https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Eflower2000&feedformat=atom AoPS Wiki - User contributions [en] 2021-10-22T11:01:53Z User contributions MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=2010_AMC_8_Problems/Problem_7&diff=136365 2010 AMC 8 Problems/Problem 7 2020-11-01T20:34:42Z <p>Eflower2000: /* Solution */</p> <hr /> <div>==Problem==<br /> Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?<br /> <br /> &lt;math&gt;\textbf{(A)}\ 6 \qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 99&lt;/math&gt;<br /> ==Solution==<br /> You need &lt;math&gt;2&lt;/math&gt; dimes, &lt;math&gt;1&lt;/math&gt; nickel, and &lt;math&gt;4&lt;/math&gt; pennies for the first &lt;math&gt;25&lt;/math&gt; cents. From &lt;math&gt;26&lt;/math&gt; cents to &lt;math&gt;50&lt;/math&gt; cents, you only need to add &lt;math&gt;1&lt;/math&gt; quarter. From &lt;math&gt;51&lt;/math&gt; cents to &lt;math&gt;75&lt;/math&gt; cents, you also only need to add &lt;math&gt;1&lt;/math&gt; quarter. The same for &lt;math&gt;76&lt;/math&gt; cents to &lt;math&gt;99&lt;/math&gt; cents. Notice that instead of &lt;math&gt;100&lt;/math&gt;, it is &lt;math&gt;99&lt;/math&gt;. We are left with &lt;math&gt;3&lt;/math&gt; quarters, &lt;math&gt;1&lt;/math&gt; nickel, &lt;math&gt;2&lt;/math&gt; dimes, and &lt;math&gt;4&lt;/math&gt; pennies. Thus, the correct answer is &lt;math&gt;3+2+1+4=\boxed{\textbf{(B)}\ 10}&lt;/math&gt;.<br /> <br /> ==See Also==<br /> {{AMC8 box|year=2010|num-b=6|num-a=8}}<br /> {{MAA Notice}}</div> Eflower2000 https://artofproblemsolving.com/wiki/index.php?title=2001_AMC_8_Problems&diff=135807 2001 AMC 8 Problems 2020-10-25T22:18:58Z <p>Eflower2000: /* Problem 1 */</p> <hr /> <div>==Problem 1==<br /> <br /> Casey's shop class is making a golf trophy. He has to paint &lt;math&gt;300&lt;/math&gt; dimples on a golf ball. If it takes him &lt;math&gt;2&lt;/math&gt; seconds to paint one dimple, how many minutes will he need to do his job?<br /> <br /> &lt;math&gt;\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 1 | Solution]]<br /> <br /> ==Problem 2==<br /> <br /> I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?<br /> <br /> &lt;math&gt;\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 12&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 2 | Solution]]<br /> <br /> ==Problem 3==<br /> <br /> Granny Smith has \$63. Elberta has \$2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?<br /> <br /> &lt;math&gt;\text{(A)}\ 17 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 23&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 3 | Solution]]<br /> <br /> ==Problem 4==<br /> <br /> The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible '''even''' five-digit number. The digit in the tens place is<br /> <br /> &lt;math&gt;\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 9&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 4 | Solution]]<br /> <br /> ==Problem 5==<br /> <br /> On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is &lt;math&gt;1088&lt;/math&gt; feet per second and one mile is &lt;math&gt;5280&lt;/math&gt; feet. Estimated, to the nearest half-mile, how far Snoopy was from the flash of lightning?<br /> <br /> &lt;math&gt;\text{(A)}\ 1 \qquad \text{(B)}\ 1\frac{1}{2} \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 2\frac{1}{2} \qquad \text{(E)}\ 3&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 5 | Solution]]<br /> <br /> ==Problem 6==<br /> <br /> Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?