KPMG Past Questions And Answers


36)

At Essex high school 100 students are taking chemistry and 80 students are taking biology. If 20 students are taking both chemistry and biology, what is the ratio of the number of students taking only chemistry to the number taking only biology?
37)

Aaron has 3 times as money as Josh. If Aaron gives Josh $50, Josh will then have 3 times as money as Aaron. How much money do the two of them have together?
 

Solution
                                 Josh        Aaron
At the beginning      x              3x
After the gift            x + 50     3x – 50
After the gift, Josh will have 3 times as much money as Aaron: x + 5 = 3(3x – 50)
⇒x + 50 = 9x – 150 ⇒8x = 200⇒ x = 25. Therefore, Josh has $25 and Aaron has
$75 for a total of $100. (B).
38)

On a certain project the only grades awarded were 75 and 100. If 85 students
completed the project and the average of their grades was 85, how many earned
100?
 

Solution
Let x = number of student earning 100; then 85 – x = number of students earning
75. Then: 85 =100x +75(85 - x)/ 85 = 100x + 6375 -75x= 25x + 6375/85 ⇒ 7225 = 25x – 6375 ⇒850
= 25x – 6375 ⇒850 = 25x⇒ x = 34. (A).
39)

As a fund-raiser, the Key Club was selling two types of candy: lollipop at 40 cents each and chocolate bars at 75 cents each. On Monday, the member sold 150 candies and raised 74 dollars. How many lollipops did they sell?
 

Solution
Let x = number of chocolate bars sold; then 150 – x = number of lollipops sold. You must use the same units, so you can write 75 cents as 0.75 dollar or 74 dollars as 7400 cents. Avoid the decimals: x chocolates sold for 40(150 – x) cents.
Therefore: 7400 = 75x + 40(150 – x) = 75x + 6000 – 40x = 6000 + 35x ⇒1400 = 35x ⇒x = 40, and 150 – 40 = 110. (D).
40)

In the afternoon, Judy read 100 pages at the rate of 60 pages per hour; in the
evening, when she was tired, she read another 100 pages at the rate of 40 pages
per hour. In pages per hour, what was her average rate of reading for the day?
 

Solution
Judy’s average rate of reading is determined by dividing the total number of pages she read (200) by the total amount of time she spent reading. In the afternoon she read for100/60 = 5/3hours, and in the evening for 100/40= 5/2hours, for the total time of 5/3 + 5/2 = 10/6+ 15/6 = 25/6 hours. Her average rate was 200 ÷  25/6= 200 × 6/25= 48 pages per hour. (B).

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