Practice GMAT Problem Solving Question

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During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A)	N/15
B)	4N/15
C)	N/5
D)	14N/15
E)	4N/5

Correct Answer: D

The number of individuals that had infection A is 1/3 of N, or N/3.
Infection A: N/3
The number of individuals that also had infection B is 1/5 of the number that had infection A. In other words, it is (1/5)A = (1/5)(N/3) = N/15.
Infection B: (1/5)A = (1/5)(N/3) = N/15
If N/15 of the N individuals have infection A and B, then N – (N/15) did not have both infection A and B. Consequently, 14N/15 individuals did not have both infection A and infection B.
Neither A or B: N - (N/15) = 14N/15

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