 KB (926 words) - 23:38, 8 April 2024
• 2011 AMC 10B Problems/Problem 23
  ...previous tens digit plus the ones digit (or one) and the hundreds digit is always the previous hundreds digit plus the previous tens digit. Knowing this, we ...previous tens digit plus the ones digit (or one) and the hundreds digit is always the previous hundreds digit plus the previous tens digit. Knowing this, we
  9 KB (1,287 words) - 20:37, 20 August 2023
• 2011 AMC 12B Problems
  ...-digit number <math>a</math>. His erroneous product was 161. What is the correct value of the product of <math>a</math> and <math>b</math>? ...ath>y</math> integers, makes successive jumps of length <math>5</math> and always lands on points with integer coordinates. Suppose that the frog starts at <
  13 KB (1,978 words) - 16:28, 12 July 2020
• 2011 AMC 12B Problems/Problem 4
  ...er <math>a</math>. His erroneous product was <math>161.</math> What is the correct value of the product of <math>a</math> and <math>b</math>? ...Therefore, <math>a = 32</math> and <math>b = 7.</math> Multiplying our two correct values of <math>a</math> and <math>b</math> yields
  1 KB (187 words) - 14:13, 19 January 2021
• 2001 AMC 10 Problems/Problem 7
  After testing, we find that <math>\boxed{\textbf{(C)}\ 0.02}</math> is the correct answer.
  940 bytes (141 words) - 14:25, 28 July 2022
• 2002 AMC 8 Problems
  ...ct answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?
  15 KB (2,102 words) - 09:58, 5 May 2024
• 2011 AIME II Problems/Problem 9
  ...answers (which contradict the problem statement), but the final answer is correct.
  3 KB (466 words) - 15:06, 16 January 2023
• 1997 PMWC Problems/Problem T10
  ...h>, we can see from the arrangement provided above that that cannot be the correct answer.
  2 KB (328 words) - 15:48, 7 January 2020
• 2000 AMC 8 Problems/Problem 4
  We can look at the graphs and note that the only one that has all the correct points is <math>\boxed{E}</math>
  3 KB (406 words) - 17:29, 22 October 2020
• 2011 AMC 10B Problems
  ...er <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>? ...>n</math> people in this room have birthdays falling in the same month" is always true?
  13 KB (2,090 words) - 18:05, 7 January 2021
• 2011 AMC 10B Problems/Problem 5
  ...er <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>?
  817 bytes (121 words) - 13:07, 24 January 2024
• 2001 AMC 8 Problems/Problem 22
  On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and eac
  1 KB (177 words) - 03:14, 12 March 2024
• 2007 AMC 10B Problems
  ...<math>10</math> will be scored by awarding <math>6</math> points for each correct response, <math>0</math> points for each incorrect response, and <math>1.5<
  15 KB (2,297 words) - 12:57, 19 February 2020
• 2007 AMC 10B Problems/Problem 6
  ...{ AMC }10</math> will be scored by awarding <math>6</math> points for each correct response, <math>0</math> points for each incorrect response, and <math>1.5<
  1 KB (184 words) - 21:15, 25 July 2018
• 2011 AMC 10B Problems/Problem 8
  ...is either cool or cloudy, which means <math>\boxed{\textbf{(B)}}</math> is correct.
  1 KB (214 words) - 21:04, 5 February 2018
• 1999 AHSME Problems/Problem 10
  Which one of the following must necessarily be correct? Three of the statements are correct, and only one digit is on the card. Thus, one of I and III are false. There
  788 bytes (137 words) - 14:34, 5 July 2013
• 2007 AMC 10B Problems/Problem 20
  ...}</math>, <math>\text{(B)}</math>, or <math>\text{(C)}</math> could be the correct answer. Clearly, there are more than <math>125</math> ways, thus yielding <
  3 KB (397 words) - 02:40, 16 January 2023
• 1998 AHSME Problems/Problem 2
  ...r, <math>\frac{A+B}{C+D} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>.
  1,008 bytes (167 words) - 14:28, 5 July 2013
• 2012 AMC 12B Problems/Problem 23
  ...s a 5th root of unity as a root. We will show that we were \textit{almost} correct in our initial assumption; that is that <math>z_0</math> is at most a 5th r
  11 KB (1,979 words) - 17:25, 6 September 2021
• 1998 AJHSME Problems/Problem 25
  .... Altogether, the three had <math>144 + 108 = 252</math> dollars, and the correct answer is <math>\boxed{D}</math>
  1 KB (216 words) - 13:56, 18 August 2019
• 1998 AJHSME Problems/Problem 23
  ...t. Thus, the answer is <math>\frac{28}{64} = \frac{7}{16}</math>, and the correct choice is <math>\boxed{C}</math>
  2 KB (279 words) - 15:23, 29 May 2021
• 1997 AJHSME Problems/Problem 3
  ...th> has the largest thousandths digit of the remaining answers, and is the correct answer. <math>A</math> has an "invisible" thousandths digit of <math>0</ma
  1 KB (154 words) - 00:26, 5 July 2013
• CEMC
  If you find a mistake, feel free to correct it or inform RTG by [http://www.artofproblemsolving.com/Forum/ucp.php?i=pm&
  4 KB (616 words) - 14:42, 28 March 2021
• 2005 CEMC Gauss (Grade 7) Problems
  = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
  16 KB (2,317 words) - 03:54, 24 October 2014
• 2005 CEMC Gauss (Grade 7) Problems/Problem 1
  <math>\frac{3\times{4}}{6}=\frac{12}{6}=2</math> The correct answer is <math>B</math>.
  372 bytes (50 words) - 01:36, 23 October 2014
• 2011 IMO Problems/Problem 1
  (Note: The above solution looks generally correct, but the actual answer should be <math>\{11a, a, 5a, 7a\}</math>,<math>\{a,
  9 KB (1,718 words) - 23:08, 26 June 2014
• 2002 AMC 8 Problems/Problem 17
  ...ct answer. If Olivia answered every problem and her score was 29, how many correct answers did she have? ...he got <math>10 - x</math> questions wrong. Since she gains 5 points for a correct answer and loses 2 for an incorrect one, we can solve <math>5x - 2(10 - x)
  2 KB (288 words) - 18:31, 20 January 2024
• 2002 AMC 8 Problems/Problem 16
  ...=Z</math>, which is one of the answer choices. Since there can only be one correct answer, and there is already one, we see that the answer must be <math>\box
  2 KB (336 words) - 20:00, 15 April 2023
• 2000 AMC 8 Problems/Problem 18
  Thus, the correct answer is <math>\boxed{E}</math>.
  3 KB (516 words) - 20:05, 15 April 2023
• 2005 AMC 8 Problems/Problem 1
  ...ivided the number by <math>2</math> to get the correct answer. What is the correct answer?
  832 bytes (128 words) - 09:10, 8 January 2024
• 2008 iTest Problems/Problem 9
  Joshua finds an answer which Michael confirms is correct. What is Joshua's correct answer (the units digit of <math>2008^{2008}</math>)?
  2 KB (245 words) - 19:23, 4 August 2018
• 1999 AMC 8 Problems/Problem 18
  ...<math>\left\lceil \frac{162}{15} \right\rceil = 11</math> batches, and the correct answer is <math>\boxed{E}</math>. ...raph above to find that there needs to be <math>11</math> batches, and the correct answer is <math>\boxed{E}</math>.
  2 KB (296 words) - 02:00, 28 February 2022
• 1997 AJHSME Problems/Problem 13
  ...{ 42} \cdot 100\% = 30.9\%</math> of all jellybeans are yellow. Thus, the correct answer is <math>\boxed{A}</math>
  2 KB (226 words) - 00:26, 5 July 2013
• 1996 AJHSME Problems/Problem 5
  ...th> is thus indeed a negative number. So option <math>\boxed{A}</math> is correct. Option <math>B</math> is the product of two negatives, which is always positive.
  3 KB (506 words) - 00:24, 5 July 2013
• 1997 AHSME Problems/Problem 15
  ...e is <math>6\cdot \frac{1}{2}\cdot\frac{16}{3}\cdot 4 = 64</math>, and the correct answer is <math>\boxed{D}</math>.
  2 KB (406 words) - 20:44, 15 February 2024
• 2010 AMC 8 Problems/Problem 9
  Ryan got <math>80\%</math> of the problems correct on a <math>25</math>-problem test, <math>90\%</math> on a <math>40</math>-p ...on the third. This amounts to a total of <math>20+36+7=63</math> problems correct. The total number of problems is <math>25+40+10=75.</math> Therefore, the p
  946 bytes (131 words) - 23:30, 6 January 2024
• 2010 AMC 8 Problems/Problem 24
  What is the correct ordering of the three numbers, <math>10^8</math>, <math>5^{12}</math>, and ...follows that <math>\boxed{\textbf{(A)}\ 2^{24}<10^8<5^{12}}</math> is the correct answer.
  2 KB (324 words) - 16:08, 31 December 2023
• 1996 AHSME Problems
  ...orrect. What is the largest digit that can be changed to make the addition correct?
  15 KB (2,343 words) - 13:39, 19 February 2020
• 1996 AHSME Problems/Problem 1
  ...orrect. What is the largest digit that can be changed to make the addition correct?
  1,005 bytes (141 words) - 16:06, 14 July 2021
• 1996 AHSME Problems/Problem 14
  ...6\cdot 20 + 8\cdot 20 = (0 + 2 + 4 + 6 + 8)\cdot 20 = 400</math>, and the correct answer is <math>\boxed{C}</math>.
  1 KB (166 words) - 14:07, 5 July 2013
• 1996 AHSME Problems/Problem 28
  ...6</math>, this number should be just a little over <math>2</math>, and the correct answer is <math>\boxed{\text{(C)}}</math>.
