If $20\%$ of a number is $12$, what is $30\%$ of the same number? $\textbf{(A)}\ 15 \qquad \textbf{(B)}\ 18 \qquad \textbf{(C)}\ 20 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 30$

A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by $ 25\%$ without altering the volume, by what percent must the height be decreased? $ \textbf{(A)}\ 10 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 36 \qquad \textbf{(D)}\ 50 \qquad \textbf{(E)}\ 60$

Abe can paint the room in 15 hours, Bea can paint 50 percent faster than Abe, and Coe can paint twice as fast as Abe. Abe begins to paint the room and works alone for the first hour and a half. Then Bea joins Abe, and they work together until half the room is painted. Then Coe joins Abe and Bea, and they work together until the entire room is painted. Find the number of minutes after Abe begins for the three of them to finish painting the room.

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 $

In a school, more than $90\% $ of the students know both English and German, and more than $90\%$ percent of the students know both English and French. Prove that more than $90\%$ percent of the students who know both German and French also know English.

Carlos took $70\%$ of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left? $\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 15\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 30\%\qquad\textbf{(E)}\ 35\%$

A positive number $ x$ has the property that $ x\%$ of $ x$ is $ 4$. What is $ x$? $ \textbf{(A)}\ 2 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 20 \qquad \textbf{(E)}\ 40$

Mr. Green receives a $ 10 \%$ raise every year. His salary after four such raises has gone up by what percent? \[ \textbf{(A)}\ \text{less than }40 \% \qquad \textbf{(B)}\ 40 \% \qquad \textbf{(C)}\ 44 \% \qquad \textbf{(D)}\ 45 \% \qquad \textbf{(E)}\ \text{More than }45 \% \]

The student population at one high school consists of freshmen, sophomores, juniors, and seniors. There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?

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] $\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 17 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 25$

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$

Last summer $30\%$ of the birds living on Town Lake were geese, $25\%$ were swans, $10\%$ were herons, and $35\%$ were ducks. What percent of the birds that were not swans were geese? $ \textbf{(A)}\ 20 \qquad\textbf{(B)}\ 30 \qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 50\qquad\textbf{(E)}\ 60 $

Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia's trip was, compared to Jerry's trip? $\textbf{(A)}\ 30 \%\qquad\textbf{(B)}\ 40 \%\qquad\textbf{(C)}\ 50 \%\qquad\textbf{(D)}\ 60 \%\qquad\textbf{(E)}\ 70 \%$

Find all real solutions $x$ of the equation $\cos\cos\cos\cos x=\sin\sin\sin\sin x$. (Angles are measured in radians.)

Ryan got $80\%$ of the problems on a $25$-problem test, $90\%$ on a $40$-problem test, and $70\%$ on a $10$-problem test. What percent of all problems did Ryan answer correctly? $ \textbf{(A)}\ 64 \qquad\textbf{(B)}\ 75\qquad\textbf{(C)}\ 80\qquad\textbf{(D)}\ 84\qquad\textbf{(E)}\ 86 $

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] $\text{(A)}\ 30\% \qquad \text{(B)}\ 31\% \qquad \text{(C)}\ 32\% \qquad \text{(D)}\ 33\% \qquad \text{(E)}\ 34\%$

An article costing $ C$ dollars is sold for $ \$100$ at a lostt of $ x$ percent of the selling price. It is then resold at a profit of $ x$ percent of the new selling price $ S'$. If the difference between $ S'$ and $ C$ is $ 1\frac {1}{9}$ dollars, then $ x$ is: $ \textbf{(A)}\ \text{undetermined} \qquad \textbf{(B)}\ \frac {80}{9} \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ \frac {95}{9} \qquad \textbf{(E)}\ \frac {100}{9}$

At the 2013 Winnebago County Fair a vendor is offering a ``fair special" on sandals. If you buy one pair of sandals at the regular price of \$50, you get a second pair at a 40\% discount, and a third pair at half the regular price. Javier took advantage of the ``fair special" to buy three pairs of sandals. What percentage of the \$150 regular price did he save? $\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 40 \qquad \textbf{(E)}\ 45$

A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience? $\text{(A)} \ 24 \qquad \text{(B)} \ 27 \qquad \text{(C)} \ 30 \qquad \text{(D)} \ 33 \qquad \text{(E)} \ 36$

$x$ and $y$ are positive real numbers where $x$ is $p$ percent of $y$, and $y$ is $4p$ percent of $x$. What is $p$?