McGraw-Hill Education GRE 2019

QUANTITY A QUANTITY B

78 89 A B C D

SOLUTION: Express both fractions with a denominator of 72. Quantity A:

7

8 =

7 × 9

8 × 9 =

63

72. Quantity B:

8

9 =

8 × 8

9 × 8 =

64

72. Now the comparison is

63

72 to

64

72.

The fractions have the same denominator, but the numerator of the second

fraction is greater. Thus Quantity B is greater.

Multiplying Fractions

The product of two positive fractions will always be smaller than either of the

factors, for example,^25 × 14 = 202 = 101.

Why is this the case? When you multiply fractions, you are essentially taking a

piece of a piece. In other words, multiplying^14 by^25 means that you are looking for

2

5 of

1

4. Or it can mean that you are taking

1

4 of

2

5. In either case, the result is a piece

of both original fractions, meaning that the result will be smaller than either

fraction. Look at the following Quantitative Comparison question.

1 > x > y > 0

QUANTITY A QUANTITY B

xy (^1) x ×^1 y A B C D
SOLUTION: Since x and y are between 0 and 1, their product must be a fraction.
Thus the value in Quantity A must be a fraction. Since x and y are between
zero and 1, their respective reciprocals must be greater than 1. Thus the
factors of the product in Quantity B are each greater than 1. Since both
factors are greater than 1, the product must be greater than 1. Thus Quantity
B is greater.
Generally, when multiplying fractions, you should multiply all the numerators and
all the denominators. For example:
3
7 ×^
5
4 =
3 × 5
7 × 4 =
15
28
However, sometimes you will be able to reduce the fractions before multiplying:
(^25 )(^156 ) =?
SOLUTION: Before multiplying, cancel out the common factors:
2
5
15
×= 6
2
5
3 × 5
×13 × 2 =
The answer is 1.
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