  3 KB (545 words) - 10:21, 16 September 2022
• 1996 AHSME Problems/Problem 29
  ...count the factors of <math>2n</math>, to see which prime factorization is correct and has <math>28</math> factors.
  5 KB (828 words) - 05:52, 26 October 2023
• 2010 PUMaC Problems
  // NOTE: I've tampered with the angles to make the diagram not-to-scale. The correct numbers should be 72 instead of 76, and 45 instead of 55.
  22 KB (3,694 words) - 23:58, 3 June 2022
• 2016 AMC 10A Problems/Problem 20
  ...s that <math>N</math> is around these numbers. This suspicion proves to be correct, as we see that <math>\binom{14}{4} = 1001</math>, giving us our answer of
  4 KB (630 words) - 15:13, 8 October 2023
• 1984 AHSME Problems/Problem 26
  ...so <math>[BED]=12</math>, which makes <math>\boxed{\textbf{B}}</math> the correct answer.
  2 KB (303 words) - 20:28, 2 October 2023
• 1984 AHSME Problems/Problem 30
  Therefore the correct answer is <math>\boxed{\textbf{(B)}}</math>.
  3 KB (447 words) - 21:21, 17 July 2020
• 1950 AHSME Problems
  ...es zero}\qquad\\ \textbf{(E)}\ \text{Only some of the above statements are correct} </math> Of these statements, the correct ones are:
  22 KB (3,306 words) - 19:50, 3 May 2023
• 1951 AHSME Problems/Problem 50
  The journey took 8 hours, so the correct answer is <math>\boxed{\textbf{(D)}}</math>.
  2 KB (327 words) - 15:55, 6 April 2020
• 2006 AMC 8 Problems/Problem 2
  As the AMC 8 only rewards 1 point for each correct answer, everything is irrelevant except the number Billy answered correctly
  526 bytes (71 words) - 01:13, 5 July 2013
• 2006 AMC 8 Problems/Problem 12
  Adding them up gets <math> 7+16+27=50 </math>. The overall percentage correct would be <math> \frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overl
  778 bytes (98 words) - 01:13, 5 July 2013
• 1985 AHSME Problems
  ...},</cmath> where <math>i^2 = -1</math>, then which of the following is not correct?
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 23
  ...},</cmath> where <math>i^2 = -1</math>, then which of the following is not correct?
  3 KB (578 words) - 00:47, 20 March 2024
• 2010 AMC 8 Problems
  Ryan got <math>80\%</math> of the problems correct on a <math>25</math>-problem test, <math>90\%</math> on a <math>40</math>-p What is the correct ordering of the three numbers, <math>10^8</math>, <math>5^{12}</math>, and
  18 KB (2,768 words) - 21:05, 9 January 2024
• Alcumus
  Occasionally you will encounter multiple choice problems. Simply enter the correct letter for these problems. Probabilities, decimal values, and ratios should always be expressed as simplified common fractions unless otherwise specified.
  3 KB (533 words) - 10:55, 7 February 2023
• 1950 AHSME Problems/Problem 39
  Of these statments, the correct ones are: ...we can choose some term that is less than any given positive quantity. The correct answer is therefore <math>\boxed{\textbf{(E)}\ \text{Only }4\text{ and }5}<
  1 KB (217 words) - 16:13, 9 May 2015
• 1950 AHSME Problems/Problem 37
  \textbf{(D)}\ \text{If }0<x<1,y\text{ is always less than 0 and decreases without limit as }x\text{ approaches zero} \qquad \textbf{(E)}\ \text{Only some of the above statements are correct}</math>
  2 KB (313 words) - 17:09, 15 March 2017
• 2012 AMC 10A Problems/Problem 23
  ...the total amount of combinations is <math>6!=720</math>. However, we must correct for our overcounting because of rotation and reflection. We have that ther
  5 KB (815 words) - 17:53, 12 October 2023
• 2012 AMC 12A Problems/Problem 17
  [Errors to correct below: We don't totally discard 0 (mod 5), since we can still have one of t
  3 KB (519 words) - 19:01, 30 March 2024
• 2012 AMC 10B Problems
  ...acted her rounded values. Which of the following statements is necessarily correct? ...or screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, th
  18 KB (2,350 words) - 18:48, 9 July 2023
• 2012 AMC 12B Problems/Problem 6
  ...acted her rounded values. Which of the following statements is necessarily correct?
  1 KB (246 words) - 07:32, 29 June 2023
• 2012 AMC 10B Problems/Problem 6
  ...acted her rounded values. Which of the following statements is necessarily correct?
  1 KB (187 words) - 16:07, 18 January 2020
• 2012 AMC 12B Problems
  ...acted her rounded values. Which of the following statements is necessarily correct?
  20 KB (2,681 words) - 09:47, 29 June 2023
• 2012 AMC 12B Problems/Problem 17
  ....4 = 32/5</math>. Thus, answer choice <math>\boxed{\textbf{(C)}}</math> is correct.
  12 KB (2,183 words) - 21:05, 23 December 2023
• 2012 AMC 12B Problems/Problem 19
  ...\sqrt{2}}{4}</math>. Thus, Answer choice <math>\boxed{\text{A}}</math> is correct.
  5 KB (815 words) - 21:59, 19 September 2023
• 2012 AMC 10B Problems/Problem 13
  ...dfrac{3c}{2}} = 40</math> seconds. Answer choice <math>\boxed{B}</math> is correct.
  2 KB (351 words) - 21:42, 21 August 2023
• 2010 AMC 8 Problems/Problem 20
  ...s that <math>x=3</math>. Thus, <math>\boxed{\textbf{(A)}\ 3}</math> is the correct answer.
  2 KB (297 words) - 09:05, 10 March 2023
• 2010 AMC 8 Problems/Problem 2
  Thus, answer choice <math>\boxed{\textbf{(D)}\ \frac{10}{3}}</math> is correct.
  669 bytes (94 words) - 19:59, 5 February 2023
• 2010 AMC 8 Problems/Problem 13
  ...= 11</math>. Thus, answer choice <math>\boxed{\textbf{(E)}\ 11}</math> is correct. ...+9=30</math>. Thus, answer choice <math>\boxed{\textbf{(E)}\ 11}</math> is correct.
  1 KB (212 words) - 20:54, 22 January 2023
• How to run Pygame Programs
  ...p up when you run the program. Once you are confident that your program is correct, you can double-click on the Python file directly to run it.
  2 KB (373 words) - 21:44, 15 March 2012
• 2012 AIME I Problems/Problem 3
  ...t for the <math>9</math> different ways in which the person to receive the correct meal could be picked. Note, this implies that the dishes are indistinguisha Note: This solution gets the correct answer through coincidence and should not be used.
  3 KB (572 words) - 18:56, 13 June 2023
• 2017 AMC 8 Problems
  ...h> of the problems she solved alone. What was Zoe's overall percentage of correct answers?
  12 KB (1,771 words) - 21:13, 20 January 2024
• 2012 USAMO Problems/Problem 3
  This construction is correct because, for any <math>k> 1</math>,
  4 KB (790 words) - 06:38, 27 October 2022
• 1951 AHSME Problems/Problem 10
  ...ement <math>\boxed{\textbf{(C)}}</math> is therefore incorrect, and is the correct answer choice. ...th>A = \frac{1}{2} bh</math>). Statement <math>\textbf{(D)}</math> is also correct: let <math>q = \frac{a}{b}</math>. Then <math>q' = \frac{a \div 2}{2b} = \f
  2 KB (255 words) - 12:20, 5 July 2013
• 1951 AHSME Problems/Problem 14
  <math> \textbf{(B)}\ \text{In some instances there is more than one correct order in proving certain propositions.}</math> <math> \textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposi
  1,021 bytes (157 words) - 12:20, 5 July 2013
• 1951 AHSME Problems/Problem 15
  ...^3</math> - <math>n</math> always for any integer <math>n</math>.Hence,the correct answer is <math>6</math>.
  1 KB (191 words) - 06:08, 6 April 2024
• 1951 AHSME Problems/Problem 21
  ...x > y</math> and <math> z\ne 0</math>. The inequality which is not always correct is:
  1 KB (189 words) - 02:34, 28 June 2017
• 1974 AHSME Problems
  Which statement is correct?
  15 KB (2,151 words) - 14:04, 19 February 2020
• 1974 AHSME Problems/Problem 14
  Which statement is correct?
  866 bytes (136 words) - 12:43, 5 July 2013
• 2006 SMT/Calculus Problems
  ...th> (0.6, 0.4) </math>. Assuming for the moment that this approximation is correct (it is, to better than <math> 1\% </math>) and so the point lies on Alan's
  3 KB (525 words) - 13:59, 27 May 2012
• 2006 SMT/General Problems
  ...et right <math> 3\frac{1}{2} </math> hours ago. Now another clock which is correct shows noon. In how many minutes, to the nearest minute, will the alarm cloc ...nd/or minus signs between the digits on the left side to make the equation correct: <math> 1+2+3-4+5+6+78+9=100 </math>. Do this with only three plus or minus
  10 KB (1,477 words) - 16:02, 27 May 2012
• 1950 AHSME Answer Key
  37: <math>\textbf{(E)}\ \text{Only some of the above statements are correct}</math>
  3 KB (443 words) - 06:25, 20 January 2023
• 1953 AHSME Problems
  Then if <math>x = \overline{CD}</math> and <math>y = \overline{BD}</math> the correct proportion is: ...ed. The intersections of the pairs of trisectors adjacent to the same side always form:
  21 KB (3,123 words) - 14:24, 20 February 2020
• 1953 AHSME Problems/Problem 45
  ...s are <math>a</math> units and <math>b</math> units respectively. Then the correct relation between them is: Since both lengths are positive, the [[AM-GM Inequality]] is satisfied. The correct relationship between <math>a</math> and <math>b</math> is <math>\boxed{\tex
  689 bytes (111 words) - 23:02, 14 February 2020
• 1954 AHSME Problems
  ...}\\ \textbf{(D)}\ \text{are always acute angles}\\ \textbf{(E)}\ \text{are always unequal to each other} </math> ...The expression has only the value 1.}\\ \textbf{(D)}\ \text{The expression always has a value between }-1\text{ and }+2.\\ \textbf{(E)}\ \text{The expression
  23 KB (3,535 words) - 16:29, 24 April 2020
• 1955 AHSME Problems
  To correct the total obtained the clerk must: ...{(A)}\ \text{always increases as }x\text{ increases}\\ \textbf{(B)}\ \text{always decreases as }x\text{ decreases to 1}\\ \textbf{(C)}\ \text{cannot equal 0}
  22 KB (3,509 words) - 21:29, 31 December 2023
• 1985 USAMO Problems
  correct to four decimal places.
