Antonette gets $ 70\%$ on a 10-problem test, $ 80\%$ on a 20-problem test and $ 90\%$ on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score? $ \textbf{(A)}\ 40 \qquad \textbf{(B)}\ 77 \qquad \textbf{(C)}\ 80 \qquad \textbf{(D)}\ 83 \qquad \textbf{(E)}\ 87$

We choose random a unitary polynomial of degree $n$ and coefficients in the set $1,2,...,n!$. Prove that the probability for this polynomial to be special is between $0.71$ and $0.75$, where a polynomial $g$ is called special if for every $k>1$ in the sequence $f(1), f(2), f(3),...$ there are infinitely many numbers relatively prime with $k$.

A positive number is mistakenly divided by $6$ instead of being multiplied by $6$. Based on the correct answer, the error thus comitted, to the nearest percent, is: $\textbf{(A)}\ 100 \qquad \textbf{(B)}\ 97 \qquad \textbf{(C)}\ 83 \qquad \textbf{(D)}\ 17 \qquad \textbf{(E)}\ 3 $

The pie charts below indicate the percent of students who prefer golf, bowling, or tennis at East Junior High School and West Middle School. The total number of students at East is $2000$ and at West, $2500$. In the two schools combined, the percent of students who prefer tennis is [asy] unitsize(18); draw(circle((0,0),4)); draw(circle((9,0),4)); draw((-4,0)--(0,0)--4*dir(352.8)); draw((0,0)--4*dir(100.8)); draw((5,0)--(9,0)--(4*dir(324)+(9,0))); draw((9,0)--(4*dir(50.4)+(9,0))); label("$48\%$",(0,-1),S); label("bowling",(0,-2),S); label("$30\%$",(1.5,1.5),N); label("golf",(1.5,0.5),N); label("$22\%$",(-2,1.5),N); label("tennis",(-2,0.5),N); label("$40\%$",(8.5,-1),S); label("tennis",(8.5,-2),S); label("$24\%$",(10.5,0.5),E); label("golf",(10.5,-0.5),E); label("$36\%$",(7.8,1.7),N); label("bowling",(7.8,0.7),N); label("$\textbf{East JHS}$",(0,-4),S); label("$\textbf{2000 students}$",(0,-5),S); label("$\textbf{West MS}$",(9,-4),S); label("$\textbf{2500 students}$",(9,-5),S); [/asy] $\text{(A)}\ 30\% \qquad \text{(B)}\ 31\% \qquad \text{(C)}\ 32\% \qquad \text{(D)}\ 33\% \qquad \text{(E)}\ 34\%$

If $ a$ is $ 50\%$ larger than $ c$, and $ b$ is $ 25\%$ larger than $ c$,then $ a$ is what percent larger than $ b$? $ \textbf{(A)}\ 20\%\qquad \textbf{(B)}\ 25\%\qquad \textbf{(C)}\ 50\%\qquad \textbf{(D)}\ 100\%\qquad \textbf{(E)}\ 200\%$

A cube has edge length $2$. Suppose that we glue a cube of edge length $1$ on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to [asy] draw((0,0)--(2,0)--(3,1)--(3,3)--(2,2)--(0,2)--cycle); draw((2,0)--(2,2)); draw((0,2)--(1,3)); draw((1,7/3)--(1,10/3)--(2,10/3)--(2,7/3)--cycle); draw((2,7/3)--(5/2,17/6)--(5/2,23/6)--(3/2,23/6)--(1,10/3)); draw((2,10/3)--(5/2,23/6)); draw((3,3)--(5/2,3)); [/asy] $\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 17 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 25$

Seller reduced price of one shirt for $20\%$,and they raised it by $10\%$. Does he needs to reduce or raise the price and how many, so that price of shirt will be reduced by $10\%$ from the original price

Suppose $a$ is $150\%$ of $b$. What percent of $a$ is $3b$? $\textbf{(A) } 50 \qquad \textbf{(B) } 66\frac{2}{3} \qquad \textbf{(C) } 150 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 450$

Last year a bicycle cost $\$160$ and a cycling helmet cost $ \$ 40$. This year the cost of the bicycle increased by $5\%$, and the cost of the helmet increased by $10\%$. The percent increase in the combined cost of the bicycle and the helmet is $ \textbf{(A)}\ 6\% \qquad\textbf{(B)}\ 7\% \qquad\textbf{(C)}\ 7.5\% \qquad\textbf{(D)}\ 8\% \qquad\textbf{(E)}\ 15\% $

During the softball season, Judy had $35$ hits. Among her hits were $1$ home run, $1$ triple and $5$ doubles. The rest of her hits were single. What percent of her hits were single? $\text{(A)}\ 28\% \qquad \text{(B)}\ 35\% \qquad \text{(C)}\ 70\% \qquad \text{(D)}\ 75\% \qquad \text{(E)}\ 80\% $

Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice? $\text{(A)}\ 30 \qquad \text{(B)}\ 40 \qquad \text{(C)}\ 50 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 70$

The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is [i]bad[/i] if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there? $ \textbf {(A) } 1 \qquad \textbf {(B) } 2 \qquad \textbf {(C) } 3 \qquad \textbf {(D) } 4 \qquad \textbf {(E) } 5 $

A group of $ 100$ students numbered $ 1$ through $ 100$ are playing the following game. The judge writes the numbers $ 1$, $ 2$, $ \ldots$, $ 100$ on $ 100$ cards, places them on the table in an arbitrary order and turns them over. The students $ 1$ to $ 100$ enter the room one by one, and each of them flips $ 50$ of the cards. If among the cards flipped by student $ j$ there is card $ j$, he gains one point. The flipped cards are then turned over again. The students cannot communicate during the game nor can they see the cards flipped by other students. The group wins the game if each student gains a point. Is there a strategy giving the group more than $ 1$ percent of chance to win?

