During the past month, a disease control center tested X

During the past month, a disease control center tested X individuals for two viruses. If 1/3 of those tested had virus C and, of those with virus C, 1/5 also had virus D, how many individuals did not have both virus C and D?

A. X/4
B. 4X/15
C. 10X/5
D. 14X/15
E. 4 / 5

The number of individuals that had virus C is 1/3 of X, or X/3.

The number of individuals that also had virus D is 1/5 of the number that had virus C.

Thus (1/5)C= (1/5)(X/3) = X/15.

If X/15 of the X individuals have virus C and D, then X - (X/15) did not have both virus C and D.

Neither C or D: X - (X/15) = 14X/15.

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