  2 KB (284 words) - 14:44, 18 July 2016
• Rapid Rabbit Relays
  ...other mathlete's problem, so it's critical that Role 1 gets his/her answer correct.
  931 bytes (153 words) - 17:05, 4 October 2012
• 2010 AMC 8 Problems/Problem 7
  .../math> nickel, <math>2</math> dimes, and <math>4</math> pennies. Thus, the correct answer is <math>3+2+1+4=\boxed{\textbf{(B)}\ 10}</math>.
  1 KB (183 words) - 14:33, 28 December 2023
• 2012 AMC 8 Problems
  ...as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? What is the correct ordering of the three numbers <math> \frac{5}{19} </math>, <math> \frac{7}{
  13 KB (1,835 words) - 08:51, 8 March 2024
• 2012 AMC 8 Problems/Problem 3
  ...as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
  1 KB (234 words) - 21:18, 28 June 2022
• 2012 AMC 8 Problems/Problem 13
  ...h>, looking into the answers, <math>2</math> or <math>4</math> is possibly correct. It gives us the price of each pencil should be <math> 0.44/2=0.22 </math>
  2 KB (309 words) - 15:36, 28 December 2023
• 2012 AMC 8 Problems/Problem 20
  What is the correct ordering of the three numbers <math> \frac{5}{19} </math>, <math> \frac{7}{ ...\frac{14}{(x+14)^2}</math> and this is positive. Because the derivative is always positive and the values of <math>x</math> given by this question <math>(5,
  4 KB (513 words) - 18:34, 20 January 2024
• 2013 AMC 10A Problems/Problem 2
  ...{4}</math> cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
  978 bytes (150 words) - 13:10, 1 July 2023
• 2013 AMC 10A Problems
  ...{4}</math> cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
  12 KB (1,894 words) - 15:59, 3 January 2024
• 2013 AMC 12B Problems/Problem 13
  ...is lower than 240. Therefore, <math>\boxed{\textbf{(D) }240}</math> is the correct answer.
  3 KB (443 words) - 12:32, 8 January 2021
• 1951 AHSME Problems/Problem 45
  ...ithout the use of a table (note: in 1951, calculators were very rare). The correct answer is therefore <math>\boxed{\textbf{(A)}\ \log 17}</math>.
  1 KB (194 words) - 12:27, 5 July 2013
• 1991 AHSME Problems/Problem 29
  ...frac{(21)(49)}{400}</cmath> so <cmath>PQ=\frac{7}{20}\sqrt{21}</cmath> The correct answer is <math>\fbox{(B)}</math>.
  1 KB (193 words) - 22:05, 20 April 2024
• 2003 AMC 12B Problems/Problem 11
  Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch rea
  1 KB (168 words) - 00:54, 5 January 2014
• 2003 AMC 12B Problems/Problem 12
  ...th>3 \cdot 5 = 15</math>, so <math>{\boxed{\textbf{(D)15}}}</math> is the correct answer.
  2 KB (357 words) - 16:43, 29 June 2021
• CSS: Pseudo-class and Pseudo-element
  ...e first curly bracket, always starts with a colon ( : ), and this colon is always immediately followed by the name of the pseudo-class. is not correct; you cannot nest a :not() pseudo-class inside a :not() pseudo-class. <!-- S
  15 KB (2,197 words) - 22:49, 24 July 2023
• 2005 CEMC Gauss (Grade 7) Problems/Problem 2
  Calculating, <math>0.8 - 0.07 = 0.80 - 0.07 = 0.73</math> The correct answer is <math>E</math>.
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• Fundamental Theorem of Sato
  Whatever AoPS says is correct, and AoPS says that Mr. Sato is amazing. Thus, Mr. Sato is amazing. (Proved
  605 bytes (95 words) - 16:50, 28 January 2024
• Mock AIME I 2015 Problems/Problem 2
  Note: It is correct, original one was the first one posted but was incorrect.
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• 2014 AIME II Problems/Problem 14
  -edited by srisainandan6 to clarify and correct a small mistake
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• 2013 USAJMO Problems/Problem 6
  ...t{y - 1} + \sqrt{z - 1}</math> for x = y = z. We suspect if the inequality always holds. We are almost done, but we need to find the correct argument. (How frustrating!)
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• 2016 AMC 10A Problems
  ...ath>1</math> and <math>2016</math>, inclusive. Which of the following is a correct statement about the probability <math>p</math> that the product of the thre
  14 KB (2,104 words) - 22:26, 16 September 2022
• 2006 SMT/General Problems/Problem 3
  ...of its correct envelope, so it is not possible to have exactly nine in the correct envelopes. Therefore, the answer is <math>\boxed{0}</math>.
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• 1962 AHSME Problems/Problem 2
  Since we cannot simplify further, the correct answer is <math>\boxed{\textbf{(A)}\ \frac{\sqrt{3}}{6}}</math>
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• 1962 AHSME Problems/Problem 23
  <math>\textbf{(E)}\ \text{none of these is correct} </math>
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• 1962 AHSME Problems/Problem 27
  ..., with <math>a ! a = a</math>. Which of the following three rules is (are) correct? The first rule must be correct as both sides of the equation pick the larger out of a and b.
  1 KB (258 words) - 22:25, 17 April 2023
• 1962 AHSME Problems/Problem 31
  ...math>2</math>, leaving us with <math>\boxed{\textbf{(C)}\ 3}</math> as the correct answer.
  2 KB (261 words) - 18:19, 25 March 2021
• 1962 AHSME Problems/Problem 40
  Testing the answer choices, we see that <math>\boxed{B}</math> is the correct answer.
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• 1962 AHSME Problems
  \textbf{(E)}\ \text{none of these is correct} </math> Which of the following three rules is (are) correct?
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• 1951 AHSME Problems/Problem 36
  Which of the following methods of proving a geometric figure a locus is not correct?
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• 2013 AMC 8 Problems
  ...er hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. .... By which of the following might her incorrect sum have differed from the correct one?
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• 2013 AMC 8 Problems/Problem 13
  .... By which of the following might her incorrect sum have differed from the correct one? The correct score was <math>10a+b</math>. Clara misinterpreted it as <math>10b+a</math>
  1 KB (203 words) - 21:40, 3 January 2024
• 1994 AHSME Problems
  ...th>14</math>. After these mistakes, the result was <math>16</math>. If the correct operations had been used, the value produced would have been
  14 KB (2,124 words) - 13:39, 19 February 2020
• 1952 AHSME Problems/Problem 11
  <math> f(1)=\frac{3}{0} </math>, which is undefined. Hence, the (in)correct answer is <math> \boxed{\textbf{(C)}\ f(1)=0} </math>.
  870 bytes (142 words) - 20:45, 2 January 2014
• Utah State Math Contest
  ...questions in both tests, with 2 1/2 hours given to complete the problems. Correct answers are worth 4 points, incorrect answers worth -1, and unanswered ques
  554 bytes (87 words) - 12:01, 15 February 2014
• 1967 AHSME Problems/Problem 31
  <math>\textbf{(A)}\ \text{always an even integer}\qquad \textbf{(C)}\ \text{always an odd integer}\qquad
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• 1968 AHSME Problems
  ...<math>6</math> instead of being multiplied by <math>6.</math> Based on the correct answer, the error thus committed, to the nearest percent, is : ...OG</math> increases toward the value <math>a</math>, while <math>JH</math> always equals <math>HG</math>, the ratio <math>K:R</math> becomes arbitrarily clos
  16 KB (2,571 words) - 14:13, 20 February 2020
• 1994 AHSME Problems/Problem 5
  ...th>14</math>. After these mistakes, the result was <math>16</math>. If the correct operations had been used, the value produced would have been We reverse the operations that he did and then use the correct operations. His end result is <math>16</math>. Before that, he subtracted <
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• 2014 AMC 8 Problems/Problem 1
  ...and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If
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• 2014 AMC 12A Problems/Problem 12
  We will estimate the answer using a wrong method then guess the correct answer choice. ...ead ''about'' 4. We can asume that the closest other answer choice to 4 is correct: <cmath>\boxed{\textbf{(D) }2+\sqrt3}</cmath>
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• Alabama School of Fine Arts
  Scored +4 points correct, 0 for blank, -1 for incorrect '''PLUS''' 3 tie breaker completion question Scored 5 points for correct in first interval, 2 points for correct in second interval<br>
  885 bytes (129 words) - 19:56, 13 February 2014
• 2014 AIME I Problems/Problem 9
  ...traint that the answer is an integer, we can be certain that our answer is correct.)
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• 1968 AHSME Problems/Problem 8
  ...<math>6</math> instead of being multiplied by <math>6.</math> Based on the correct answer, the error thus committed, to the nearest percent, is :
  472 bytes (66 words) - 01:52, 16 August 2023
• 1990 AHSME Problems/Problem 13
  So the correct answer is <math>201</math>, which is <math>\fbox{E}</math>
  1 KB (189 words) - 20:13, 23 January 2017
• 1970 AHSME Problems/Problem 4
  ...f <math>S</math> which is divisible by 11. Thus, <math>\fbox{B}</math> is correct.
