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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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k a AMC 10/12 A&B Coming up Soon!
jlacosta   0
Nov 1, 2024
There is still time to train for the November 6th and November 12th AMC 10A/12A and AMC 10B/12B, respectively! Enroll in our weekend seminars to be held on November 2nd and 3rd (listed below) and you will learn problem strategies, test taking techniques, and be able to take a full practice test! Note that the “B” seminars will have different material from the “A” seminars which were held in October.

[list][*]Special AMC 10 Problem Seminar B
[*]Special AMC 12 Problem Seminar B[/list]
For those who want to take a free practice test before the AMC 10/12 competitions, you can simulate a real competition experience by following this link. As you assess your performance on these exams, be sure to gather data!

[list][*]Which problems did you get right?
[list][*]Was the topic a strength (e.g. number theory, geometry, counting/probability, algebra)?
[*]How did you prepare?
[*]What was your confidence level?[/list]
[*]Which problems did you get wrong?
[list][list][*]Did you make an arithmetic error?
[*]Did you misread the problem?
[*]Did you have the foundational knowledge for the problem?
[*]Which topics require more fluency through practice (e.g. number theory, geometry, counting/probability, algebra)?
[*]Did you run out of time?[/list][/list]
Once you have analyzed the results with the above questions, you will have a plan of attack for future contests! BEST OF LUCK to all competitors at this year’s AMC 10 and AMC 12!

Did you know that the day after both the AMC 10A/12A and AMC 10B/12B you can join a free math jam where our AoPS team will go over the most interesting problems? Find the schedule below under “Mark your calendars”.

Mark your calendars for these upcoming free math jams!
[list][*]November 20th: Amherst College Info Session, 7:30 pm ET: Matt McGann, Dean of Admission and Financial Aid at Amherst College, and Nathan Pflueger, math professor at Amherst College, will host an info session exploring both Amherst College specifically and liberal arts colleges generally. Topics include opportunities in math, the admission process, and financial aid for both US and international students.
[*]November 7th: 2024 AMC 10/12 A Discussion, Thursday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 A, administered November 6. We will discuss some of the most interesting problems from each test!
[*]November 13th: 2024 AMC 10/12 B Discussion, Wednesday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 B, administered November 12. We will discuss some of the most interesting problems from each test![/list]
AoPS Spring classes are open for enrollment. Get a jump on the New Year and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!

Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile!

Whether you've taken our classes at AoPS Online or AoPS Academies or reached the top echelons of our competition training with our Worldwide Online Olympiad Training (WOOT) program, you can now add your AoPS experience to the education section on your LinkedIn profile.

Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!

Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Nov 1, 2024
0 replies
Logical guessing game!
Mathdreams   22
N an hour ago by JH_K2IMO
Source: 2021 Fall AMC10B P10
Fourty slips of paper numbered $1$ to $40$ are placed in a hat. Alice and Bob each draw one number from the hat without replacement, keeping their numbers hidden from each other. Alice says, "I can't tell who has the larger number." Then Bob says, "I know who has the larger number." Alice says, "You do? Is your number prime?" Bob replies, "Yes." Alice says, "In that case, if I multiply your number by $100$ and add my number, the result is a perfect square. " What is the sum of the two numbers drawn from the hat?

$\textbf{(A) }27\qquad\textbf{(B) }37\qquad\textbf{(C) }47\qquad\textbf{(D) }57\qquad\textbf{(E) }67$
22 replies
Mathdreams
Nov 17, 2021
JH_K2IMO
an hour ago
Possibility of USAMO?
MathXplorer10   4
N an hour ago by MathXplorer10
Hi guys!


I got a 118.5 on the 12B test this year. I am wondering if it is possible to make USAMO (what do you think the cutoffs would be this year?)

For some background, I got 121.5/127.5 on the 10s last year, and got a 7 on AIME with no extra prep. Is it possible to go from a 7 to a 10 (or whatever I need to get on AIME)?

Thank you!
4 replies
MathXplorer10
4 hours ago
MathXplorer10
an hour ago
10a vs 10b
golden_star_123   111
N an hour ago by happyfish0922
Post the difference between your 10a and 10b score!
111 replies
golden_star_123
Wednesday at 6:24 PM
happyfish0922
an hour ago
What do next?
FuturePanda   2
N an hour ago by Tem8
Hi everyone,

I think I got an 81 and 102 for 12A and 10B, sillying way too much on both. I read all of the AOPS books, and I know most of the theorems for the AMC’s I just don’t know which ones to apply to solve the problems. Additionally, I suck at trig, complex, and logarithms. What should I do to improve?

For example, should I be grinding past AIME’s?
I plan on reading most of the Awesomemath books for L3
2 replies
FuturePanda
3 hours ago
Tem8
an hour ago
No more topics!
sum of 7th powers
gracemoon124   18
N Wednesday at 9:44 PM by aleyang
Source: 2024 AMC 10B #7
What is the remainder when $7^{2024}+7^{2025}+7^{2026}$ is divided by $19$?

