MathDB

2009 AMC 8

Part of AMC 8

Subcontests

(25)
25
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AMC 8 2009 Problem 25 - Cube parts

A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cub is 12\tfrac12 foot from the top face. The second cut is 13\tfrac13 foot below the first cut, and the third cut is 117\tfrac1{17} foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
[asy] import three; real d=11/102; defaultpen(fontsize(8)); defaultpen(linewidth(0.8)); currentprojection=orthographic(1,8/15,7/15); draw(unitcube, white, thick(), nolight); void f(real x) { draw((0,1,x)--(1,1,x)--(1,0,x)); } f(d); f(1/6); f(1/2); label("A", (1,0,3/4), W); label("B", (1,0,1/3), W); label("C", (1,0,1/6-d/4), W); label("D", (1,0,d/2), W); label("1/2", (1,1,3/4), E); label("1/3", (1,1,1/3), E); label("1/17", (0,1,1/6-d/4), E);[/asy]
[asy] import three; real d=11/102; defaultpen(fontsize(8)); defaultpen(linewidth(0.8)); currentprojection=orthographic(2,8/15,7/15); int t=0; void f(real x) { path3 r=(t,1,x)--(t+1,1,x)--(t+1,1,0)--(t,1,0)--cycle; path3 f=(t+1,1,x)--(t+1,1,0)--(t+1,0,0)--(t+1,0,x)--cycle; path3 u=(t,1,x)--(t+1,1,x)--(t+1,0,x)--(t,0,x)--cycle; draw(surface(r), white, nolight); draw(surface(f), white, nolight); draw(surface(u), white, nolight); draw((t,1,x)--(t+1,1,x)--(t+1,1,0)--(t,1,0)--(t,1,x)--(t,0,x)--(t+1,0,x)--(t+1,1,x)--(t+1,1,0)--(t+1,0,0)--(t+1,0,x)); t=t+1; } f(d); f(1/2); f(1/3); f(1/17); label("D", (1/2, 1, 0), SE); label("A", (1+1/2, 1, 0), SE); label("B", (2+1/2, 1, 0), SE); label("C", (3+1/2, 1, 0), SE);[/asy]
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 41951<spanclass=′latex−bold′>(D)</span> 15817<spanclass=′latex−bold′>(E)</span> 11<span class='latex-bold'>(A)</span>\:6\qquad <span class='latex-bold'>(B)</span>\:7\qquad <span class='latex-bold'>(C)</span>\:\frac{419}{51}\qquad <span class='latex-bold'>(D)</span>\:\frac{158}{17}\qquad <span class='latex-bold'>(E)</span>\:11
7
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2009 AMC 8 Problem 7-Square miles in plot of ACD

The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD? [asy] size(250); defaultpen(linewidth(0.55)); pair A=(-6,0), B=origin, C=(0,6), D=(0,12); pair ac=C+2.828*dir(45), ca=A+2.828*dir(225), ad=D+2.828*dir(A--D), da=A+2.828*dir(D--A), ab=(2.828,0), ba=(-6-2.828, 0);
fill(A--C--D--cycle, gray); draw(ba--ab); draw(ac--ca); draw(ad--da); draw((0,-1)--(0,15)); draw((1/3, -1)--(1/3, 15)); int i; for(i=1; i<15; i=i+1) { draw((-1/10, i)--(13/30, i)); }
label("AA", A, SE); label("BB", B, SE); label("CC", C, SE); label("DD", D, SE); label("33", (1/3,3), E); label("33", (1/3,9), E); label("33", (-3,0), S); label("Main", (-3,0), N); label(rotate(45)*"Aspen", A--C, SE); label(rotate(63.43494882)*"Brown", A--D, NW); [/asy] <spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4.5<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 9<span class='latex-bold'>(A)</span>\ 2\qquad <span class='latex-bold'>(B)</span>\ 3 \qquad <span class='latex-bold'>(C)</span>\ 4.5 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 9
4
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AMC 8 2009 Problem 4

