A jar was filled with jelly beans so that $54\%$ of the beans were red, $30\%$ of the beans were green, and $16\%$ of the beans were blue. Alan then removed the same number of red jelly beans and green jelly beans from the jar so that now $20\%$ of the jelly beans in the jar are blue. What percent of the jelly beans in the jar are now red?

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 farmer bought $749$ sheeps. He sold $700$ of them for the price paid for the $749$ sheep. The remaining $49$ sheep were sold at the same price per head as the other $700$. Based on the cost, the percent gain on the entire transaction is: ${{ \textbf{(A)}\ 6.5 \qquad\textbf{(B)}\ 6.75 \qquad\textbf{(C)}\ 7 \qquad\textbf{(D)}\ 7.5 }\qquad\textbf{(E)}\ 8 } $

In $1991$ the population of a town was a perfect square. Ten years later, after an increase of $150$ people, the population was $9$ more than a perfect square. Now, in $2011$, with an increase of another $150$ people, the population is once again a perfect square. Which of the following is closest to the percent growth of the town's population during this twenty-year period? $ \textbf{(A)}\ 42 \qquad\textbf{(B)}\ 47 \qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 57\qquad\textbf{(E)}\ 62 $

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 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.

Basketball star Shanille O'Keal's team statistician keeps track of the number, $S(N),$ of successful free throws she has made in her first $N$ attempts of the season. Early in the season, $S(N)$ was less than 80% of $N,$ but by the end of the season, $S(N)$ was more than 80% of $N.$ Was there necessarily a moment in between when $S(N)$ was exactly 80% of $N$?

An urn is filled with coins and beads, all of which are either silver or gold. Twenty percent of the objects in the urn are beads. Forty percent of the coins in the urn are silver. What percent of the objects in the urn are gold coins? $ \textbf{(A)}\ 40\%\qquad\textbf{(B)}\ 48\%\qquad\textbf{(C)}\ 52\%\qquad\textbf{(D)}\ 60\%\qquad\textbf{(E)}\ 80\% $

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 grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman's class were: \[ \begin{tabular}[t]{lllllllll}89, & 72, & 54, & 97, & 77, & 92, & 85, & 74, & 75,\\ 63, & 84, & 78, & 71, & 80, & 90. & & &\\ \end{tabular} \] In Mr. Freeman's class, what percent of the students received a grade of C? \[ \boxed{\begin{tabular}[t]{cc}A: & 93-100\\ B: & 85-92\\ C: & 75-84\\ D: & 70-74\\ F: & 0-69\end{tabular}} \] $ \text{(A)}\ 20\%\qquad\text{(B)}\ 25\%\qquad\text{(C)}\ 30\%\qquad\text{(D)}\ 33\frac{1}{3}\%\qquad\text{(E)}\ 40\% $

A customer who intends to purchase an appliance has three coupons, only one of which may be used: Coupon 1: $10\%$ off the listed price if the listed price is at least $\$50$ Coupon 2: $\$20$ off the listed price if the listed price is at least $\$100$ Coupon 3: $18\%$ off the amount by which the listed price exceeds $\$100$ For which of the following listed prices will coupon $1$ offer a greater price reduction than either coupon $2$ or coupon $3$? $\textbf{(A) }\$179.95\qquad \textbf{(B) }\$199.95\qquad \textbf{(C) }\$219.95\qquad \textbf{(D) }\$239.95\qquad \textbf{(E) }\$259.95\qquad$