  2 KB (297 words) - 20:09, 6 January 2018
• 1970 AHSME Problems/Problem 13
  ..., the LHS is always equal to the RHS, so <math>\fbox{D}</math> is the only correct statement.
  2 KB (287 words) - 21:34, 13 July 2019
• 1970 AHSME Problems/Problem 17
  ...math>, which directly contradicts <math>A</math>. Thus, <math>A</math> is always false. ...s do not follow from the premises, leading to <math>\fbox{E}</math> as the correct answer.
  2 KB (282 words) - 02:37, 17 December 2021
• 1970 AHSME Problems/Problem 25
  ...cents of first-class postage on a letter weighing <math>W</math> ounces is always .../math> cents, while option <math>E</math> gives <math>12</math> cents, the correct answer. Thus, the answer is <math>\fbox{E}</math>.
  1 KB (244 words) - 06:54, 15 July 2019
• 1952 AHSME Problems/Problem 49
  We can force this triangle to be equilateral because the ratios are always <math>3:3:1</math> no matter which rotation, and with the symmetry of the e ...o this, the coordinate bash with all these calculations should get you the correct answer. Also, there is an even bashier way using all the points and shoelac
  7 KB (1,136 words) - 10:01, 23 December 2023
• 1988 AHSME Problems
  That is, whatever <math>C</math> is, the announced value must be the correct result when <math>C</math> is rounded to that number of digits.
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• 1986 AHSME Problems
  ...new scoring system that year, one received <math>5</math> points for each correct answer, ...started with <math>30</math> points, received <math>4</math> more for each correct answer,
  17 KB (2,512 words) - 18:30, 12 October 2023
• 1958 AHSME Problems/Problem 45
  ...ath> dollars and <math> x</math> cents, the incorrect amount exceeding the correct amount by <math> &#036;17.82</math>. Then: \textbf{(D)}\ \text{the incorrect amount can equal twice the correct amount}\qquad \\
  795 bytes (124 words) - 06:29, 3 October 2014
• 1975 AHSME Problems
  ...^3</math>, and <math>a-b = x</math>, which of the following conclusions is correct? ...th>CD</math> intersects side <math>AC</math> at <math>N</math>. Then it is always true that
  16 KB (2,512 words) - 04:48, 27 November 2021
• 1971 AHSME Problems
  If <math>(1.0025)^{10}</math> is evaluated correct to <math>5</math> decimal places, then the digit in the fifth decimal place
  18 KB (2,703 words) - 20:50, 11 September 2023
• 1965 AHSME Problems
  ...<math>\frac {1}{1 + y}, |y| < 1</math>, the ratio of the error made to the correct value is: ...atter how <math>a, b, c, d</math>, and <math>e</math> are chosen, we shall always have:
  19 KB (2,873 words) - 18:57, 16 August 2023
• 1961 AHSME Problems
  If a certain operation on one or more members of the set always yields a member of the set, \textbf{(E)}\ \text{None of these are correct}</math>
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• Utah Math Olympiad
  ...7 points. Partial credit will be awarded for significant progress toward a correct solution.
  1 KB (215 words) - 18:48, 5 July 2021
• 2014 UNC) Math Contest II Problems
  The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
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• 2014 UNCO Math Contest II Problems/Problem 10
  The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
  2 KB (297 words) - 03:33, 13 January 2019
• 2014 UNCO Math Contest II Problems
  The guests know that the March Hare always does this, but they has more correct guesses than all the others, that guest wins. When
  7 KB (1,228 words) - 15:10, 20 August 2020
• 1988 AHSME Problems/Problem 10
  That is, whatever <math>C</math> is, the announced value must be the correct result when <math>C</math> is rounded to that number of digits.
  1 KB (148 words) - 18:11, 26 February 2018
• 2005 CEMC Gauss (Grade 7) Problems/Problem 12
  ...the height of the plant on May 8th is <math>2 + 7.35 = 9.35 m</math>. The correct answer is <math>E</math>.
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• 2005 CEMC Gauss (Grade 7) Problems/Problem 13
  ...1}{2}bh = \frac{1}{2}(9)(4) = \frac{1}{2}(36) = 18</math>. Therefore, the correct answer is <math>D</math>
  1,020 bytes (149 words) - 02:14, 23 October 2014
• 2005 CEMC Gauss (Grade 7) Problems/Problem 14
  ...of the numbers on the six unseen faces is <math>42 - 21 = 21</math>. The correct answer is <math>C</math>.
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• 2005 CEMC Gauss (Grade 7) Problems/Problem 15
  ...d the area of triangle <math>PVT</math>, or <math>12 + 6 = 18</math>. The correct answer is <math>A</math>.
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• 1986 AHSME Problems/Problem 12
  ...new scoring system that year, one receives <math>5</math> points for each correct answer, ...started with <math>30</math> points, received <math>4</math> more for each correct answer, lost <math>1</math> point for each wrong answer, and neither gained
  1 KB (208 words) - 18:32, 1 April 2018
• 1986 AHSME Problems/Problem 15
  <math>\textbf{(A)}\ \text{correct}\quad \textbf{(B)}\ \text{always less than A}\quad
  1 KB (185 words) - 18:43, 1 April 2018
• 1998 CEMC Gauss (Grade 7) Problems
  = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
  10 KB (1,590 words) - 16:43, 29 January 2021
• 1999 CEMC Gauss (Grade 7) Problems
  = Part A: Each correct answer is worth 5 points = = Part B: Each correct answer is worth 6 points =
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• 2014 AMC 8 Problems
  ...and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If ...ntify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random wil
  13 KB (1,957 words) - 12:08, 13 January 2024
• 2014 AMC 8 Problems/Problem 11
  ...math>10-6=4</math> paths possible. <math>\boxed{(\text{A})4}</math> is the correct answer.
  2 KB (352 words) - 21:47, 6 January 2024
• 2014 AMC 8 Problems/Problem 12
  ...ntify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random wil There is a <math>\frac{1}{3}</math> chance that the reader will choose the correct baby picture for the first person. Next, the second person gives a <math>\f
  2 KB (310 words) - 11:12, 2 July 2023
• 2015 AMC 10A Problems/Problem 14
  ...ratio of 1/3, so the angle it carves is 120 degrees, which leads us to the correct answer of 4 o' clock. <math>\boxed{\textbf{(C) }4 \ \text{o' clock}}</math
  9 KB (1,380 words) - 09:00, 1 December 2023
• 2015 AMC 12B Problems/Problem 4
  Let --- denote any of the 6 racers not named. Then the correct order looks like this:
  1 KB (224 words) - 14:57, 23 November 2023
• 2015 AIME II Problems/Problem 5
  ...we can conclude that for a grid that is <math>n \times n</math>, there are always <math>4</math> corners squares, <math>4(n-2)</math> edge squares, and <math ...plication and simplification finds us with <math>\boxed{090}</math> as the correct answer.
  4 KB (653 words) - 17:40, 1 July 2023
• 2015 AIME II Problems/Problem 8
  ...ing both sides of the inequality by 2b - 3, but otherwise this solution is correct)
  5 KB (856 words) - 22:39, 14 February 2024
• Greedy algorithm
  ...[[algorithm|algorithms]] are formed by adjusting the greedy process to be correct, often through the use of clever [[sorting]]. ...rally very interesting unless they're <i>correct</i>; in other words, they always produce the maximal overall benefit. In order to prove the correctness of a
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• 1954 AHSME Problems/Problem 50
  The times between <math>7</math> and <math>8</math> o'clock, correct to the nearest minute, when the hands of a clock will form an angle of <mat ...for the two hands to make <math>84^{\circ}</math> angles. Thus the times, correct to the nearest minute, at which the hands of the clock will form an <math>8
  2 KB (361 words) - 11:59, 21 January 2021
• 2018 UNCO Math Contest II Problems
  (c) Give an explanation that shows that the formula you give is correct.
  6 KB (1,055 words) - 12:37, 30 July 2021
• 2018 UNCO Math Contest II Problems/Problem 9
  (c) Give an explanation that shows that the formula you give is correct.
  1 KB (176 words) - 21:02, 28 October 2023
• 2016 AIME I Problems/Problem 11
  ...tion <math>\frac{P(x+1)}{P(x)}=\frac{x+2}{x-1}</math> but will give us the correct values of <math>P(2)</math> and <math>P(3)</math>. Thus <math>P(x)=a(x-1)x(
  8 KB (1,415 words) - 14:00, 22 December 2021
• 2016 AIME II Problems/Problem 9
  ...th>, so <math>b=9, 7, 5, 3</math>. Testing out <math>b=9</math> yields the correct answer of <math>\boxed{262}</math>. Note that even if this answer were asso
  6 KB (983 words) - 01:18, 2 February 2023
• 2006 iTest Problems
  ...<math>12</math> of these <math>20</math> multiple choice questions correct, given that you don't know how to work any of them and are for ...robability that exactly <math>6</math> of the books were returned to their correct (original) position can be expressed as <math>\frac{m}{n}</math>, where <ma
  31 KB (4,811 words) - 00:02, 4 November 2023
• 1954 AHSME Problems/Problem 37
  \textbf{(E)}\ \text{none of these is correct} </math>
  3 KB (560 words) - 10:11, 3 May 2020
• 1975 AHSME Problems/Problem 12
  ...^3</math>, and <math>a-b = x</math>, which of the following conclusions is correct?
  850 bytes (151 words) - 17:09, 19 January 2021
• 1985 USAMO Problems/Problem 2
  correct to four decimal places.
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• 1975 Canadian MO Problems
  ...l after they have sat down, and it turns out that no one is sitting in the correct seat. Prove that the table can be rotated so that at least two of the guest
  3 KB (499 words) - 12:17, 11 August 2016
• 1975 Canadian MO Problems/Problem 6
  ...l after they have sat down, and it turns out that no one is sitting in the correct seat. Prove that the table can be rotated so that at least two of the guest
  717 bytes (123 words) - 16:45, 4 August 2016
• Mock AIME 3 2010 Problems
  be placed in the envelopes so that no letter is in a correct envelope?