The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot be formed?
[asy] defaultpen(linewidth(0.6)); size(80); real r=0.5, s=1.5; path p=origin--(1,0)--(1,1)--(0,1)--cycle; draw(p); draw(shift(s,r)*p); draw(shift(s,-r)*p); draw(shift(2s,2r)*p); draw(shift(2s,0)*p); draw(shift(2s,-2r)*p); draw(shift(3s,3r)*p); draw(shift(3s,-3r)*p); draw(shift(3s,r)*p); draw(shift(3s,-r)*p); draw(shift(4s,-4r)*p); draw(shift(4s,-2r)*p); draw(shift(4s,0)*p); draw(shift(4s,2r)*p); draw(shift(4s,4r)*p);[/asy]
[asy] size(350); defaultpen(linewidth(0.6)); path p=origin--(1,0)--(1,1)--(0,1)--cycle; pair[] a={(0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (2,0), (2,1), (3,0), (3,1), (3,2), (3,3), (3,4)}; pair[] b={(5,3), (5,4), (6,2), (6,3), (6,4), (7,1), (7,2), (7,3), (7,4), (8,0), (8,1), (8,2), (9,0), (9,1), (9,2)}; pair[] c={(11,0), (11,1), (11,2), (11,3), (11,4), (12,1), (12,2), (12,3), (12,4), (13,2), (13,3), (13,4), (14,3), (14,4), (15,4)}; pair[] d={(17,0), (17,1), (17,2), (17,3), (17,4), (18,0), (18,1), (18,2), (18,3), (18,4), (19,0), (19,1), (19,2), (19,3), (19,4)}; pair[] e={(21,4), (22,1), (22,2), (22,3), (22,4), (23,0), (23,1), (23,2), (23,3), (23,4), (24,1), (24,2), (24,3), (24,4), (25,4)};
int i; for(int i=0; i<15; i=i+1) { draw(shift(a)*p); draw(shift(b)*p); draw(shift(c)*p); draw(shift(d)*p); draw(shift(e)*p); } [/asy] (A)\qquad\qquad\qquad(B) \qquad\qquad(C)\:\qquad\qquad\qquad(D) \qquad\qquad(E)
10
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2009 AMC 8 Problem 10-Checkerboard Probability

On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board? [asy] unitsize(10); draw((0,0)--(8,0)--(8,8)--(0,8)--cycle); draw((1,8)--(1,0)); draw((7,8)--(7,0)); draw((6,8)--(6,0)); draw((5,8)--(5,0)); draw((4,8)--(4,0)); draw((3,8)--(3,0)); draw((2,8)--(2,0)); draw((0,1)--(8,1)); draw((0,2)--(8,2)); draw((0,3)--(8,3)); draw((0,4)--(8,4)); draw((0,5)--(8,5)); draw((0,6)--(8,6)); draw((0,7)--(8,7)); fill((0,0)--(1,0)--(1,1)--(0,1)--cycle,black); fill((2,0)--(3,0)--(3,1)--(2,1)--cycle,black); fill((4,0)--(5,0)--(5,1)--(4,1)--cycle,black); fill((6,0)--(7,0)--(7,1)--(6,1)--cycle,black); fill((0,2)--(1,2)--(1,3)--(0,3)--cycle,black); fill((2,2)--(3,2)--(3,3)--(2,3)--cycle,black); fill((4,2)--(5,2)--(5,3)--(4,3)--cycle,black); fill((6,2)--(7,2)--(7,3)--(6,3)--cycle,black); fill((0,4)--(1,4)--(1,5)--(0,5)--cycle,black); fill((2,4)--(3,4)--(3,5)--(2,5)--cycle,black); fill((4,4)--(5,4)--(5,5)--(4,5)--cycle,black); fill((6,4)--(7,4)--(7,5)--(6,5)--cycle,black); fill((0,6)--(1,6)--(1,7)--(0,7)--cycle,black); fill((2,6)--(3,6)--(3,7)--(2,7)--cycle,black); fill((4,6)--(5,6)--(5,7)--(4,7)--cycle,black); fill((6,6)--(7,6)--(7,7)--(6,7)--cycle,black); fill((1,1)--(2,1)--(2,2)--(1,2)--cycle,black); fill((3,1)--(4,1)--(4,2)--(3,2)--cycle,black); fill((5,1)--(6,1)--(6,2)--(5,2)--cycle,black); fill((7,1)--(8,1)--(8,2)--(7,2)--cycle,black); fill((1,3)--(2,3)--(2,4)--(1,4)--cycle,black); fill((3,3)--(4,3)--(4,4)--(3,4)--cycle,black); fill((5,3)--(6,3)--(6,4)--(5,4)--cycle,black); fill((7,3)--(8,3)--(8,4)--(7,4)--cycle,black); fill((1,5)--(2,5)--(2,6)--(1,6)--cycle,black); fill((3,5)--(4,5)--(4,6)--(3,6)--cycle,black); fill((5,5)--(6,5)--(6,6)--(5,6)--cycle,black); fill((7,5)--(8,5)--(8,6)--(7,6)--cycle,black); fill((1,7)--(2,7)--(2,8)--(1,8)--cycle,black); fill((3,7)--(4,7)--(4,8)--(3,8)--cycle,black); fill((5,7)--(6,7)--(6,8)--(5,8)--cycle,black); fill((7,7)--(8,7)--(8,8)--(7,8)--cycle,black);[/asy] <spanclass=′latex−bold′>(A)</span>116<spanclass=′latex−bold′>(B)</span>716<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>916<spanclass=′latex−bold′>(E)</span>4964 <span class='latex-bold'>(A)</span>\frac{1}{16}\qquad<span class='latex-bold'>(B)</span>\frac{7}{16}\qquad<span class='latex-bold'>(C)</span>\frac12\qquad<span class='latex-bold'>(D)</span>\frac{9}{16}\qquad<span class='latex-bold'>(E)</span>\frac{49}{64}
3
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AMC 8 2009 Problem 3-Reading a graph

