Practice GMAT Problem Solving Question

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In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 4 to 6 at bats in a recent game and had anywhere from 2 to 3 hits in the same game, the player’s actual batting average for that game could fall anywhere between

A)	0.25 and 1.00
B)	0.25 and 0.75
C)	0.33 and 0.75
D)	0.33 and 0.50
E)	0.50 and 0.66

Correct Answer: C

The ratio of a batting average is a fraction. As you decrease the numerator or increase the denominator, the fraction becomes smaller. Likewise, as you increase the numerator or decrease the denominator, the fraction becomes larger.
In the case of a batting average, the numerator is "hits" (H) while the denominator is "at bats" (B). Thus, the ratio we are looking at is:
H/B, where 2<H<3 and 4<B<6.
To find the lowest value that the batting average could be, we want to assume the lowest numerator (hits of 2) and the highest denominator (at bats of 6): 2/6 = 0.333.
Likewise, to find the highest value that the batting average could be, we want to assume the highest numerator (hits of 3) and the lowest denominator (at bats of 4): 3/4 = 0.75.
Combining these answers yields the correct answer C: between 0.33 and 0.75.

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