Given two positive integers $ x$ and $ y$ with $ x < y$. The percent that $ x$ is less than $ y$ is: $ \textbf{(A)}\ \frac {100(y \minus{} x)}{x} \qquad\textbf{(B)}\ \frac {100(x \minus{} y)}{x} \qquad\textbf{(C)}\ \frac {100(y \minus{} x)}{y} \qquad\textbf{(D)}\ 100(y \minus{} x)$ $ \textbf{(E)}\ 100(x \minus{} y)$

The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to $ \textbf{(A)} \ 50 \qquad \textbf{(B)} \ 52 \qquad \textbf{(C)} \ 54 \qquad \textbf{(D)} \ 56 \qquad \textbf{(E)} \ 58 \qquad$ [asy]unitsize(3mm); defaultpen(linewidth(0.8pt)); path p1=(0,0)--(3,0)--(3,3)--(0,3)--(0,0); path p2=(0,1)--(1,1)--(1,0); path p3=(2,0)--(2,1)--(3,1); path p4=(3,2)--(2,2)--(2,3); path p5=(1,3)--(1,2)--(0,2); path p6=(1,1)--(2,2); path p7=(2,1)--(1,2); path[] p=p1^^p2^^p3^^p4^^p5^^p6^^p7; for(int i=0; i<3; ++i) { for(int j=0; j<3; ++j) { draw(shift(3*i,3*j)*p); } }[/asy]

A merchant bought some goods at a discount of $ 20\%$ of the list price. He wants to mark them at such a price that he can give a discount of $ 20 \%$ of the marked price and still make a profit of $ 20\%$ of the selling price. The percent of the list price at which he should mark them is: $ \textbf{(A)}\ 20 \qquad\textbf{(B)}\ 100 \qquad\textbf{(C)}\ 125 \qquad\textbf{(D)}\ 80 \qquad\textbf{(E)}\ 120$

The work team was working at a rate fast enough to process $1250$ items in ten hours. But after working for six hours, the team was given an additional $165$ items to process. By what percent does the team need to increase its rate so that it can still complete its work within the ten hours?

Makayla attended two meetings during her 9-hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings? $ \textbf{(A)}\ 15 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 25 \qquad \textbf{(D)}\ 30 \qquad \textbf{(E)}\ 35$

Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by $10$ percent. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost $40$ dollars on Thursday? $\textbf{(A)}\ 36 \qquad \textbf{(B)}\ 39.60 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 40.40 \qquad \textbf{(E)}\ 44$

A biologist wants to calculate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To calculate the number of fish in the lake on May 1, she assumes that $25\%$ of these fish are no longer in the lake on September 1 (because of death and emigrations), that $40\%$ of the fish were not in the lake May 1 (because of births and immigrations), and that the number of untagged fish and tagged fish in the September 1 sample are representative of the total population. What does the biologist calculate for the number of fish in the lake on May 1?

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

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 $k$.

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

At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for \$5. This week they are on sale at 5 boxes for \$4. The percent decrease in the price per box during the sale was closest to $\textbf{(A)}\ 30\% \qquad \textbf{(B)}\ 35\% \qquad \textbf{(C)}\ 40\% \qquad \textbf{(D)}\ 45\% \qquad \textbf{(E)}\ 65\%$

A jacket and a shirt originally sold for $ \$80$ and $ \$40$, respectively. During a sale Chris bought the $ \$80$ jacket at a $40\%$ discount and the $ \$40$ shirt at a $55\%$ discount. The total amount saved was what percent of the total of the original prices? $\text{(A)}\ 45\% \qquad \text{(B)}\ 47\dfrac{1}{2}\% \qquad \text{(C)}\ 50\% \qquad \text{(D)}\ 79\dfrac{1}{6}\% \qquad \text{(E)}\ 95\%$.

For the reaction: $2X + 3Y \rightarrow 3Z$, the combination of $2.00$ moles of $X$ with $2.00$ moles of $Y$ produces $1.75 $ moles of $Z$. What is the percent yield of this reaction? $\textbf{(A)}\hspace{.05in}43.8\%\qquad\textbf{(B)}\hspace{.05in}58.3\%\qquad\textbf{(C)}\hspace{.05in}66.7\%\qquad\textbf{(D)}\hspace{.05in}87.5\%\qquad $

At the 4 PM show, all the seats in the theater were taken, and 65 percent of the audience was children. At the 6 PM show, again, all the seats were taken, but this time only 50 percent of the audience was children. Of all the people who attended either of the shows, 57 percent were children although there were 12 adults and 28 children who attended both shows. How many people does the theater seat?

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 $

Successive discounts of $10\%$ and $20\%$ are equivalent to a single discount of: $\textbf{(A)}\ 30\% \qquad \textbf{(B)}\ 15\% \qquad \textbf{(C)}\ 72\% \qquad \textbf{(D)}\ 28\% \qquad \textbf{(E)}\ \text{None of these}$

Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by 20% on every pair of shoes. Carlos also knew that he had to pay a 7.5% sales tax on the discounted price. He had 43 dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy? A)$46$ B)$50$ C)$48$ D)$47$ E)$49$