The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden? [asy] size(200); import graph; /* this is a label */ Label f; f.p=fontsize(0); xaxis(-0.9,20,Ticks(f, 5.0, 5.0)); yaxis(-0.9,20, Ticks(f, 22.0,5.0)); // real f(real x) { return x; } draw(graph(f,-1,22),black+linewidth(1)); label("1", (-1,5), black); label("2", (-1, 10), black); label("3", (-1, 15), black); label("4", (-1, 20), black); dot((5,5), black+linewidth(5)); dot((10,10), black+linewidth(5)); dot((15, 15), black+linewidth(5)); dot((20,20), black+linewidth(5)); label("MINUTES", (11,-5), S); label(rotate(90)*"MILES", (-5,11), W);[/asy] <spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>5.5<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>6.5<spanclass=′latex−bold′>(E)</span>7 <span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>5.5\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>6.5\qquad<span class='latex-bold'>(E) </span>7
9
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AMC 8 2009 Problem 9 - Regular Polygons

Construct a square on one side of an equilateral triangle. One on non-adjacent side of the square, construct a regular pentagon, as shown. One a non-adjacent side of the pentagon, construct a hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?
[asy] defaultpen(linewidth(0.6)); pair O=origin, A=(0,1), B=A+1*dir(60), C=(1,1), D=(1,0), E=D+1*dir(-72), F=E+1*dir(-144), G=O+1*dir(-108); draw(O--A--B--C--D--E--F--G--cycle); draw(O--D, dashed); draw(A--C, dashed);[/asy]
<spanclass=′latex−bold′>(A)</span>21<spanclass=′latex−bold′>(B)</span>23<spanclass=′latex−bold′>(C)</span>25<spanclass=′latex−bold′>(D)</span>27<spanclass=′latex−bold′>(E)</span>29<span class='latex-bold'>(A)</span> 21 \qquad <span class='latex-bold'>(B)</span> 23 \qquad <span class='latex-bold'>(C)</span> 25 \qquad <span class='latex-bold'>(D)</span> 27 \qquad <span class='latex-bold'>(E)</span> 29
12
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Spinners