The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price? [asy] import graph; size(12.5cm); real lsf=2; pathpen=linewidth(0.5); pointpen=black; pen fp = fontsize(10); pointfontpen=fp; real xmin=-1.33,xmax=11.05,ymin=-9.01,ymax=-0.44; pen ycycyc=rgb(0.55,0.55,0.55); pair A=(1,-6), B=(1,-2), D=(1,-5.8), E=(1,-5.6), F=(1,-5.4), G=(1,-5.2), H=(1,-5), J=(1,-4.8), K=(1,-4.6), L=(1,-4.4), M=(1,-4.2), N=(1,-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,-6), P_1=(14,-5), Q_1=(14,-4), R_1=(14,-3), S_1=(14,-2), C_1=(1.4,-6), D_1=(1.8,-6), G_1=(2.4,-6), H_1=(2.8,-6), I_1=(3.4,-6), J_1=(3.8,-6), K_1=(4.4,-6), L_1=(4.8,-6), M_1=(5.4,-6), N_1=(5.8,-6), T_1=(6.4,-6), U_1=(6.8,-6), V_1=(7.4,-6), W_1=(7.8,-6), Z_1=(8.4,-6), A_2=(8.8,-6), B_2=(9.4,-6), C_2=(9.8,-6), D_2=(10.4,-6), E_2=(10.8,-6), L_2=(2.4,-3.2), M_2=(2.8,-3.2), N_2=(3.4,-4), O_2=(3.8,-4), P_2=(4.4,-3.6), Q_2=(4.8,-3.6), R_2=(5.4,-3.6), S_2=(5.8,-3.6), T_2=(6.4,-3.4), U_2=(6.8,-3.4), V_2=(7.4,-3.8), W_2=(7.8,-3.8), Z_2=(8.4,-2.8), A_3=(8.8,-2.8), B_3=(9.4,-3.2), C_3=(9.8,-3.2), D_3=(10.4,-3.8), E_3=(10.8,-3.8); filldraw(C_1--E_1--F_1--D_1--cycle,ycycyc); filldraw(G_1--L_2--M_2--H_1--cycle,ycycyc); filldraw(I_1--N_2--O_2--J_1--cycle,ycycyc); filldraw(K_1--P_2--Q_2--L_1--cycle,ycycyc); filldraw(M_1--R_2--S_2--N_1--cycle,ycycyc); filldraw(T_1--T_2--U_2--U_1--cycle,ycycyc); filldraw(V_1--V_2--W_2--W_1--cycle,ycycyc); filldraw(Z_1--Z_2--A_3--A_2--cycle,ycycyc); filldraw(B_2--B_3--C_3--C_2--cycle,ycycyc); filldraw(D_2--D_3--E_3--E_2--cycle,ycycyc); D(B--A,linewidth(0.4)); D(H--(8,-5),linewidth(0.4)); D(N--(8,-4),linewidth(0.4)); D(T--(8,-3),linewidth(0.4)); D(B--(8,-2),linewidth(0.4)); D(B--S_1); D(T--R_1); D(N--Q_1); D(H--P_1); D(A--O_1); D(C_1--E_1); D(E_1--F_1); D(F_1--D_1); D(D_1--C_1); D(G_1--L_2); D(L_2--M_2); D(M_2--H_1); D(H_1--G_1); D(I_1--N_2); D(N_2--O_2); D(O_2--J_1); D(J_1--I_1); D(K_1--P_2); D(P_2--Q_2); D(Q_2--L_1); D(L_1--K_1); D(M_1--R_2); D(R_2--S_2); D(S_2--N_1); D(N_1--M_1); D(T_1--T_2); D(T_2--U_2); D(U_2--U_1); D(U_1--T_1); D(V_1--V_2); D(V_2--W_2); D(W_2--W_1); D(W_1--V_1); D(Z_1--Z_2); D(Z_2--A_3); D(A_3--A_2); D(A_2--Z_1); D(B_2--B_3); D(B_3--C_3); D(C_3--C_2); D(C_2--B_2); D(D_2--D_3); D(D_3--E_3); D(E_3--E_2); D(E_2--D_2); label("0",(0.52,-5.77),SE*lsf,fp); label("\$ 5",(0.3,-4.84),SE*lsf,fp); label("\$ 10",(0.2,-3.84),SE*lsf,fp); label("\$ 15",(0.2,-2.85),SE*lsf,fp); label("\$ 