McGraw-Hill Education GRE 2019

SOLUTION: Since the numerators of the fractions are the same, the fraction

with the smaller denominator will be greater. 100 < 100^2. Thus Quantity A

is greater.

x > 0

QUANTITY A QUANTITY B

x

1 +^1 x^

x

1 +^2 x^ A^ B^ C^ D

SOLUTION: The fractions in the two quantities have the same numerator.

Thus the fraction with the smaller denominator will be greater. Since

the numerator in (^1 x) is smaller than the numerator in (^2 x), (^1 x) is a smaller

fraction, which means the denominator in Quantity A is smaller. Since the

denominator in Quantity A is smaller, the value of the fraction in Quantity A

is greater. The correct answer is A.

What if the fractions are negative? The opposite relationships apply:

As the denominator of a negative fraction increases, the value of the fraction

increases.

As the numerator of a negative fraction increases, the value of the fraction decreases.

To understand why this is the case, compare –(^35 ) and –(^25 ). You know that^35 is a

larger piece of a pie than is^25. But since^35 >^25 , the negative version of^35 will be more

negative than the negative version of^25. If –(^35 ) is more negative than –(^25 ), then –(^35 )

must be smaller. See the number line below for illustration:

<>

–2

5

–3

5

2

5

3

(^05)
–2
5
–3
5
3
5
2
5
Improper Fractions
Any fraction in which the numerator is larger than the denominator is an
improper fraction. Look at the fraction^74. In this case, the denominator is 4, which
means the pie you are working with is cut up into 4 slices. The numerator tells you
that you have 7 slices of this pie. If you have 7 slices of a 4-slice pie, then you have
more than one pie. In fact, you have one 4-slice pie (^44 ) and 3 additional slices of
that pie (^34 ).
4
4 +
3
4 =
7
4
CHAPTER 10 ■ PART-TO-WHOLE RELATIONSHIPS 211
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