The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? [asy]unitsize(30); draw(unitcircle); draw((0,0)--(0,-1)); draw((0,0)--(cos(pi/6),sin(pi/6))); draw((0,0)--(-cos(pi/6),sin(pi/6))); label("11",(0,.5)); label("33",((cos(pi/6))/2,(-sin(pi/6))/2)); label("55",(-(cos(pi/6))/2,(-sin(pi/6))/2));[/asy] [asy]unitsize(30); draw(unitcircle); draw((0,0)--(0,-1)); draw((0,0)--(cos(pi/6),sin(pi/6))); draw((0,0)--(-cos(pi/6),sin(pi/6))); label("22",(0,.5)); label("44",((cos(pi/6))/2,(-sin(pi/6))/2)); label("66",(-(cos(pi/6))/2,(-sin(pi/6))/2));[/asy] <spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 34<spanclass=′latex−bold′>(D)</span> 79<spanclass=′latex−bold′>(E)</span> 56 <span class='latex-bold'>(A)</span>\ \frac {1}{2} \qquad <span class='latex-bold'>(B)</span>\ \frac {2}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac {3}{4} \qquad <span class='latex-bold'>(D)</span>\ \frac {7}{9} \qquad <span class='latex-bold'>(E)</span>\ \frac {5}{6}
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Addition and Subtraction

The letters A A, B B, C C and D D represent digits. If \begin{tabular}{ccc} &A&B \\ \plus{}&C&A \\ \hline &D&A \end{tabular} and \begin{tabular}{ccc} &A&B \\ \minus{}&C&A \\ \hline &&A \end{tabular}, what digit does D D represent? <spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 5 \qquad <span class='latex-bold'>(B)</span>\ 6 \qquad <span class='latex-bold'>(C)</span>\ 7 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 9
18
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Floor Tiling

The diagram represents a 7 7-foot-by-7 7-foot floor that is tiled with 1 1-square-foot black tiles and white tiles. Notice that the corners have white tiles. If a 15 15-foot-by-15 15-foot floor is to be tiled in the same manner, how many white tiles will be needed? [asy]unitsize(10); draw((0,0)--(7,0)--(7,7)--(0,7)--cycle); draw((1,7)--(1,0)); draw((6,7)--(6,0)); draw((5,7)--(5,0)); draw((4,7)--(4,0)); draw((3,7)--(3,0)); draw((2,7)--(2,0)); draw((0,1)--(7,1)); draw((0,2)--(7,2)); draw((0,3)--(7,3)); draw((0,4)--(7,4)); draw((0,5)--(7,5)); draw((0,6)--(7,6)); fill((1,0)--(2,0)--(2,7)--(1,7)--cycle,black); fill((3,0)--(4,0)--(4,7)--(3,7)--cycle,black); fill((5,0)--(6,0)--(6,7)--(5,7)--cycle,black); fill((0,5)--(0,6)--(7,6)--(7,5)--cycle,black); fill((0,3)--(0,4)--(7,4)--(7,3)--cycle,black); fill((0,1)--(0,2)--(7,2)--(7,1)--cycle,black);[/asy] <spanclass=′latex−bold′>(A)</span> 49<spanclass=′latex−bold′>(B)</span> 57<spanclass=′latex−bold′>(C)</span> 64<spanclass=′latex−bold′>(D)</span> 96<spanclass=′latex−bold′>(E)</span> 126 <span class='latex-bold'>(A)</span>\ 49 \qquad <span class='latex-bold'>(B)</span>\ 57 \qquad <span class='latex-bold'>(C)</span>\ 64 \qquad <span class='latex-bold'>(D)</span>\ 96 \qquad <span class='latex-bold'>(E)</span>\ 126
23
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Jelly Beans

On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class? <spanclass=′latex−bold′>(A)</span> 26<spanclass=′latex−bold′>(B)</span> 28<spanclass=′latex−bold′>(C)</span> 30<spanclass=′latex−bold′>(D)</span> 32<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ 26 \qquad <span class='latex-bold'>(B)</span>\ 28 \qquad <span class='latex-bold'>(C)</span>\ 30 \qquad <span class='latex-bold'>(D)</span>\ 32 \qquad <span class='latex-bold'>(E)</span>\ 34
21
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Array of Random Numbers

Andy and Bethany have a rectangular array of numbers with 40 40 rows and 75 75 columns. Andy adds the numbers in each row. The average of his 40 40 sums is A A. Bethany adds the numbers in each column. The average of her 75 75 sums is B B. What is the value of AB \frac{A}{B}? <spanclass=′latex−bold′>(A)</span> 64225<spanclass=′latex−bold′>(B)</span> 815<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 158<spanclass=′latex−bold′>(E)</span> 22564 <span class='latex-bold'>(A)</span>\ \frac{64}{225} \qquad <span class='latex-bold'>(B)</span>\ \frac{8}{15} \qquad <span class='latex-bold'>(C)</span>\ 1 \qquad <span class='latex-bold'>(D)</span>\ \frac{15}{8} \qquad <span class='latex-bold'>(E)</span>\ \frac{225}{64}
20
1