<br /> <br /> &lt;math&gt;\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 6 | Solution]]<br /> <br /> ==Kites on Parade==<br /> <br /> ''Problems 7, 8 and 9 are about these kites.''<br /> <br /> To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram below. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.<br /> ￼&lt;asy&gt;<br /> for (int a = 0; a &lt; 7; ++a) { for (int b = 0; b &lt; 8; ++b) { dot((a,b)); } } <br /> draw((3,0)--(0,5)--(3,7)--(6,5)--cycle); <br /> &lt;/asy&gt;<br /> <br /> ===Problem 7===<br /> <br /> What is the number of square inches in the area of the small kite?<br /> <br /> &lt;math&gt;\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 23 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 25&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 7 | Solution]]<br /> <br /> ===Problem 8===<br /> <br /> Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?<br /> <br /> &lt;math&gt;\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 38 \qquad \text{(E)}\ 39&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 8 | Solution]]<br /> <br /> ===Problem 9===<br /> <br /> The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?<br /> <br /> &lt;math&gt;\text{(A)}\ 63 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 189 \qquad \text{(E)}\ 264&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 9 | Solution]]<br /> <br /> ==Problem 10==<br /> <br /> A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?<br /> <br /> &lt;math&gt;\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 10 | Solution]]<br /> <br /> ==Problem 11==<br /> <br /> Points &lt;math&gt;A&lt;/math&gt;, &lt;math&gt;B&lt;/math&gt;, &lt;math&gt;C&lt;/math&gt; and &lt;math&gt;D&lt;/math&gt; have these coordinates: &lt;math&gt;A(3,2)&lt;/math&gt;, &lt;math&gt;B(3,-2)&lt;/math&gt;, &lt;math&gt;C(-3,-2)&lt;/math&gt; and &lt;math&gt;D(-3, 0)&lt;/math&gt;. The area of quadrilateral &lt;math&gt;ABCD&lt;/math&gt; is<br /> <br /> &lt;asy&gt;<br /> for (int i = -4; i &lt;= 4; ++i)<br /> {<br /> for (int j = -4; j &lt;= 4; ++j)<br /> {<br /> dot((i,j));<br /> }<br /> }<br /> <br /> draw((0,-4)--(0,4),linewidth(1));<br /> draw((-4,0)--(4,0),linewidth(1));<br /> for (int i = -4; i &lt;= 4; ++i)<br /> {<br /> draw((i,-1/3)--(i,1/3),linewidth(0.5));<br /> draw((-1/3,i)--(1/3,i),linewidth(0.5));<br /> }<br /> &lt;/asy&gt;<br /> <br /> &lt;math&gt;\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 24&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 11 | Solution]]<br /> <br /> ==Problem 12==<br /> <br /> If &lt;math&gt;a\otimes b = \dfrac{a + b}{a - b}&lt;/math&gt;, then &lt;math&gt;(6\otimes 4)\otimes 3 = &lt;/math&gt;<br /> <br /> &lt;math&gt;\text{(A)}\ 4 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 72&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 12 | Solution]]<br /> <br /> ==Problem 13==<br /> <br /> Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?<br /> <br /> &lt;math&gt;\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 72&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 13 | Solution]]<br /> <br /> ==Problem 14==<br /> <br /> Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?<br /> <br /> *Meat: beef, chicken, pork<br /> *Vegetables: baked beans, corn, potatoes, tomatoes<br /> *Dessert: brownies, chocolate cake, chocolate pudding, ice cream<br /> <br /> &lt;math&gt;\text{(A)}\ 4 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 72 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 144&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 14 | Solution]]<br /> <br /> ==Problem 15==<br /> <br /> Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?