20",(0.2,-1.85),SE*lsf,fp); label("$\mathrm{Price}$",(-.65,-3.84),SE*lsf,fp); label("$1$",(1.45,-5.95),SE*lsf,fp); label("$2$",(2.44,-5.95),SE*lsf,fp); label("$3$",(3.44,-5.95),SE*lsf,fp); label("$4$",(4.46,-5.95),SE*lsf,fp); label("$5$",(5.43,-5.95),SE*lsf,fp); label("$6$",(6.42,-5.95),SE*lsf,fp); label("$7$",(7.44,-5.95),SE*lsf,fp); label("$8$",(8.43,-5.95),SE*lsf,fp); label("$9$",(9.44,-5.95),SE*lsf,fp); label("$10$",(10.37,-5.95),SE*lsf,fp); label("Month",(5.67,-6.43),SE*lsf,fp); D(A,linewidth(1pt)); D(B,linewidth(1pt)); D(D,linewidth(1pt)); D(E,linewidth(1pt)); D(F,linewidth(1pt)); D(G,linewidth(1pt)); D(H,linewidth(1pt)); D(J,linewidth(1pt)); D(K,linewidth(1pt)); D(L,linewidth(1pt)); D(M,linewidth(1pt)); D(N,linewidth(1pt)); D(P,linewidth(1pt)); D(Q,linewidth(1pt)); D(R,linewidth(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth(1pt)); D(F_1,linewidth(1pt)); D(O_1,linewidth(1pt)); D(P_1,linewidth(1pt)); D(Q_1,linewidth(1pt)); D(R_1,linewidth(1pt)); D(S_1,linewidth(1pt)); D(C_1,linewidth(1pt)); D(D_1,linewidth(1pt)); D(G_1,linewidth(1pt)); D(H_1,linewidth(1pt)); D(I_1,linewidth(1pt)); D(J_1,linewidth(1pt)); D(K_1,linewidth(1pt)); D(L_1,linewidth(1pt)); D(M_1,linewidth(1pt)); D(N_1,linewidth(1pt)); D(T_1,linewidth(1pt)); D(U_1,linewidth(1pt)); D(V_1,linewidth(1pt)); D(W_1,linewidth(1pt)); D(Z_1,linewidth(1pt)); D(A_2,linewidth(1pt)); D(B_2,linewidth(1pt)); D(C_2,linewidth(1pt)); D(D_2,linewidth(1pt)); D(E_2,linewidth(1pt)); D(L_2,linewidth(1pt)); D(M_2,linewidth(1pt)); D(N_2,linewidth(1pt)); D(O_2,linewidth(1pt)); D(P_2,linewidth(1pt)); D(Q_2,linewidth(1pt)); D(R_2,linewidth(1pt)); D(S_2,linewidth(1pt)); D(T_2,linewidth(1pt)); D(U_2,linewidth(1pt)); D(V_2,linewidth(1pt)); D(W_2,linewidth(1pt)); D(Z_2,linewidth(1pt)); D(A_3,linewidth(1pt)); D(B_3,linewidth(1pt)); D(C_3,linewidth(1pt)); D(D_3,linewidth(1pt)); D(E_3,linewidth(1pt)); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);[/asy] $\textbf{(A)}\ 50 \qquad \textbf{(B)}\ 62 \qquad \textbf{(C)}\ 70 \qquad \textbf{(D)}\ 89 \qquad \textbf{(E)}\ 100$

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$

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 $m + n$.

A walnut-salesman knows that 20% of the nuts are empty. He has found a test for picking these out. This discards 20% of the nuts. However, when cracking the nuts that were discarded, one fourth of them were not empty after all. What proportion of the nuts that passed the test are then empty? A. 4% B. 6 and 1/4 % C. 8% D. 16% E. None of these

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? $\textbf{(A)}\ 125\% \qquad \textbf{(B)}\ 100\% \qquad \textbf{(C)}\ 120\% \qquad \textbf{(D)}\ 80\% \qquad \textbf{(E)}\ 75\%$

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? $\textbf{(A)}\ 30 \%\qquad\textbf{(B)}\ 40 \%\qquad\textbf{(C)}\ 50 \%\qquad\textbf{(D)}\ 60 \%\qquad\textbf{(E)}\ 70 \%$

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