Triangles

How many non-congruent triangles have vertices at three of the eight points in the array shown below? [asy]dot((0,0)); dot((0,.5)); dot((.5,0)); dot((.5,.5)); dot((1,0)); dot((1,.5)); dot((1.5,0)); dot((1.5,.5));[/asy] <spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 5 \qquad <span class='latex-bold'>(B)</span>\ 6 \qquad <span class='latex-bold'>(C)</span>\ 7 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 9
19
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Isosceles Triangles

Two angles of an isosceles triangle measure 70∘ 70^\circ and x∘ x^\circ. What is the sum of the three possible values of x x? <spanclass=′latex−bold′>(A)</span> 95<spanclass=′latex−bold′>(B)</span> 125<spanclass=′latex−bold′>(C)</span> 140<spanclass=′latex−bold′>(D)</span> 165<spanclass=′latex−bold′>(E)</span> 180 <span class='latex-bold'>(A)</span>\ 95 \qquad <span class='latex-bold'>(B)</span>\ 125 \qquad <span class='latex-bold'>(C)</span>\ 140 \qquad <span class='latex-bold'>(D)</span>\ 165 \qquad <span class='latex-bold'>(E)</span>\ 180
17
1

Squares and Cubes

The positive integers x x and y y are the two smallest positive integers for which the product of 360 360 and x x is a square and the product of 360 360 and y y is a cube. What is the sum of x x and y y? <spanclass=′latex−bold′>(A)</span> 80<spanclass=′latex−bold′>(B)</span> 85<spanclass=′latex−bold′>(C)</span> 115<spanclass=′latex−bold′>(D)</span> 165<spanclass=′latex−bold′>(E)</span> 610 <span class='latex-bold'>(A)</span>\ 80 \qquad <span class='latex-bold'>(B)</span>\ 85 \qquad <span class='latex-bold'>(C)</span>\ 115 \qquad <span class='latex-bold'>(D)</span>\ 165 \qquad <span class='latex-bold'>(E)</span>\ 610
16
1
22
1
15
1

Recipe

A recipe that makes 5 5 servings of hot chocolate requires 2 2 squares of chocolate, 14 \frac{1}{4} cup sugar, 1 1 cup water and 4 4 cups milk. Jordan has 5 5 squares of chocolate, 2 2 cups of sugar, lots of water and 7 7 cups of milk. If she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make? <spanclass=′latex−bold′>(A)</span> 518<spanclass=′latex−bold′>(B)</span> 614<spanclass=′latex−bold′>(C)</span> 712<spanclass=′latex−bold′>(D)</span> 834<spanclass=′latex−bold′>(E)</span> 978 <span class='latex-bold'>(A)</span>\ 5 \frac18 \qquad <span class='latex-bold'>(B)</span>\ 6\frac14 \qquad <span class='latex-bold'>(C)</span>\ 7\frac12 \qquad <span class='latex-bold'>(D)</span>\ 8 \frac34 \qquad <span class='latex-bold'>(E)</span>\ 9\frac78
14
1

Average Speed

Austin and Temple are 50 50 miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging 60 60 miles per hour. Leaving the car with her daughter, Bonnie rod a bus back to Austin along the same route and averaged 40 40 miles per hour on the return trip. What was the average speed for the round trip, in miles per hour? <spanclass=′latex−bold′>(A)</span> 46<spanclass=′latex−bold′>(B)</span> 48<spanclass=′latex−bold′>(C)</span> 50<spanclass=′latex−bold′>(D)</span> 52<spanclass=′latex−bold′>(E)</span> 54 <span class='latex-bold'>(A)</span>\ 46 \qquad <span class='latex-bold'>(B)</span>\ 48 \qquad <span class='latex-bold'>(C)</span>\ 50 \qquad <span class='latex-bold'>(D)</span>\ 52 \qquad <span class='latex-bold'>(E)</span>\ 54
13
1