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• 2017 AMC 10A Problems/Problem 5
  Note: we can easily verify that this is the correct answer; for example, <math>\left(\frac{1}{2}, \frac{1}{2}\right)</math> wor
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• 2017 AMC 10A Problems/Problem 6
  ...has been negated as well as reversed.) We know that the contrapositive is always true if the given statement is true. Note: An A is usually 90%-100% of the questions correct.
  3 KB (485 words) - 16:50, 5 August 2022
• 2017 AMC 10A Problems/Problem 15
  <math>\fbox{C}</math> is the correct answer.
  4 KB (533 words) - 19:01, 15 March 2024
• 2017 AMC 12A Problems/Problem 9
  ...uantities is no greater than the common value. Which of the following is a correct description of <math>S</math>?
  3 KB (446 words) - 14:58, 10 June 2023
• 2017 AMC 10A Problems/Problem 12
  ...antities is no greater than this common value. Which of the following is a correct description for <math>S?</math>
  2 KB (421 words) - 00:34, 1 August 2021
• 2017 AMC 10A Problems
  ...antities is no greater than this common value. Which of the following is a correct description for <math>S?</math>
  15 KB (2,285 words) - 18:02, 28 October 2023
• 2017 AMC 10A Problems/Problem 17
  ...h>\textbf{(E)}</math> tried? This is because the problem can only have one correct answer, so if we have an option that already works, we can conclude that no
  5 KB (864 words) - 01:42, 17 August 2023
• 2017 AMC 10A Problems/Problem 20
  ...that we can use for this problem is that a multiple of <math>9</math> will always have its digits sum to a multiple of <math>9</math>. We can find out that t ...sible by <math>9</math>). But since it does not, <math>1</math> is not the correct answer.
  5 KB (798 words) - 14:35, 14 October 2022
• 2017 AMC 12A Problems
  ...uantities is no greater than the common value. Which of the following is a correct description of <math>S</math>?
  15 KB (2,418 words) - 16:58, 7 November 2022
• 2017 AMC 10B Problems/Problem 9
  ...e 3 ways has a probability associated with it, so probability of getting 1 correct is <math>3 * \frac{4}{27} = \frac{4}{9} </math>
  3 KB (452 words) - 08:16, 4 November 2021
• 2017 AIME I Problems/Problem 2
  .../math> is divided by the positive integer <math>n</math>, the remainder is always the positive integer <math>s \neq r</math>. Find <math>m+n+r+s</math>. ...so yields remainders of <math>5</math>, which means our work up to here is correct.
  4 KB (580 words) - 03:08, 5 January 2024
• 2017 AIME I Problems/Problem 5
  First, note that the first two digits will always be a positive number. We will start with base twelve because of its repetit ...h> and <math>64.30_8</math>. Since <math>d\neq0</math>, the first value is correct. Compiling the necessary digits leaves us a final answer of <math>\boxed{32
  6 KB (961 words) - 22:03, 18 January 2024
• 2017 AIME I Problems/Problem 15
  ...math>n=2\sqrt{3}</math>. When we plug in these two values, we recover the correct answer of <math>\frac{75\sqrt3}{67}</math>.
  22 KB (3,622 words) - 17:11, 6 January 2024
• 1992 IMO Problems/Problem 1
  Since <math>21</math> is a factor of <math>63</math>, this solutions is correct. ...e <math>112</math> is a factor of <math>224</math>, this solutions is also correct.
  3 KB (503 words) - 00:40, 17 November 2023
• 2017 AMC 8 Problems/Problem 14
  ...h> of the problems she solved alone. What was Zoe's overall percentage of correct answers? ...= \frac{93}{100} = \boxed{\textbf{(C) } 93}</math> percent of the problems correct.
  4 KB (649 words) - 13:49, 14 January 2024
• 2008 iTest Problems/Problem 15
  *Feel free to edit answer if this is not correct, but do not edit the process.
  1,002 bytes (137 words) - 13:25, 22 June 2018
• MIE 2016
  Choose the correct answer. ...epetition, such that the sum of the numbers of three adjacent triangles is always a multiple of 3? Solutions obtained by rotation or reflection are different
  8 KB (1,278 words) - 09:46, 11 January 2018
• MIE 2016/Problem 1
  Choose the correct answer.
  502 bytes (63 words) - 20:57, 7 January 2018
• 1956 AHSME Problems/Problem 44
  ...math>x^2, a^2,</math> and <math>ax</math> are all positive. Hence the only correct answer is <math>\fbox{B}</math>.
  603 bytes (103 words) - 22:17, 7 July 2018
• 2018 AMC 10A Problems/Problem 23
  ...145}{147}</math>, so <math>\boxed{\textbf{(D) } \frac{145}{147}}</math> is correct.
  16 KB (2,454 words) - 13:30, 23 September 2023
• 2018 AMC 10A Problems/Problem 21
  ...4</math> total roots (counting multiplicity). We see that <math>x=0</math> always has at least one intersection at <math>(0,-a)</math> (and is in fact a doub ...from the vertex. Therefore, <math>\boxed{\textbf{(E) }a>\frac12}</math> is correct.
  9 KB (1,502 words) - 23:31, 19 August 2023
• 2018 AMC 10B Problems/Problem 11
  ...a non-multiple of 3 is always <math>1 \pmod{3}</math>, the only expression always a multiple of <math>3</math> is <math>\boxed{\textbf{(C) } p^2+26} </math>. Therefore, <math>\framebox{C}</math> is the correct answer.
  2 KB (279 words) - 14:35, 5 November 2023
• 2018 AMC 10B Problems/Problem 9
  ...sum with equal probability as <math>10</math> is <math>39</math>. So, the correct answer is <math>\boxed{\textbf{(D)} \text{39}}</math>, and we are done. ...d on and on and on. This means that <math>P(10)=P(39)</math>, and thus the correct answer is <math>\boxed{\textbf{(D)} \text{ 39}}</math>.
  5 KB (835 words) - 13:48, 16 February 2024
• 2018 AMC 10B Problems/Problem 18
  ...<math>3</math> to get our answer of <math>32 \cdot 3 = 96</math>. So, the correct answer is <math>\boxed{\textbf{(D)} \text{ 96}}</math>. ..., <math>B</math>, and <math>C</math>. Now, notice that you can only form a correct grouping either like this:
  7 KB (1,281 words) - 17:24, 8 January 2024
• 2018 AMC 10B Problems/Problem 10
  ...of the figure we are trying to find is <math>2</math>. This means that the correct answer choice is <math>\boxed{E}</math>.
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• 1960 AHSME Problems/Problem 32
  Substitute values for each answer choice to determine which one is correct for all <math>r</math>.
  3 KB (508 words) - 20:33, 17 August 2022
• 1961 AHSME Problems/Problem 14
  \textbf{(E)}\ \text{None of these are correct}</math>
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• 1961 AHSME Problems/Problem 24
  \textbf{(E)}\ \text{None of these is correct } </math>
  2 KB (258 words) - 20:50, 22 May 2018
• 1961 AHSME Problems/Problem 38
  ...ath>. Square both sides, we find that <math>\boxed{\textbf{(A)}}</math> is correct. ...he absolute maximum, we can find that <math>\boxed{\textbf{(A)}}</math> is correct.
  3 KB (545 words) - 04:29, 17 October 2022
• 1961 AHSME Problems/Problem 32
  ...equation results in <math>\sin(30^{\circ}) = \frac{1}{2}</math>, which is correct. Thus, the answer is <math>\boxed{\textbf{(C)}}</math>.
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• 1963 AHSME Problems/Problem 31
  ...s <math>t</math> ranges from <math>0</math> to <math>127</math>. Hence,the correct answer is <math>127</math>, <math>\boxed{\textbf{(D)}}</math>.
  2 KB (342 words) - 14:07, 14 January 2024
• 2018 AIME I Problems/Problem 7
  ...ath>2</math> and the height is <math>2</math>, so <math>XBE</math> is also correct! Those are the only three cases, so there are <math>12*3=36</math> cases fo
  6 KB (1,023 words) - 10:38, 21 November 2023
• Basic Programming With Python
  Always remember; the simpler your code is the better it will preform! ...ist of integers from 1 to 51, but excludes 51. This is because python will always think of the last number as a barrier and the number before as the stopping
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• 2008 iTest Problems/Problem 33
  But Alexis scribbles some work on her napkin and declares the correct answer. What answer did Alexis find?
  2 KB (421 words) - 20:19, 6 August 2023
• 2008 iTest Problems/Problem 45
  Assuming Michael is correct, compute <math>m+n</math>. In this problem, assume that gas mileage is cons
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• 2008 iTest Problems/Problem 50
  ...f circles intersects in two points. After careful doodling, Tony finds the correct answer, and is proud that he can solve a problem from late on an AMC 10 exa
  2 KB (319 words) - 19:50, 12 July 2018
• Math Day at University of Nebraska-Lincoln
  .... Each question has answer choices A through E. 4 points are awarded for a correct answer, 0 for an incorrect answer, and 1 for a question left blank. The top
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• 1953 AHSME Problems/Problem 28
  Then if <math>x = \overline{CD}</math> and <math>y = \overline{BD}</math> the correct proportion is:
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• 2008 iTest Problems/Problem 58
  "That's correct," confirms Joshua's mother. "Also, the base <math>10</math> logarithm of <m Assuming Hannah's prediction of volume reduction is correct and effects are compounded continuously, compute the first year that the nu
  4 KB (595 words) - 20:32, 4 August 2018
• 2008 iTest Problems/Problem 63
  ...point. He smiles for a moment, then keeps jogging. If Michael’s work is correct, what distance did he compute as the shortest possible distance one of the
  3 KB (550 words) - 17:03, 7 August 2018
• 2008 iTest Problems/Problem 70
  Josh recognizes that the cubes of the sums are always larger than the sum of cubes of positive integers. For instance, What is the correct value of <math>n</math> that Joshua found?