<br /> <br /> &lt;math&gt;\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 40&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 15 | Solution]]<br /> <br /> ==Problem 16==<br /> <br /> A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?<br /> <br /> &lt;asy&gt;<br /> draw((0,8)--(0,0)--(4,0)--(4,8)--(0,8)--(3.5,8.5)--(3.5,8));<br /> draw((2,-1)--(2,9),dashed);<br /> &lt;/asy&gt;<br /> <br /> &lt;math&gt;\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{2} \qquad \text{(C)}\ \dfrac{3}{4} \qquad \text{(D)}\ \dfrac{4}{5} \qquad \text{(E)}\ \dfrac{5}{6}&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 16 | Solution]]<br /> <br /> ==Problem 17==<br /> <br /> For the game show ''Who Wants To Be A Millionaire?'', the dollar values of each question are shown in the following table (where K = 1000).<br /> <br /> &lt;cmath&gt;\begin{tabular}{rccccccccccccccc}<br /> \text{Question} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8 &amp; 9 &amp; 10 &amp; 11 &amp; 12 &amp; 13 &amp; 14 &amp; 15 \\<br /> \text{Value} &amp; 100 &amp; 200 &amp; 300 &amp; 500 &amp; 1\text{K} &amp; 2\text{K} &amp; 4\text{K} &amp; 8\text{K} &amp; 16\text{K} &amp; 32\text{K} &amp; 64\text{K} &amp; 125\text{K} &amp; 250\text{K} &amp; 500\text{K} &amp; 1000\text{K}<br /> \end{tabular}&lt;/cmath&gt;<br /> <br /> Between which two questions is the percent increase of the value the smallest?<br /> <br /> &lt;math&gt;\text{(A)}\ \text{From 1 to 2} \qquad \text{(B)}\ \text{From 2 to 3} \qquad \text{(C)}\ \text{From 3 to 4} \qquad \text{(D)}\ \text{From 11 to 12} \qquad \text{(E)}\ \text{From 14 to 15}&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 17 | Solution]]<br /> <br /> ==Problem 18==<br /> <br /> Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?<br /> <br /> &lt;math&gt;\text{(A)}\ \dfrac{1}{36} \qquad \text{(B)}\ \dfrac{1}{18} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{11}{36} \qquad \text{(E)}\ \dfrac{1}{3}&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 18 | Solution]]<br /> <br /> ==Problem 19==<br /> <br /> Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?<br /> <br /> &lt;asy&gt;<br /> unitsize(12);<br /> <br /> draw((0,9)--(0,0)--(9,0));<br /> label(&quot;time&quot;,(4.5,0),S);<br /> label(&quot;s&quot;,(0,7),W); label(&quot;p&quot;,(0,6),W); label(&quot;e&quot;,(0,5),W); label(&quot;e&quot;,(0,4),W); label(&quot;d&quot;,(0,3),W);<br /> label(&quot;(A)&quot;,(-1,9),NW);<br /> draw((0,4)--(4,4),dashed); label(&quot;M&quot;,(4,4),E);<br /> draw((0,8)--(4,8),linewidth(1)); label(&quot;N&quot;,(4,8),E);<br /> <br /> draw((15,9)--(15,0)--(24,0));<br /> label(&quot;time&quot;,(19.5,0),S);<br /> label(&quot;s&quot;,(15,7),W); label(&quot;p&quot;,(15,6),W); label(&quot;e&quot;,(15,5),W); label(&quot;e&quot;,(15,4),W); label(&quot;d&quot;,(15,3),W);<br /> label(&quot;(B)&quot;,(14,9),NW);<br /> draw((15,4)--(19,4),dashed); label(&quot;M&quot;,(19,4),E);<br /> draw((15,8)--(23,8),linewidth(1)); label(&quot;N&quot;,(23,8),E);<br /> <br /> draw((30,9)--(30,0)--(39,0));<br /> label(&quot;time&quot;,(34.5,0),S);<br /> label(&quot;s&quot;,(30,7),W); label(&quot;p&quot;,(30,6),W); label(&quot;e&quot;,(30,5),W); label(&quot;e&quot;,(30,4),W); label(&quot;d&quot;,(30,3),W);<br /> label(&quot;(C)&quot;,(29,9),NW);<br /> draw((30,4)--(34,4),dashed); label(&quot;M&quot;,(34,4),E);<br /> draw((30,2)--(34,2),linewidth(1)); label(&quot;N&quot;,(34,2),E);<br /> <br /> draw((0,-6)--(0,-15)--(9,-15));<br /> label(&quot;time&quot;,(4.5,-15),S);<br /> label(&quot;s&quot;,(0,-8),W); label(&quot;p&quot;,(0,-9),W); label(&quot;e&quot;,(0,-10),W); label(&quot;e&quot;,(0,-11),W); label(&quot;d&quot;,(0,-12),W);<br /> label(&quot;(D)&quot;,(-1,-6),NW);<br /> draw((0,-11)--(4,-11),dashed); label(&quot;M&quot;,(4,-11),E);<br /> draw((0,-7)--(2,-7),linewidth(1)); label(&quot;N&quot;,(2,-7),E);<br /> <br /> draw((15,-6)--(15,-15)--(24,-15));<br /> label(&quot;time&quot;,(19.5,-15),S);<br /> label(&quot;s&quot;,(15,-8),W); label(&quot;p&quot;,(15,-9),W); label(&quot;e&quot;,(15,-10),W); label(&quot;e&quot;,(15,-11),W); label(&quot;d&quot;,(15,-12),W);<br /> label(&quot;(E)&quot;,(14,-6),NW);<br /> draw((15,-11)--(19,-11),dashed); label(&quot;M&quot;,(19,-11),E);<br /> draw((15,-13)--(23,-13),linewidth(1)); label(&quot;N&quot;,(23,-13),E);<br /> &lt;/asy&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 19 | Solution]]<br /> <br /> ==Problem 20==<br /> <br /> Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, &quot;At least two of us have the same score.&quot; Marty thinks, &quot;I didn't get the lowest score.&quot; Shana thinks, &quot;I didn't get the highest score.&quot; List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).<br /> <br /> &lt;math&gt;\text{(A)}\ \text{S,Q,M} \qquad \text{(B)}\ \text{Q,M,S} \qquad \text{(C)}\ \text{Q,S,M} \qquad \text{(D)}\ \text{M,S,Q} \qquad \text{(E)}\ \text{S,M,Q}&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 20 | Solution]]<br /> <br /> ==Problem 21==<br /> <br /> The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is<br /> <br /> &lt;math&gt;\text{(A)}\ 19 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 40&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 21 | Solution]]<br /> <br /> ==Problem 22==<br /> <br /> On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is '''NOT''' possible?<br /> <br /> &lt;math&gt;\text{(A)}\ 90 \qquad \text{(B)}\ 91 \qquad \text{(C)}\ 92 \qquad \text{(D)}\ 95 \qquad \text{(E)}\ 97&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 22 | Solution]]<br /> <br /> ==Problem 23==<br /> <br /> Points &lt;math&gt;R&lt;/math&gt;, &lt;math&gt;S&lt;/math&gt; and &lt;math&gt;T&lt;/math&gt; are vertices of an equilateral triangle, and points &lt;math&gt;X&lt;/math&gt;, &lt;math&gt;Y&lt;/math&gt; and &lt;math&gt;Z&lt;/math&gt; are midpoints of its sides. How many noncongruent triangles can be<br /> drawn using any three of these six points as vertices?<br /> <br /> &lt;asy&gt;<br /> pair SS,R,T,X,Y,Z;<br /> SS = (2,2*sqrt(3)); R = (0,0); T = (4,0);<br /> X = (2,0); Y = (1,sqrt(3)); Z = (3,sqrt(3));<br /> dot(SS); dot(R); dot(T); dot(X); dot(Y); dot(Z);<br /> label(&quot;$S$&quot;,SS,N); label(&quot;$R$&quot;,R,SW); label(&quot;$T$&quot;,T,SE);<br /> label(&quot;$X$&quot;,X,S); label(&quot;$Y$&quot;,Y,NW); label(&quot;$Z$&quot;,Z,NE);<br /> &lt;/asy&gt;<br /> <br /> &lt;math&gt;\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 20&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 23 | Solution]]<br /> <br /> ==Problem 24==<br /> <br /> Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?<br /> <br /> &lt;asy&gt;<br /> draw((0,0)--(4,4*sqrt(3)));<br /> draw((1,-sqrt(3))--(5,3*sqrt(3)));<br /> draw((2,-2*sqrt(3))--(6,2*sqrt(3)));<br /> draw((3,-3*sqrt(3))--(7,sqrt(3)));<br /> draw((4,-4*sqrt(3))--(8,0));<br /> draw((8,0)--(4,4*sqrt(3)));<br /> draw((7,-sqrt(3))--(3,3*sqrt(3)));<br /> draw((6,-2*sqrt(3))--(2,2*sqrt(3)));<br /> draw((5,-3*sqrt(3))--(1,sqrt(3)));<br /> draw((4,-4*sqrt(3))--(0,0));<br /> draw((3,3*sqrt(3))--(5,3*sqrt(3)));<br /> draw((2,2*sqrt(3))--(6,2*sqrt(3)));<br /> draw((1,sqrt(3))--(7,sqrt(3)));<br /> draw((-1,0)--(9,0));<br /> draw((1,-sqrt(3))--(7,-sqrt(3)));<br /> draw((2,-2*sqrt(3))--(6,-2*sqrt(3)));<br /> draw((3,-3*sqrt(3))--(5,-3*sqrt(3)));<br /> &lt;/asy&gt;<br /> <br /> &lt;math&gt;\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 24 | Solution]]<br /> <br /> ==Problem 25==<br /> <br /> There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?