# GRE Math : Whole and Part

## Example Questions

### Example Question #1 : Whole And Part

If 4/13 of z is 2/7 then what is 8/11 of z?

52/77

7/13

14/17

61/83

52/77

Explanation:

First solve for z by multiplying 2/7 by the reciprocal of 4/13.

Then multiply this number by 8/11 to find the solution.

In setting up the problem, notice how “of” means to multiply z by 4/13 and “is” means to set (4/13)z equal to 2/7.

### Example Question #2 : Whole And Part

The ratio of men to women in the room is 5 to 3. 3 men in the room are seniors, which represents 30% of the men. How many people are in the room?

6

10

12

18

16

16

Explanation:

If 3 senior men = 30% * All Men →

All Men = 3/30% = 10 Men.

The Ratio Men : Women = 5 : 3 = 10 : 6.

Thus there are 6 Women. 6 + 10 = 16.

Jessica bought a few pairs of socks for $50. If there had been a 20% discount, she could have bought 5 more pairs of socks for the same total price. How many pairs of socks did she buy? Possible Answers: 10 15 2 20 5 Correct answer: 20 Explanation: Say cost of each pair of socks = y and pairs of socks = x. Since [quantity x cost per item = total cost]: First, xy = 50. Secondly, (x + 5) [y (1 - 20%)] = 50 Simplify the second equation: 80%y(x + 5) = 50 or 0.8xy + 4y = 50 Insert xy =50 here. .8(50) + 4y = 50 40 + 4y = 50 or 4y = 10 Thus y = 10/4 = 5/2 Need to find x = pairs of socks. xy = 50 = x(5/2) So 5x = 100 or x = 20 ### Example Question #4 : Whole And Part An elevated train traveling its night route drops off exactly 2/3 of all passengers currently on board at each stop. Assuming no more passengers board the train tonight, if two passengers get off at the fifth stop, how many passengers were originally on the train when it started its route? Possible Answers: 300 27 2430 243 81 Correct answer: 243 Explanation: This problem requires you to work backwards from stop 5 to the passengers present at stop 1. If 2 person gets out at stop 5, that means there were 3 people on board at stop 5. This means there were 9 people present at stop 4 (9 total, 2/3 (6) got off, leaving the 3 for stop 5), 27 people present at stop 3 (27 total, 2/3 (18) got off, leaving 9 for stop 4), 81 people present at stop 2 and 243 passengers present at stop 1. That is, the number of passengers on board the train at any stop follows a logarithmic reduction along powers of three, from 35 at stop 1 to 31 at stop 5. ### Example Question #1 : Whole And Part If you travel meters per minute for hours, how far do you travel in meters? Possible Answers: Correct answer: Explanation: We need to convert 5 hours into minutes. There are 60 minutes in an hour, so 5 hours = 5 * 60 minutes = 300 minutes. Therefore, you go 20 meters/minute for 300 minutes, or 20 * 300 = 6000 meters. ### Example Question #6 : Whole And Part For every two pounds of fudge are bought at the regular price of$4.25 per pound, the store gives a free pound of fudge to the customer.  Lauren’s fudge bill was \$21.25.  How many pounds of fudge did she leave the store with?

7

9

8

6

5

7

Explanation:

21.21/ 4.25 = 5 pounds paid for.  Since a pound is given for every 2 pounds sold, that is 5/2 = 2.5 so an extra 2 pounds is given to Lauren, totaling 7 pounds.

### Example Question #1 : Whole And Part

Bob and Nancy, while working together at the same rate, can clean their entire house in 3 hours. What fraction of the house can Bob clean in 45 minutes?

Explanation:

Since Bob and Nancy work at the same rate, each person can finish  of the job in 3 hours. Because 45 minutes is  of 3 hours, Bob working alone would get  of the job done, .

### Example Question #1 : Whole And Part

What is  of ?

Explanation:

To find the part from the whole, just take the percentage and turn it into an algebra problem.

In decimal form, 20% is .2.  To turn it into an equation, recognize that "is" means equal to and "of" means multiply.

Therefore, "17% of 325" becomes (.17)(325) = X.

A way of solving this without a calculator:

10% of 325 is easy to find: 32.5.

20% will be twice as much as 10%, so 65.

1% is easy to find: 3.25.

3% is three times 1%: 9.75.

20% – 3% = 17%

65 – 9.75 = 55.25

### Example Question #9 : Whole And Part

A given colony of ants was made up of  insects.  % of these were workers and % were drones.  If the remainder were warrirors, how many warriors were there?

Explanation:

To begin with, you know that there are , or % that are warriors.  This means that of  are warriors.  Remember, translate of as multiplication and "are" / "is" as equals.  This gives you:

warriors.

### Example Question #10 : Whole And Part

If % of students in a school have brown eyes and the rest have green, how many green-eyed students are there in a school of  students?