$
\textbf{(A) }0 \qquad
\textbf{(B) }1 \qquad
\textbf{(C) }7 \qquad
\textbf{(D) }11 \qquad
\textbf{(E) }18 \qquad
$
18 replies
gracemoon124
Wednesday at 5:20 PM
aleyang
Wednesday at 9:44 PM
sum of 7th powers
G H J
Source: 2024 AMC 10B #7
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gracemoon124
871 posts
#1
Y by
What is the remainder when $7^{2024}+7^{2025}+7^{2026}$ is divided by $19$?

$
\textbf{(A) }0 \qquad
\textbf{(B) }1 \qquad
\textbf{(C) }7 \qquad
\textbf{(D) }11 \qquad
\textbf{(E) }18 \qquad
$
This post has been edited 1 time. Last edited by LauraZed, Wednesday at 5:28 PM
Reason: changing to official wording, adding answer options, and filling out source field
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gladIasked
592 posts
#2
Y by
answer is $0$; factor out a $7^{2024}$, then $7^2+7+1\equiv 0 \pmod {19}$

i did what @below did in contest
This post has been edited 4 times. Last edited by gladIasked, Wednesday at 5:24 PM
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gracemoon124
871 posts
#3
Y by
what i did was $7^3\equiv 1\pmod{19}$ lol? so it's $7^2+7+1\equiv 0\pmod{19}$
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mathboy282
2966 posts
#4 • 1 Y
Y by beastEJ
cycled 7,11,1 mod 19, and because 2024 == 2 mod 3, we have mod 19 to be 11+1+7=19 mod 19 ==0 (A)
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MathRook7817
233 posts
#5
Y by
its just 0, find 7^4 mod 19, and work from there
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pingpongmerrily
2394 posts
#6 • 1 Y
Y by Sedro
MathRook7817 wrote:
its just 0, find 7^4 mod 19, and work from there

not necessary to bash that, just factor out $7^2+7+1=57$ which is divisible by $19$ ans is 0=A
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anticodon
8 posts
#7 • 1 Y
Y by wangzrpi
mathboy282 wrote:
cycled 7,11,1 mod 19, and because 2024 == 2 mod 3, we have mod 19 to be 11+1+7=19 mod 19 ==0 (A)

Note that 2024, 2025, and 2026 are 3 consecutive integers and the mod 19 residues of powers of 7 cycle back every 3 numbers. So you can just add the possibilities (residue of 1+11+7 mod 19) so answer is 0
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mathprodigy2011
57 posts
#8
Y by
omg I thought that said 10b #17. and if it was 17 I would've flipped cuz I took 12b
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happypi31415
658 posts
#9
Y by
I misread the 19 as a 17 and got clinical depression during the test
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anticodon
8 posts
#10
Y by
This should have been named "Lucky Sevens 2024"
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GreenBanana666
518 posts
#11
Y by
Kinda ez for a P.7. $7^{2024}+7^{2025}+7^{2026}=7^{2024}(1+7+7^2)=7^{2024}(1+7+7^2)=7^{2024}(57)=7^{2024}(3)(19).$ So $7^{2024}+7^{2025}+7^{2026}$ is divisible by $19$. Therefore the answer is $\boxed{A}$.
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andrewcheng
482 posts
#12
Y by
doing some quick modulo math we find 7^1=7 7^2=11 and 7^3=1 mod 19
notice that since 2024 2025 and 2026 are consecutive and 7^x mod 19 loops every 3 numbers we can simply add 7+1+11=19=0 mod 19
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Sabburi
200 posts
#13
Y by
The powers of seven look between 7,1,11 in some order, so the sum is 19, which is 0(mod 19), or A
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emailhy
147 posts
#14
Y by
gracemoon124 wrote:
What is the remainder when $7^{2024}+7^{2025}+7^{2026}$ is divided by $19$?

$ \textbf{(A) }0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }7 \qquad \textbf{(D) }11 \qquad \textbf{(E) }18 \qquad this was in amc 10 b $
also i just did it
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amaops1123
1645 posts
#15
Y by
I'm like the only person in my school who didn't silly this somehow
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pingpongmerrily
2394 posts
#16
Y by
how do you silly this do kids not learn to factor nowadays? what are we coming to? the world is ending!!!
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GreenBanana666
518 posts
#17
Y by
fr :skull: silling easy probs with no traps and annoying bashing is just a skill issue. Also, why does everyone use mod. They arent gonna test us on mod on a prob 7.
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amaops1123
1645 posts
#18
Y by
pingpongmerrily wrote:
how do you silly this do kids not learn to factor nowadays? what are we coming to? the world is ending!!!

Idk man
There's this one guy who got like 132 or smth around that range and this was one of his sillies
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aleyang
171 posts
#19
Y by
I used both finding a pattern and factoring to double check my answer.
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