<br /> <br /> &lt;math&gt;\text{(A)}\ 5724 \qquad \text{(B)}\ 7245 \qquad \text{(C)}\ 7254 \qquad \text{(D)}\ 7425 \qquad \text{(E)}\ 7542&lt;/math&gt;<br /> <br /> [[2001 AMC 8 Problems/Problem 25 | Solution]]<br /> <br /> ==See Also==<br /> {{AMC8 box|year=2001|before=[[2000 AMC 8 Problems|2000 AMC 8]]|after=[[2002 AMC 8 Problems|2002 AMC 8]]}}<br /> * [[AMC 8]]<br /> * [[AMC 8 Problems and Solutions]]<br /> * [[Mathematics competition resources]]<br /> <br /> <br /> {{MAA Notice}}</div> Eflower2000 https://artofproblemsolving.com/wiki/index.php?title=User:Piphi&diff=128839 User:Piphi 2020-07-22T00:07:02Z <p>Eflower2000: /* User Count */</p> <hr /> <div>{{User:Piphi/Template:Header}}<br /> &lt;br&gt;<br /> __NOTOC__&lt;div style=&quot;border:2px solid black; -webkit-border-radius: 10px; background:#dddddd&quot;&gt;<br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;User Count&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-bottom:10px&quot;&gt;&lt;font color=&quot;black&quot;&gt;If this is your first time visiting this page, edit it by incrementing the user count below by one.&lt;/font&gt;&lt;/div&gt;<br /> &lt;center&gt;&lt;font size=&quot;101px&quot;&gt;255<br /> &lt;/font&gt;&lt;/center&gt;<br /> &lt;/div&gt;<br /> &lt;div style=&quot;border:2px solid black; background:#cccccc;-webkit-border-radius: 10px; align:center&quot;&gt;<br /> <br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;About Me&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-bottom:10px&quot;&gt;&lt;font color=&quot;black&quot;&gt;Piphi is legendary and made the USA IMO team in 2019.&lt;br&gt;<br /> <br /> Piphi is the creator of the [[User:Piphi/Games|AoPS Wiki Games by Piphi]], the future of games on AoPS.&lt;br&gt;<br /> <br /> Piphi started the signature trend at around May 2020.&lt;br&gt;<br /> <br /> Piphi is an extremely OP person - LJCoder619. &lt;br&gt;<br /> <br /> Piphi is OP --[[User:Aray10|Aray10]] ([[User talk:Aray10|talk]]) 23:22, 17 June 2020 (EDT) &lt;br&gt;<br /> <br /> Piphi has been very close to winning multiple [[Greed Control]] games, piphi placed 5th in game #18 and 2nd in game #19. Thanks to piphi, Greed Control games have started to be kept track of. Piphi made a spreadsheet that has all of Greed Control history [https://artofproblemsolving.com/community/c19451h2126208p15569802 here].&lt;br&gt;<br /> <br /> Piphi also found out who won [[Reaper]] games #1 and #2 as seen [https://artofproblemsolving.com/community/c19451h1826745p15526330 here].&lt;br&gt;<br /> <br /> Piphi has been called op by many AoPSers, including the legendary [[User:Radio2|Radio2]] himself [https://artofproblemsolving.com/community/c19451h1826745p15526800 here]. (note: Radio2 calls many users op.)&lt;br&gt;<br /> <br /> Piphi created the [[AoPS Administrators]] page, added most of the AoPS Admins to it, and created the scrollable table.&lt;br&gt;<br /> <br /> Piphi has also added a lot of the info that is in the [[Reaper Archives]].&lt;br&gt;<br /> <br /> Piphi has a side-project that is making the Wiki's [[Main Page]] look better, you can check that out [[User:Piphi/AoPS Wiki|here]].