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• 2006 iTest Problems/Problem U3
  ...robability that exactly <math>6</math> of the books were returned to their correct (original) position can be expressed as <math>\frac{m}{n}</math>, where <ma
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• 2019 AMC 8 Problems/Problem 3
  Which of the following is the correct order of the fractions <math>\frac{15}{11},\frac{19}{15},</math> and <math>
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• 1953 AHSME Problems/Problem 47
  If <math>x>0</math>, then the correct relationship is:
  467 bytes (74 words) - 18:51, 22 April 2020
• 2019 AMC 10A Problems/Problem 9
  ...ath>9</math>, which means it's a composite number and not prime. Thus, the correct answer must be <math>\boxed{\textbf{(B) } 996}</math>.
  3 KB (561 words) - 16:31, 5 February 2024
• 2019 AMC 10A Problems/Problem 10
  ...er, <math>\text{gcd}(16, 8) = 8</math>. Here <math>a+b-\gcd(a,b)</math> is correct when a = 17 and b = 10.
  3 KB (529 words) - 02:24, 8 September 2023
• 2019 AMC 12B Problems/Problem 9
  ..._4{x} + 3 > \log_2{x}.</cmath> The second inequality is redundant, as it's always less restrictive than the last inequality. ...quality <math>3+\log_4{x} > \log_2{x}</math> we see <math>64</math> is the correct number. Now we have <math>64 > x > 4</math> and the number of integers in b
  2 KB (345 words) - 12:25, 18 September 2021
• 2019 AMC 12B Problems/Problem 10
  ...Luckily, <math>4</math> is the largest answer choice so we know it must be correct.
  8 KB (1,306 words) - 22:18, 1 February 2020
• 2019 AIME I Problems/Problem 15
  Note : If our answer is correct, then <math>QX=\frac{11}{2}</math>, which made <math>Q</math> the midpoint
  13 KB (2,252 words) - 11:32, 1 February 2024
• Euler's formula and It's history
  ...and we can turn any point (such as 3 + 4i) into reix form (by finding the correct value of x and r)
  3 KB (543 words) - 15:24, 13 June 2019
• SASMO
  In section A, 2 points are given for a correct answer, 0 points are given for an unanswered question and 1 point is deduct
  2 KB (262 words) - 04:09, 18 July 2020
• 2006 SMT/General Problems/Problem 13
  ...nd/or minus signs between the digits on the left side to make the equation correct: <math> 1+2+3-4+5+6+78+9=100 </math>. Do this with only three plus or minus
  514 bytes (84 words) - 18:34, 14 January 2020
• 2020 AIME I Problems/Problem 7
  ...selected and the women who were not selected, the committee would have the correct number of men and women. Conversely, for every committee that could be form
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• 1964 AHSME Problems/Problem 9
  ...to <math>x = 28 \cdot \frac{5}{4}</math>, or <math>35</math> dollars. The correct answer is <math>\boxed{\textbf{(E)}}</math>
  1 KB (195 words) - 12:19, 23 July 2019
• 2005 Indonesia MO Problems/Problem 8
  ...at most three contestants have the same number of new friends, so Amin is correct. ...d and hence constructing such a graph is not possible meaning that Amin is correct.
  3 KB (508 words) - 19:58, 3 February 2024
• 1978 AHSME Problems/Problem 22
  ...the third statement ("On this card exactly three statements are false") is correct. ...false, that would mean that only <math>1</math> statement is true. This is correct since if only <math>1</math> statement is true, the card that is true is th
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• Changelog
  ...ble on the AoPS wiki. Please do take your time to get spelling and grammar correct. Please make sure your contribution sounds informational.
  518 bytes (87 words) - 14:20, 19 September 2020
• 2019 AMC 8 Problems
  Which of the following is the correct order of the fractions <math>\frac{15}{11},\frac{19}{15},</math> and <math>
  17 KB (2,585 words) - 15:27, 4 May 2024
• 2019 AMC 8 Problems/Problem 14
  ...nday occured; thus, <math>\boxed{\textbf{(C)}\ \text{Wednesday}}</math> is correct. ...0</math>, then if you minus 3 from the first number of this cycle, it will always be <math>0</math>. So, the answer is <math>\boxed{\textbf{(C) Wednesday}}</
  6 KB (903 words) - 16:23, 30 December 2023
• 2020 AMC 10A Problems/Problem 12
  .../math>, leaving <math>\boxed{\textbf{(C)}\ 96}</math> as the only possible correct answer.
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• 2020 AMC 10A Problems/Problem 24
  .../math> must be <math>7</math>, since the unit digit of <math>60y</math> is always <math>0</math> and the unit digit of <math>57</math> is <math>7</math>. The ...on, <math>\gcd(63, n + 120) = 21</math>, we know that if <math>n</math> is correct, after we add <math>120</math> to it, it should be divisible by <math>21</m
  17 KB (2,544 words) - 12:09, 1 September 2023
• 1953 AHSME Problems/Problem 44
  find <math>-9</math> and <math>-1</math> for the roots. The correct equation was: Let <math>x^2+bx+c=0</math> represent the correct equation. Since the coefficient of the <math>x^2</math> term is <math>1</ma
  1 KB (220 words) - 22:56, 14 February 2020
• 2020 AMC 10B Problems/Problem 17
  ...being correct, this solution does not work. (Arcticturn or anybody, please correct me if I am wrong. I only THINK this solution is invalid and have provided m
  4 KB (693 words) - 17:49, 12 November 2023
• 2020 AMC 10B Problems/Problem 21
  ...t{2}-1 \pm \sqrt{8-4\sqrt{2}}</math> (technically the smaller value is the correct one but it doesn’t matter for our purposes). We can then calculate <math>
  11 KB (1,850 words) - 23:33, 27 March 2024
• 2021 AMC 10A Problems
  ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
  15 KB (2,302 words) - 23:41, 14 April 2024
• Annual High School Contest
  For every correct answer: ? points
  3 KB (389 words) - 14:50, 19 February 2020
• 2008 Indonesia MO Problems/Problem 2
  ...rns to <math>(\frac{x+y}{2}+1)\geq \sqrt{2}\sqrt{x+y}</math>. It is always correct according to <math>AM-GM</math> inequality, it happens when <math>x=y=1</ma
  3 KB (473 words) - 00:09, 4 December 2021
• 2021 JMPSC Accuracy Problems
  #You will receive 4 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
  5 KB (729 words) - 18:41, 11 July 2021
• Online Physics Olympiad
  ...portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for an
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• UCSD/GSDMC High School Honors Mathematics Contest
  ...90 minutes long, but part I consists of 25 multiple choice questions. Each correct answer is worth 4 points, incorrect answer is -1 points, and 0 points for l
  1 KB (229 words) - 00:04, 29 May 2020
• 1953 AHSME Problems/Problem 32
  ...ed. The intersections of the pairs of trisectors adjacent to the same side always form: ...our points form a parallelogram with no special properties. Therefore, the correct answer is <math>\boxed{\text{C}}</math>, and we are done.
  1 KB (162 words) - 14:17, 24 April 2020
• 1954 AHSME Problems/Problem 35
  ...se requirements. Checking the answer choices, <math>\fbox{A}</math> is the correct solution.
  1 KB (240 words) - 18:31, 2 May 2022
• 1955 AHSME Problems/Problem 19
  ...the form of <math>(x - a)(x - b) = 0</math>, where a and b are roots, the correct quadratic, once factored, would look like <math>(x - 7)(x + 1) = 0</math>
  1 KB (207 words) - 11:11, 12 July 2021
• 1959 AHSME Problems/Problem 15
  ...h>\textbf{(C)}</math> is the only answer choice left and there must be one correct answer, the answer must be <math>\boxed{\textbf{(C)}}</math>.
  2 KB (263 words) - 11:33, 12 August 2020
• 2020 AIME II Problems/Problem 4
  We first draw a diagram with the correct Cartesian coordinates and a center of rotation <math>P</math>. Note that <m
  10 KB (1,542 words) - 13:29, 19 January 2024
• 2020 AIME II Problems/Problem 13
  (Edit: While the guess would be technically correct, the assumption that the radius would have to be a whole number for the ans
  13 KB (2,197 words) - 23:00, 8 January 2024
• 2020 FMC 10A Problems
  .... The AIME is a 15-question examination giving <math>10</math> points each correct answer and <math>0</math> points for each wrong or blank answer. An USAMO i
  14 KB (2,267 words) - 12:49, 9 June 2020
• 2021 AIME I Problems/Problem 11
  ...>\sqrt{4 \cdot 6 + 5 \cdot 7} = \sqrt{59}.</math> [I don't believe this is correct... are the two diagonals of <math>ABCD</math> necessarily congruent? -peace
  16 KB (2,635 words) - 19:56, 24 December 2023
• 1955 AHSME Problems/Problem 24
  ...{(A)}\ \text{always increases as }x\text{ increases}\\ \textbf{(B)}\ \text{always decreases as }x\text{ decreases to 1}\\ \textbf{(C)}\ \text{cannot equal 0} <math>\textbf{(A)}\ \text{always increases as } x\text{ increases}</math> is wrong due to the quadratic natu
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• 1955 AHSME Problems/Problem 20
  Therefore, the correct answer is <math>\textbf{(A)}</math>
  873 bytes (137 words) - 12:38, 3 August 2020
• 2021 AMC 12A Problems
  <math>\textbf{(E) }</math> It is always true. ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
  15 KB (2,383 words) - 09:49, 25 June 2023
• 2022 AIME I Problems/Problem 7
  Obviously, to find the correct answer, we need to get the largest denominator with the smallest numerator.
