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 $

In terms of $n\ge2$, find the largest constant $c$ such that for all nonnegative $a_1,a_2,\ldots,a_n$ satisfying $a_1+a_2+\cdots+a_n=n$, the following inequality holds: \[\frac1{n+ca_1^2}+\frac1{n+ca_2^2}+\cdots+\frac1{n+ca_n^2}\le \frac{n}{n+c}.\] [i]Calvin Deng.[/i]

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.

Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket? $\text{(A)}\ 4\% \qquad \text{(B)}\ 25\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 41\% \qquad \text{(E)}\ 59\%$

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$

A mixture of 30 liters of paint is $25\%$ red tint, $30\%$ yellow tint, and $45\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint that is the mixture? $\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 35 \qquad \textbf{(C)}\ 40\qquad \textbf{(D)}\ 45 \qquad \textbf{(E)}\ 50$

The yearly changes in the population census of a town for four consecutive years are, respectively, $25\%$ increase, $25\%$ increase, $25\%$ decrease, $25\%$ decrease. The net change over the four years, to the nearest percent, is: ${{ \textbf{(A)}\ -12 \qquad\textbf{(B)}\ -1 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 1}\qquad\textbf{(E)}\ 12} $

Suppose that the euro is worth $1.30$ dollars. If Diana has $500$ dollars and Etienne has $400$ euros, by what percent is the value of Etienne's money greater than the value of Diana's money? ${{ \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6.5\qquad\textbf{(D)}\ 8}\qquad\textbf{(E)}\ 13} $

A train car held $6000$ pounds of mud which was $88$ percent water. Then the train car sat in the sun, and some of the water evaporated so that now the mud is only $82$ percent water. How many pounds does the mud weigh now?

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 $\textbf{(A)}\ 30\% \qquad \textbf{(B)}\ 35\% \qquad \textbf{(C)}\ 40\% \qquad \textbf{(D)}\ 45\% \qquad \textbf{(E)}\ 65\%$

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

In a high school with $500$ students, $40\%$ of the seniors play a musical instrument, while $30\%$ of the non-seniors do not play a musical instrument. In all, $46.8\%$ of the students do not play a musical instrument. How many non-seniors play a musical instrument? $\textbf{(A) } 66 \qquad\textbf{(B) } 154 \qquad\textbf{(C) } 186 \qquad\textbf{(D) } 220 \qquad\textbf{(E) } 266$

The percent that $ M$ is greater than $ N$ is: $ \textbf{(A)}\ \frac {100(M \minus{} N)}{M} \qquad\textbf{(B)}\ \frac {100(M \minus{} N)}{N} \qquad\textbf{(C)}\ \frac {M \minus{} N}{N} \qquad\textbf{(D)}\ \frac {M \minus{} N}{M}$ $ \textbf{(E)}\ \frac {100(M \plus{} N)}{N}$

If $10\%$ of $\left(x+10\right)$ is $\left(x-10\right)$, what is $10\%$ of $x$? $\text{(A) }\frac{11}{90}\qquad\text{(B) }\frac{9}{11}\qquad\text{(C) }1\qquad\text{(D) }\frac{11}{9}\qquad\text{(E) }\frac{110}{9}$

After Jennifer walked $r$ percent of the way from her home to the store, she turned around and walked home, got on her bicycle, and bicycled to the store and back home. Jennifer bicycles two and a half times faster than she walks. Find the largest value of $r$ so that returning home for her bicycle was not slower than her walking all the way to and from the store without her bicycle.

Northside's Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. According to the double bar graph, in what month did one group's sales exceed the other's by the greatest percent? [asy] unitsize(12); fill((2,0)--(2,9)--(3,9)--(3,0)--cycle,lightgray); draw((3,0)--(3,9)--(2,9)--(2,0)); draw((2,7)--(1,7)--(1,0)); draw((2,8)--(3,8)); draw((2,7)--(3,7)); for (int a = 1; a <= 6; ++a) { draw((1,a)--(3,a)); } fill((5,0)--(5,3)--(6,3)--(6,0)--cycle,lightgray); draw((6,0)--(6,3)--(5,3)--(5,0)); draw((5,3)--(5,5)--(4,5)--(4,0)); draw((4,4)--(5,4)); draw((4,3)--(5,3)); draw((4,2)--(6,2)); draw((4,1)--(6,1)); fill((8,0)--(8,6)--(9,6)--(9,0)--cycle,lightgray); draw((9,0)--(9,6)--(8,6)--(8,0)); draw((8,6)--(8,9)--(7,9)--(7,0)); draw((7,8)--(8,8)); draw((7,7)--(8,7)); draw((7,6)--(8,6)); for (int a = 1; a <= 5; ++a) { draw((7,a)--(9,a)); } fill((11,0)--(11,12)--(12,12)--(12,0)--cycle,lightgray); draw((12,0)--(12,12)--(11,12)--(11,0)); draw((11,9)--(10,9)--(10,0)); draw((11,11)--(12,11)); draw((11,10)--(12,10)); draw((11,9)--(12,9)); for (int a = 1; a <= 8; ++a) { draw((10,a)--(12,a)); } fill((14,0)--(14,10)--(15,10)--(15,0)--cycle,lightgray); draw((15,0)--(15,10)--(14,10)--(14,0)); draw((14,8)--(13,8)--(13,0)); draw((14,9)--(15,9)); draw((14,8)--(15,8)); for (int a = 1; a <= 7; ++a) { draw((13,a)--(15,a)); } draw((16,0)--(0,0)--(0,13),black); label("Jan",(2,0),S); label("Feb",(5,0),S); label("Mar",(8,0),S); label("Apr",(11,0),S); label("May",(14,0),S); label("$\textbf{MONTHLY SALES}$",(8,14),N); label("S",(0,8),W); label("A",(0,7),W); label("L",(0,6),W); label("E",(0,5),W); label("S",(0,4),W); draw((4,12.5)--(4,13.5)--(5,13.5)--(5,12.5)--cycle); label("Drums",(4,13),W); fill((15,12.5)--(15,13.5)--(16,13.5)--(16,12.5)--cycle,lightgray); draw((15,12.5)--(15,13.5)--(16,13.5)--(16,12.5)--cycle); label("Bugles",(15,13),W);[/asy] $\text{(A)}\ \text{Jan} \qquad \text{(B)}\ \text{Feb} \qquad \text{(C)}\ \text{Mar} \qquad \text{(D)}\ \text{Apr} \qquad \text{(E)}\ \text{May}$