&lt;br&gt;<br /> <br /> Piphi published Greed Control Game 19 statistics [https://artofproblemsolving.com/community/c19451h2126212 here].<br /> <br /> Piphi has a post that was made an announcement on a official AoPS Forum [https://artofproblemsolving.com/community/c68h2175116 here].<br /> <br /> Piphi is a proud member of [https://artofproblemsolving.com/community/c562043 The Interuniversal GMAAS Society].<br /> &lt;/font&gt;&lt;/div&gt;<br /> &lt;/div&gt;<br /> &lt;div style=&quot;border:2px solid black; background:#bbbbbb;-webkit-border-radius: 10px; align:center&quot;&gt;<br /> <br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;Goals&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-right: 10px; margin-bottom:10px&quot;&gt;A User Count of 330<br /> {{User:Piphi/Template:Progress_Bar|74.85|width=100%}}<br /> <br /> 200 subpages of [[User:Piphi]]<br /> {{User:Piphi/Template:Progress_Bar|51.5|width=100%}}<br /> <br /> 200 signups for [[User:Piphi/Games|AoPS Wiki Games by Piphi]]<br /> {{User:Piphi/Template:Progress_Bar|30.5|width=100%}}<br /> <br /> Make 10,000 edits<br /> {{User:Piphi/Template:Progress_Bar|15.14|width=100%}}&lt;/div&gt;<br /> &lt;/div&gt;</div> Eflower2000 https://artofproblemsolving.com/wiki/index.php?title=User:Piphi&diff=124101 User:Piphi 2020-06-06T16:31:54Z <p>Eflower2000: /* User Count */</p> <hr /> <div>{{User:Piphi/Template:Header}}<br /> &lt;br&gt;<br /> &lt;div style=&quot;border:2px solid black; -webkit-border-radius: 10px; background:#dddddd&quot;&gt;<br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;User Count&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-bottom:10px&quot;&gt;&lt;font color=&quot;black&quot;&gt;If this is your first time visiting this page, edit it by incrementing the user count below by one.&lt;/font&gt;&lt;/div&gt;<br /> &lt;center&gt;&lt;font size=&quot;100px&quot;&gt;140&lt;/font&gt;&lt;/center&gt;<br /> &lt;/div&gt;<br /> &lt;div style=&quot;border:2px solid black; background:#cccccc;-webkit-border-radius: 10px; align:center&quot;&gt;<br /> <br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;About Me&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-bottom:10px&quot;&gt;&lt;font color=&quot;black&quot;&gt;A legendary AoPSer.&lt;br&gt;<br /> <br /> My main project on the AoPS wiki is [[AoPS_Administrators#Current_Admins | a list of all the AoPS admins]], everyone is welcome to add more admins to the list by clicking [https://artofproblemsolving.com/wiki/index.php?title=AoPS_Administrators&amp;action=edit&amp;section=1 here]. I've also added a lot of the info in the [[Reaper Archives]]. Another one of my projects on the Wiki is trying to make the [[Main Page]] look better, you can check that out [[User:Piphi/AoPS Wiki|here]]<br /> <br /> You can also check out Greed Control Game 19 statistics that I found, [https://artofproblemsolving.com/community/c19451h2126212 here].<br /> <br /> Want to play chess on the wiki? Go [[User:Piphi/Chess | here]]!&lt;/font&gt;&lt;/div&gt;<br /> &lt;/div&gt;<br /> &lt;div style=&quot;border:2px solid black; background:#bbbbbb;-webkit-border-radius: 10px; align:center&quot;&gt;<br /> <br /> ==&lt;font color=&quot;black&quot; style=&quot;font-family: ITC Avant Garde Gothic Std, Verdana&quot;&gt;&lt;div style=&quot;margin-left:10px&quot;&gt;[[User:Piphi/Asymptote|Asymptote]]&lt;/div&gt;&lt;/font&gt;==<br /> &lt;div style=&quot;margin-left: 10px; margin-bottom:10px&quot;&gt;For a complete list of my Asymptote drawings, go [[User:Piphi/Asymptote|here]].&lt;/div&gt;<br /> &lt;/div&gt;</div> Eflower2000