  4 KB (684 words) - 12:04, 16 January 2023
• CIME Problems and Solutions
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  812 bytes (128 words) - 18:54, 2 January 2021
• Christmas Invitational Mathematics Examination
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  3 KB (416 words) - 18:13, 31 August 2020
• 2022 AMC 12B Problems/Problem 17
  ...you go with <math>\boxed{\textbf{(D) }576}</math>, and this is indeed the correct answer!
  7 KB (1,071 words) - 00:19, 10 July 2023
• 2021 Fall AMC 12A Problems/Problem 4
  So the correct option is either <math>\textbf{(B)}</math> or <math>\textbf{(E)}</math>. Le ...math>20210A</math> divisible by <math>11</math>. Thus, by elimination, the correct choice must be option <math>\boxed{\textbf{(E)}\ 9}</math>.
  3 KB (491 words) - 21:13, 12 July 2023
• 2021 AMC 12A Problems/Problem 2
  <math>\textbf{(E) }</math> It is always true. ...ues only holds true for nonnegative values of <math>a+b</math>, making the correct answer <math>\boxed{\textbf{(D)}}.</math>
  3 KB (472 words) - 00:02, 30 August 2023
• 2021 AMC 12A Problems/Problem 4
  ...very conditional statement <math>\boldsymbol{p\Longrightarrow q}</math> is always logically equivalent to its contrapositive <math>\boldsymbol{\lnot q\Longri ...le. That leaves statement D. <math>\boxed{\textbf{(D)}}</math> is the only correct statement.
  7 KB (1,027 words) - 22:45, 28 October 2022
• 2021 AMC 12A Problems/Problem 5
  ...}.</math> Later he found that his answer is <math>0.5</math> less than the correct answer. What is the <math>2</math>-digit number <math>\underline{a} \ \unde
  4 KB (569 words) - 22:46, 28 October 2022
• 2021 AMC 12A Problems/Problem 11
  ...</math> the ray entering <math>P</math> and the ray leaving <math>P</math> always have negative slopes. In this problem, <math>\overline{AB}</math> and <math .../math> all involve <math>\sqrt2,</math> we suspect that one of them is the correct answer. We take a guess in faith that <math>\overline{AB},\overline{BC},</m
  10 KB (1,514 words) - 01:28, 1 November 2023
• 2021 AMC 12A Problems/Problem 17
  So, <math>AD=2\sqrt{760}=4\sqrt{190}</math>. The correct answer is <math>\boxed{\textbf{(D) }194}</math>
  10 KB (1,548 words) - 00:08, 12 February 2024
• Solution Writing Mathematics Competitions
  ...ir solution writing skills, since grading is not just based on getting the correct answer.
  308 bytes (48 words) - 04:08, 5 October 2020
• 1955 AHSME Problems/Problem 23
  ...nted as quarters and <math>x</math> of the dimes were counted as cents. To correct the total obtained the clerk must: ...hen every mistake inflates the total by <math>20</math> cents. In order to correct this, we have to subtract <math>20</math> cents <math>x</math> times, for a
  1 KB (211 words) - 12:57, 18 November 2020
• 1955 AHSME Problems/Problem 26
  ...B loses } \textdollar{ 100}\qquad\textbf{(E)}\ \text{none of the above is correct}</math> ...nse, but none of the options says this. We can therefore conclude that the correct answer is <math>\boxed{\textbf{(C)}}</math>.
  1 KB (227 words) - 13:01, 18 November 2020
• 2021 AMC 10A Problems/Problem 11
  ...</math> are either both correct or both incorrect. Since there is only one correct answer, <math>\textbf{(A)}</math> and <math>\textbf{(C)}</math> are both in
  3 KB (527 words) - 11:05, 16 June 2023
• 2021 AIME II Problems/Problem 7
  ...receive <math>d=\frac{3}{2},d=-5</math>. So, we have to test which one is correct. We repeat a similar process as we did above for equations 1 and 2. We fact ...ac{10}{3}</math> or <math>c=-2</math>. So, we must AGAIN test which one is correct.
  10 KB (1,680 words) - 00:20, 28 April 2024
• 1971 AHSME Problems/Problem 4
  If there are any mistakes, feel free to edit so that it is correct.
  1 KB (168 words) - 11:52, 27 April 2024
• 1985 AJHSME Problem 25
  ...ave to show a card with a vowel. However, this is not possible. If Jane is correct, then the contrapositive ("If an odd number is on one side of the card, the
  1 KB (217 words) - 20:20, 26 February 2024
• Tennessee Middle School Mathematics Competition
  ...tes to solve 40 multiple choice problems. Four points are awarded for each correct answer, one point is deducted for each wrong answer, and zero points are aw
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• Number Sense Round
  Each correct answer bags 5 points, while <i>either an incorrect answer or a skipped prob
  972 bytes (156 words) - 16:41, 2 April 2024
• 1956 AHSME Problems/Problem 38
  ...get <math>x=\frac{ab}{\sqrt{a^2+b^2}}</math>, and we can observe that the correct answer is <math>\boxed{\textbf{(D) \ }}</math>.
  1 KB (176 words) - 23:35, 2 January 2024
• 2021 AIME II Problems/Problem 15
  ...^2-n+f((k+1)^2)=k^2+3k+2-n</math>. Note that this formula also returns the correct value when <math>n=(k+1)^2</math>, but not when <math>n=k^2</math>. Thus <m ...than <math>k^2</math>, so <math>k-10>0, k>10</math>. The LHS expression is always even (since <math>3k^2+k-10</math> factors to <math>k(3k+1)-10</math>, and
  14 KB (2,569 words) - 09:28, 28 March 2024
• Advanced Gmaasology
  ...een reproduced here. It was published in <math>1321</math>, if the date is correct. We apologize for any errors in transcript. What follows is the manuscript,
  744 bytes (119 words) - 13:08, 19 April 2023
• Division of Zero by Zero
  ...of the Indian-Mathematical-Scientist '''[[Jyotiraditya Jadhav]]''' has got correct solution set for the process with a proof.
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• 2022 AIME II Problems/Problem 5
  Although the answer is correct, solution 2 below is a more accurate way to approach this problem. I agree,
  3 KB (481 words) - 11:08, 28 January 2024
• 2022 AIME I Problems/Problem 2
  ...gging this back into the original problem shows that this answer is indeed correct. Therefore, <math>\underline{a}\,\underline{b}\,\underline{c}=\boxed{227}.<
  5 KB (755 words) - 16:05, 2 February 2024
• 2021 JMPSC Sprint Problems
  #You will receive 3 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
  7 KB (1,100 words) - 18:40, 11 July 2021
• 2021 JMPSC Invitationals Problems
  #You will receive 15 points for each correct answer, and 0 points for each problem left unanswered or incorrect.
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• 2021 Fall AMC 12B Problems/Problem 5
  ...th>\frac{13}{2}+\frac96=\frac{12}{3}+\frac{12}{3}=8</math>. Therefore, the correct answer is actually <math>12-1=\boxed{\textbf{(C)}\ 11}</math>.
  4 KB (603 words) - 21:25, 8 August 2023
• 2021 Fall AMC 10B Problems/Problem 20
  ...tps://en.wikipedia.org/wiki/Bayes%27_theorem Bayes' theorem], and they are correct.
  8 KB (1,345 words) - 08:19, 19 January 2023
• 2021 Fall AMC 12A Problems/Problem 17
  Putting all cases together, the correct answer is <math>\boxed{\textbf{(B) } 6}</math>. ...ath> is <math>0.</math> Also, <math>x^2+3x+3, x^2+2x+2, x^2+x+1</math> are always imaginary for both <math>b</math> and <math>c.</math> We also have <math>x^
  8 KB (1,277 words) - 16:26, 5 February 2024
• WSMO
  ...nutes individually. These questions range from AMC 8 to AMC 10 level. Each correct question is worth 4 points, each blank answer is worth 0 points, and each i ...es individually. These questions range from late AMC 8 to AIME level. Each correct question is worth 6 points, each blank answer is worth 0 points, and each i
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• 2021 WSMO Speed Round Answer Key
  ...g the test, the problem was phrased unclearly so 558 was also counted as a correct answer)
  142 bytes (16 words) - 12:06, 23 December 2021
• 2022 AMC 8 Problems/Problem 19
  So, the correct answer is <math>\boxed{(C)4}</math>.
  2 KB (327 words) - 22:36, 10 January 2024
• 2021 GMC 12B Problems/Problem 11
  Since statement 3 is the only correct statement, the answer is <math>\boxed{\textbf{(B)}~1}</math>.
  1 KB (175 words) - 15:43, 7 March 2022
• Wordle
  ...r not each letter is in the word as well as if the letter is placed in the correct location. ...n, your task is to eliminate as many possible words as possible to get the correct word. One way to do this is to make a WordleBot using code. Another way is
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• Bisection method
  ...y because <math>f(x)</math> does not change sign at such roots. One way to correct the omission is to use the bisection method on the [[derivative]] <math>f'(
  2 KB (279 words) - 11:53, 16 May 2022
• AoPSWiki:Sandbox
  The angle for the dir command always starts facing east. So dir(0) would label the part exactly east of what you ...fferent variables. Make sure that when you are labeling points you use the correct command.
  28 KB (4,808 words) - 19:43, 3 June 2022
• Forum Etiquette
  : Always be nice. This is one of the most important etiquette rules that should be f : Make sure you are posting it in the correct forum.
  2 KB (413 words) - 14:41, 9 October 2022
• Caltech Harvey Mudd Math Competition
  ...stify their answers. To get full credit, they will need only to submit the correct answer. ...nly once, and they will be ranked according to the time when they submit a correct answer.