Three-Digit Integers

A three-digit integer contains one of each of the digits 1 1, 3 3, and 5 5. What is the probability that the integer is divisible by 5 5? <spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 23<spanclass=′latex−bold′>(E)</span> 56 <span class='latex-bold'>(A)</span>\ \frac{1}{6} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{2} \qquad <span class='latex-bold'>(D)</span>\ \frac{2}{3} \qquad <span class='latex-bold'>(E)</span>\ \frac{5}{6}
11
1

Cost of Pencils

The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of $1.43 \$1.43. Some of the 30 30 sixth graders each bought a pencil, and they paid a total of $1.95 \$1.95. How many more sixth graders than seventh graders bought a pencil? <spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ 3 \qquad <span class='latex-bold'>(D)</span>\ 4 \qquad <span class='latex-bold'>(E)</span>\ 5
8
1

Rectangle Scaling

The length of a rectangle is increased by 10% 10\% and the width is decreased by 10% 10\%. What percent of the old area is the new area?
<spanclass=′latex−bold′>(A)</span> 90<spanclass=′latex−bold′>(B)</span> 99<spanclass=′latex−bold′>(C)</span> 100<spanclass=′latex−bold′>(D)</span> 101<spanclass=′latex−bold′>(E)</span> 110 <span class='latex-bold'>(A)</span>\ 90 \qquad <span class='latex-bold'>(B)</span>\ 99 \qquad <span class='latex-bold'>(C)</span>\ 100 \qquad <span class='latex-bold'>(D)</span>\ 101 \qquad <span class='latex-bold'>(E)</span>\ 110
6
1

Filling a Swimming Pool

Steve's empty swimming pool will hold 24,000 24,000 gallons of water when full. It will be filled by 4 4 hoses, each of which supplies 2.5 2.5 gallons of water per minute. How many hours will it take to fill Steve's pool? <spanclass=′latex−bold′>(A)</span> 40<spanclass=′latex−bold′>(B)</span> 42<spanclass=′latex−bold′>(C)</span> 44<spanclass=′latex−bold′>(D)</span> 46<spanclass=′latex−bold′>(E)</span> 48 <span class='latex-bold'>(A)</span>\ 40 \qquad <span class='latex-bold'>(B)</span>\ 42 \qquad <span class='latex-bold'>(C)</span>\ 44 \qquad <span class='latex-bold'>(D)</span>\ 46 \qquad <span class='latex-bold'>(E)</span>\ 48
5
1

Sequence of Numbers

A sequence of numbers starts with 1 1, 2 2, and 3 3. The fourth number of the sequence is the sum of the previous three numbers in the sequence: 1\plus{}2\plus{}3\equal{}6. In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence? <spanclass=′latex−bold′>(A)</span> 11<spanclass=′latex−bold′>(B)</span> 20<spanclass=′latex−bold′>(C)</span> 37<spanclass=′latex−bold′>(D)</span> 68<spanclass=′latex−bold′>(E)</span> 99 <span class='latex-bold'>(A)</span>\ 11 \qquad <span class='latex-bold'>(B)</span>\ 20 \qquad <span class='latex-bold'>(C)</span>\ 37 \qquad <span class='latex-bold'>(D)</span>\ 68 \qquad <span class='latex-bold'>(E)</span>\ 99
2
1

Sports Cars and Sedans

On average, for every 4 sports cars sold at the local dealership, 7 sedans are sold. The dealership predicts that it will sell 28 sports cars next month. How many sedans does it expect to sell? <spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 35<spanclass=′latex−bold′>(D)</span> 49<spanclass=′latex−bold′>(E)</span> 112 <span class='latex-bold'>(A)</span>\ 7 \qquad <span class='latex-bold'>(B)</span>\ 32 \qquad <span class='latex-bold'>(C)</span>\ 35 \qquad <span class='latex-bold'>(D)</span>\ 49 \qquad <span class='latex-bold'>(E)</span>\ 112
1
1

Apples

Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 3 apples, keeping 4 apples for herself. How many apples did Bridget buy? <spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> 14 <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 7 \qquad <span class='latex-bold'>(D)</span>\ 11 \qquad <span class='latex-bold'>(E)</span>\ 14