Percentage change

Practice Questions

1. If $x$ is $200\%$ greater than $y$, and $y$ is $300\%$ of $z$, $x$ is what $\%$ greater than $z$?
   1. $\quad 400\%$
   2. $\quad 500\%$
   3. $\quad 600\%$
   4. $\quad 800\%$
   5. $\quad 900\%$

   Choice D
    
2. The population of County X was $3$ million people in year $2000$. If the population of County X were to increase by $5\%$ per year then which of the following functions gives the population, $p$, in millions, after $t$ years of gain at this rate?
   1. $\quad p(t) = 3 + 0.05t$
   2. $\quad p(t) = 3(0.05)^t$
   3. $\quad p(t)=3(0.95)^t$
   4. $\quad p(t)=3(1.05)^t$
   5. $\quad p(t)=3(1.05t)$

   Choice D
    
3. What was the percent change in the average(arithmetic mean) profit per car sold by car dealer X from $1999$ to $2009$?
   
   1. (1) The total profit from car sales at dealer X increased by $70\%$ from $1999$ to $2009$.
   2. (2) The number of cars sold at dealer X increased from $1253$ in $1999$ to $1687$ in $2009$.

   1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
   3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   4. EACH statement ALONE is sufficient.
   5. Statements (1) and (2) TOGETHER are NOT sufficient.
   Choice C
    
4. The price of a certain stock increased by $x$ percent in the first half of year $2010$, and then dropped by $y$ percent of this new price during the second half of $2010$. What is the net percent change in the price of the stock from the beginning of the year $2010$ to the end of the year?
   1. $\quad x – y$
   2. $\quad x-y-0.1xy$
   3. $\quad x-y+0.1xy$
   4. $\quad x-y-0.01xy$
   5. $\quad x-y+0.01xy$

   Choice D
    
5. The original price of a jacket was $\$80$. This price was discounted $x$ percent during a sale. Mary used a coupon to buy the jacket for $y$ percent off the sale price. How much did Mary pay for the jacket?
   
   1. (1) $x + y – \dfrac{xy}{100} = 32$
   2. (2) $x+y=35$

   1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
   3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   4. EACH statement ALONE is sufficient.
   5. Statements (1) and (2) TOGETHER are NOT sufficient.
   Choice A
    
6. The price of a share of a certain company went up by $x\%$ on Monday and on the following day it went down by $y\%$ of its opening share price on Tuesday. Is the share price at the end of the day on Tuesday higher than the opening price on Monday?
   
   1. (1) $x>y$
   2. (2) $x-y>\dfrac{xy}{100}$

   1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
   3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   4. EACH statement ALONE is sufficient.
   5. Statements (1) and (2) TOGETHER are NOT sufficient.
   Choice B
    
7. What was the percent increase in the earnings per share of Company X from year $2000$ to $2010$ ?
   
   1. (1) The total earnings of Company X increased by $70\%$ from $2000$ to $2010$.
   2. (2) The total number of shares of Company X increased by $30\%$ from $2000$ to $2010$.

   1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
   2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
   3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   4. EACH statement ALONE is sufficient.
   5. Statements (1) and (2) TOGETHER are NOT sufficient.
   Choice C
    
8. The workforce of Company $\textit{X}$ is $60\%$ female. The company hired $20$ additional male workers, and as a result, the percent of female workers dropped to $55\%$. How many employees did the company have after hiring the additional male workers?
   1. $\quad 160$
   2. $\quad 220$
   3. $\quad 240$
   4. $\quad 360$
   5. $\quad 420$

   Choice C