A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations? $ \textbf{(A)}\ 15\qquad\textbf{(B)}\ 30\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 60\qquad\textbf{(E)}\ 70 $

Mary mixes $2$ gallons of a solution that is $40$ percent alcohol with $3$ gallons of a solution that is $60$ percent alcohol. Sandra mixes $4$ gallons of a solution that is $30$ percent alcohol with $\frac{m}{n}$ gallons of a solution that is $80$ percent alcohol, where $m$ and $n$ are relatively prime positive integers. Mary and Sandra end up with solutions that are the same percent alcohol. Find $m + n$.

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 $150$ 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?

Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Approximately what percent of the design is black? [asy] real d=320; pair O=origin; pair P=O+8*dir(d); pair A0 = origin; pair A1 = O+1*dir(d); pair A2 = O+2*dir(d); pair A3 = O+3*dir(d); pair A4 = O+4*dir(d); pair A5 = O+5*dir(d); filldraw(Circle(A0, 6), white, black); filldraw(circle(A1, 5), black, black); filldraw(circle(A2, 4), white, black); filldraw(circle(A3, 3), black, black); filldraw(circle(A4, 2), white, black); filldraw(circle(A5, 1), black, black); [/asy] $ \textbf{(A)}\ 42\qquad \textbf{(B)}\ 44\qquad \textbf{(C)}\ 45\qquad \textbf{(D)}\ 46\qquad \textbf{(E)}\ 48\qquad$

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 vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss company have worked there for $5$ years or more? [asy] for(int a=1; a<11; ++a) { draw((a,0)--(a,-.5)); } draw((0,10.5)--(0,0)--(10.5,0)); label("$1$",(1,-.5),S); label("$2$",(2,-.5),S); label("$3$",(3,-.5),S); label("$4$",(4,-.5),S); label("$5$",(5,-.5),S); label("$6$",(6,-.5),S); label("$7$",(7,-.5),S); label("$8$",(8,-.5),S); label("$9$",(9,-.5),S); label("$10$",(10,-.5),S); label("Number of years with company",(5.5,-2),S); label("X",(1,0),N); label("X",(1,1),N); label("X",(1,2),N); label("X",(1,3),N); label("X",(1,4),N); label("X",(2,0),N); label("X",(2,1),N); label("X",(2,2),N); label("X",(2,3),N); label("X",(2,4),N); label("X",(3,0),N); label("X",(3,1),N); label("X",(3,2),N); label("X",(3,3),N); label("X",(3,4),N); label("X",(3,5),N); label("X",(3,6),N); label("X",(3,7),N); label("X",(4,0),N); label("X",(4,1),N); label("X",(4,2),N); label("X",(5,0),N); label("X",(5,1),N); label("X",(6,0),N); label("X",(6,1),N); label("X",(7,0),N); label("X",(7,1),N); label("X",(8,0),N); label("X",(9,0),N); label("X",(10,0),N); label("Gauss Company",(5.5,10),N); [/asy] $\text{(A)}\ 9\% \qquad \text{(B)}\ 23\frac{1}{3}\% \qquad \text{(C)}\ 30\% \qquad \text{(D)}\ 42\frac{6}{7}\% \qquad \text{(E)}\ 50\% $

While Peter was driving from home to work, he noticed that after driving 21 miles, the distance he had left to drive was 30 percent of the total distance from home to work. How many miles was his complete trip home to work?

Jerry purchased some stock for $ \$14,400$ at the same time that Susan purchased a bond for $ \$6,250$. Jerry’s investment went up $20$ percent the first year, fell $10$ percent the second year, and rose another $20$ percent the third year. Susan’s investment grew at a constant rate of compound interest for three years. If both investments are worth the same after three years, what was the annual percentage increase of Susan’s investment?

A solid box is $ 15$ cm by $ 10$ cm by $ 8$ cm. A new solid is formed by removing a cube $ 3$ cm on a side from each corner of this box. What percent of the original volume is removed? $ \textbf{(A)}\ 4.5 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 12 \qquad \textbf{(D)}\ 18 \qquad \textbf{(E)}\ 24$