  2 KB (307 words) - 06:10, 3 November 2022
• 2022 AMC 10A Problems/Problem 12
  can be classified into three types: Some always lie; some always tell the truth; and How many pieces of candy in all did the principal give to the children who always
  6 KB (956 words) - 09:53, 11 February 2024
• 2022 AMC 10A Problems/Problem 7
  ...gnore or mess up the LCM, and get <math>n=15</math>, you'll still get the correct answer.
  2 KB (343 words) - 13:29, 8 February 2024
• 2022 AMC 12A Problems/Problem 21
  ...That leaves choice <math>\boxed{E}</math>, and we can confirm that this is correct by noticing that <math>9</math> divides <math>3033</math> but not <math>101 ...ial doesn't equal <math>0</math> suggesting that <math>B</math> is not the correct answer choice.
  8 KB (1,325 words) - 02:14, 11 April 2024
• 2022 AMC 10A Problems/Problem 24
  ==Solution 4 (Fake solve, incorrect logic, correct answer by coincidence)== ...h>(n+1)^{(n-1)}</math> as shown by Solution 1 (Parking Function), which is always equivalent to 1 (mod n). Thus you can choose <math>\boxed{\textbf{(E) }1296
  12 KB (1,898 words) - 12:48, 26 March 2024
• 2022 AMC 10B Problems/Problem 17
  ...5 \equiv 0\pmod{5}</math>. We eliminate choice E, and we are left with the correct answer: choice <math>\boxed{(\text{C}) \hspace{0.1in} 2^{607}-1}</math>
  8 KB (1,199 words) - 22:24, 27 October 2023
• 2022 AMC 10B Problems/Problem 11
  ...xtbf{(E)}</math>, leaving us with <math>\boxed{\textbf{(B)}}</math> as the correct answer.
  2 KB (415 words) - 02:14, 28 April 2023
• 2023 AMC 8 Problems/Problem 3
  ...>. As <math>\frac{2}{3}</math> is slightly less than <math>0.7</math>, the correct answer is slightly less than <math>24</math>. Therefore, the answer is <mat
  2 KB (314 words) - 13:31, 17 January 2024
• 1976 AHSME Problems/Problem 22
  We can now determine which of the answer choices is correct: <math>\textbf{(A) }\text{is a circle if }a>s^2</math> - This is correct, as the radius of the circle will be greater than zero when <math>a>s^2</ma
  2 KB (449 words) - 19:45, 10 November 2023
• Gossard perspector
  The Claim is correct in the case of non convex <math>ABCD.</math> One can simplify the proof of
  18 KB (3,046 words) - 06:44, 19 January 2023
• 2023 AMC 8 Problems/Problem 11
  ...ces are far apart from each other, we can ensure that the approximation is correct.
  3 KB (352 words) - 03:51, 24 January 2024
• 2023 AMC 8 Problems/Problem 17
  ...)}, \textbf{(D)},</math> and <math>\textbf{(E)}</math> are clearly not the correct answer. Thus, the only choice left is <math>\boxed{\textbf{(A)}\ 1}</math>.
  7 KB (1,010 words) - 15:04, 25 January 2024
• 2023 AMC 8 Problems/Problem 14
  ...~Math-X note from InterstellerApex: this is wrong, he didn’t choose the correct answer. :(
  3 KB (515 words) - 14:42, 19 January 2024
• How to set up your new computer the right way
  ...s to come. This is the way to set up another PC or personal computer the correct way, bit by bit, whether or not you’re running Windows 10 or Windows 11.
  7 KB (1,110 words) - 04:45, 20 January 2023
• 2019 Mock AMC 10B Problems/Problem 21
  ...ases in which one value is below itself is <math>24</math>. But we have to correct for overcounting. Number of arrangements in which both <math>1</math> and <
  2 KB (336 words) - 16:13, 4 February 2023
• 2023 AIME I Problems/Problem 6
  ...esses across all stages is the sum of the expected values of the number of correct card color guesses at each stage; that is, we add the probabilities of corr There are always <math>3</math> unrevealed cards of each color, so the probability of guessi
  11 KB (1,654 words) - 17:28, 31 January 2024
• 2023 AIME II Problems/Problem 8
  To obtain the correct exponents, we seperately add each element of the lower row to one element o
  9 KB (1,284 words) - 23:37, 31 January 2024
• 2023 AMC 10A Problems/Problem 24
  ...have side length <math>x</math>, the side length of the large hexagon will always be <math>3x</math>. ...{3}}{2}</math>. Alternatively, we can also deduce <math>\text{C}</math> is correct since it is the only fraction whose denominator is <math>{2}</math>. Theref
  13 KB (1,886 words) - 22:08, 10 April 2024
• 2024 AIME I Answer Key
  ...nd another person on AoPS got 385 for problem 12. It seems that 385 is the correct answer, and someone verified it by Desmos. The [[2024_AIME_I_Problems/Probl ...<math>\left( 1, 1 \right)</math> (beyond the solution at this point). The correct answer is YES, there is one more solution. This point is very very close to
  3 KB (515 words) - 03:57, 4 February 2024
• Making AI with Python
  Now, as long as the characters are correct (and in the right order), It will say '''Hello!''' or '''Bye... :(''' corre
  2 KB (308 words) - 16:42, 15 September 2023
• 1993 IMO Problems/Problem 3
  ...s on the video. I made sure my animated gif for when <math>n=5</math> was correct.
  3 KB (512 words) - 21:50, 21 November 2023
• User/LEDStrip
  ...tics of LED lights, ensuring optimal performance and compatibility. It’s always best to consult the manufacturer’s recommendations to choose the most sui ...ofitting may vary depending on the type of dimmer and LED lights you have. Always refer to the manufacturer’s recommendations for retrofitting procedures t
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• Korean Mathematical Olympiad
  ...ale (inclusive and integers only). Full credit is only given for complete, correct solutions. Each solution is intended to be in the form of a mathematical pr
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• 2006 iTest Problems/Problem 12
  ...getting <math>12</math> of these <math>20</math> multiple choice questions correct, given that you don't know how to work any of them and are forced to blindl The highest probability occurs when the first <math>8</math> problems are correct. The probability is thus <cmath>\frac{1}{1}\cdot\frac{1}{2}\cdot\frac{1}{3}
  2 KB (259 words) - 23:43, 3 November 2023
• 2006 iTest Problems/Ultimate Question
  ...robability that exactly <math>6</math> of the books were returned to their correct (original) position can be expressed as <math>\frac{m}{n}</math>, where <ma
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• 2023 AMC 10A Problems/Problem 12
  Multiples of <math>5</math> will always end in <math>0</math> or <math>5</math>, and since the numbers have to be a According to the official answer key, choice (B) is correct. However, some have argued that it is ambiguous whether the number <math>56
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• 2023 AMC 12B Problems/Problem 15
  <math>\textbf{First, we prove that Statement I is not correct.}</math> <math>\textbf{Second, we prove that Statement III is correct.}</math>
  7 KB (1,115 words) - 13:34, 21 April 2024
• 2024 AMC 8 Problems/Problem 24
  The correct answer choice on the test(or at least the one i took) had 5 as C.
  4 KB (537 words) - 09:37, 28 April 2024
• Olimpiada Iberoamericana de Matemáticas
  ...le (inclusive and integers only). Full credit is only given for complete, correct solutions. Each solution is intended to be in the form of a [[proof writin
  3 KB (469 words) - 11:46, 13 December 2023
• 1992 OIM Problems/Problem 1
  ...from <math>a_1</math> through <math>a_{12}</math> and despite getting the correct numerical answer, I was not awarded the full points for not sufficient proo
  4 KB (521 words) - 09:43, 23 December 2023
• 2024 AMC 8 Problems/Problem 12
  Therefore, the correct answer is <math>\boxed{\textbf{(E)}\ 26}</math>.
  2 KB (378 words) - 23:29, 3 March 2024
• 2024 AMC 8 Problems/Problem 14
  ...ess for each unvisited node (in order of its distance estimate) yields the correct distance <math>d(Z) = \boxed{\textbf{(A) } 28}</math> once the algorithm is
  5 KB (887 words) - 14:09, 3 April 2024
• 2002 AMC 12P Problems/Problem 2
  ...so on. This means that our original guess of the series being periodic was correct. Summing up our findings in a nice table,
  2 KB (264 words) - 21:57, 30 December 2023
• 2002 AMC 12P Problems
  ...stion, and <math>7</math> incorrect answers, and also with <math>12</math> correct answers and <math>13</math> unanswered questions. There are scores that can
  10 KB (1,606 words) - 01:46, 31 December 2023
• 2002 AMC 12P Problems/Problem 4
  ...distinct, <math>a</math> cannot be <math>1</math> so the latter option is correct, giving us our answer of <math>\boxed{\textbf{(E) } 0.8}.</math>
  1 KB (251 words) - 19:31, 14 January 2024
• 2002 AMC 12P Problems/Problem 17
  ...pt for <math>\frac{7\pi}{4} + 2\pi k</math> result in equality between the correct answer and one or more wrong answers, which one could quickly verify by set
  3 KB (455 words) - 19:16, 11 March 2024
• 2002 AMC 12P Problems/Problem 22
  ...stion, and <math>7</math> incorrect answers, and also with <math>12</math> correct answers and <math>13</math> unanswered questions. There are scores that can
  937 bytes (138 words) - 22:15, 10 March 2024
• 2024 AMC 8 Problems/Problem 15
  So, the correct answer is <math>\boxed{\textbf{(C)}\ 1107}</math>.
  4 KB (559 words) - 01:46, 18 April 2024
• Proofs of trig identities
  We can note that the functions are correct by similar triangles.
  16 KB (2,796 words) - 13:12, 21 January 2024
• 2005 iTest Problems
  Kathryn always beat Joe at competitions, too. Joe admired her resolve and unwillingness to ...developed a method for calculating all prime numbers?” Kathryn gave the correct response. What name did she say?
  25 KB (3,738 words) - 10:53, 23 April 2024

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