A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler? $\textbf{(A)}\ 60\%\qquad \textbf{(B)}\ 65\% \qquad \textbf{(C)}\ 70\%\qquad \textbf{(D)}\ 75\% \qquad \textbf{(E)}\ 90\%$

The students in Mrs. Sawyer's class were asked to do a taste test of five kinds of candy. Each student chose one kind of candy. A bar graph of their preferences is shown. What percent of her class chose candy E? [asy] real[] r={6, 8, 4, 2, 5}; int i; for(i=0; i<5; i=i+1) { filldraw((4i,0)--(4i+3,0)--(4i+3,2r[i])--(4i,2r[i])--cycle, black, black); } draw(origin--(19,0)--(19,16)--(0,16)--cycle, linewidth(0.9)); for(i=1; i<8; i=i+1) { draw((0,2i)--(19,2i)); } label("$0$", (0,2*0), W); label("$1$", (0,2*1), W); label("$2$", (0,2*2), W); label("$3$", (0,2*3), W); label("$4$", (0,2*4), W); label("$5$", (0,2*5), W); label("$6$", (0,2*6), W); label("$7$", (0,2*7), W); label("$8$", (0,2*8), W); label("$A$", (0*4+1.5, 0), S); label("$B$", (1*4+1.5, 0), S); label("$C$", (2*4+1.5, 0), S); label("$D$", (3*4+1.5, 0), S); label("$E$", (4*4+1.5, 0), S); label("SWEET TOOTH", (9.5,18), N); label("Kinds of candy", (9.5,-2), S); label(rotate(90)*"Number of students", (-2,8), W); [/asy] $ \text{(A)}\ 5\qquad\text{(B)}\ 12\qquad\text{(C)}\ 15\qquad\text{(D)}\ 16\qquad\text{(E)}\ 20 $

The number of ounces of water needed to reduce $ 9$ ounces of shaving lotion containing $ 50\%$ alcohol to a lotion containing $ 30\%$ alcohol is: $ \textbf{(A)}\ 3 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 7$

The Nationwide Basketball Society (NBS) has $8001$ teams, numbered $2000$ through $10000$. For each $n$, team $n$ has $n+1$ players, and in a sheer coincidence, this year each player attempted $n$ shots and on team $n$, exactly one player made $0$ shots, one player made $1$ shot, . . ., one player made $n$ shots. A player's [i]field goal percentage[/i] is defined as the percentage of shots the player made, rounded to the nearest tenth of a percent (For instance, $32.45\%$ rounds to $32.5\%$). A player in the NBS is randomly selected among those whose field goal percentage is $66.6\%$. If this player plays for team $k$, the probability that $k\geq 6000$ can be expressed as $\tfrac{p}{q}$ for relatively prime positive integers $p$ and $q$. Find $p+q$.

A rectangle has area $1100$. If the length is increased by ten percent and the width is decreased by ten percent, what is the area of the new rectangle?

A merchant buys goods at $ 25\%$ of the list price. He desires to mark the goods so that he can give a discount of $ 20\%$ on the marked price and still clear a profit of $ 25\%$ on the selling price. What percent of the list price must he mark the goods? $\textbf{(A)}\ 125\% \qquad \textbf{(B)}\ 100\% \qquad \textbf{(C)}\ 120\% \qquad \textbf{(D)}\ 80\% \qquad \textbf{(E)}\ 75\%$

The area of a pizza with radius $4$ inches is $N$ percent larger than the area of a pizza with radius $3$ inches. What is the integer closest to $N$? $\textbf{(A) } 25 \qquad\textbf{(B) } 33 \qquad\textbf{(C) } 44\qquad\textbf{(D) } 66 \qquad\textbf{(E) } 78$

If a worker receives a $ 20$ percent cut in wages, he may regain his original pay exactly by obtaining a raise of: $ \textbf{(A)}\ \text{20 percent} \qquad \textbf{(B)}\ \text{25 percent} \qquad \textbf{(C)}\ 22\frac{1}{2} \text{ percent} \qquad \textbf{(D)}\ \$20 \qquad \textbf{(E)}\ \$25$

Aisha went shopping. At the first store she spent $40$ percent of her money plus four dollars. At the second store she spent $50$ percent of her remaining money plus $5$ dollars. At the third store she spent $60$ percent of her remaining money plus six dollars. When Aisha was done shopping at the three stores, she had two dollars left. How many dollars did she have with her when she started shopping?

Suppose $15\%$ of $x$ equals $20\%$ of $y$. What percentage of $x$ is $y$? $\textbf{(A)}\ 5~~\qquad\textbf{(B)}\ 35~~\qquad~~\textbf{(C)}\ 75\qquad~~\textbf{(D)}\ 133\frac13\qquad~~ \textbf{(E)}\ 300$

A carton contains milk that is $ 2\%$ fat, and amount that is $ 40\%$ less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk? $ \textbf{(A)}\ \frac{12}{5} \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ \frac{10}{3} \qquad \textbf{(D)}\ 38 \qquad \textbf{(E)}\ 42$

At Jefferson Summer Camp, $ 60\%$ of the children play soccer, $ 30\%$ of the children swim, and $ 40\%$ of the soccer players swim. To the nearest whole percent, what percent of the non-swimmers play soccer? $ \textbf{(A)}\ 30\% \qquad \textbf{(B)}\ 40\% \qquad \textbf{(C)}\ 49\% \qquad \textbf{(D)}\ 51\% \qquad \textbf{(E)}\ 70\%$