Venn Diagrams

Categories : Venn Diagrams, Sets

On your GMAT, you will encounter 1-3 questions that contain overlapping groups with specific characteristics. You will almost never see more than two characteristics (since you can’t draw 3D on your scratch paper). For illustration, let’s take a look at the following Data Sufficiency example:

Q) Of the 70 children who visited a certain doctor last week, how many had neither a cold nor a cough?

(1) 40 of the 70 children had a cold but not a cough.
(2) 20 of the 70 children had both a cold and a cough.

There are two characteristics (cough and cold) and two categories for each (yes and no), so there are four total categories, as indicated by this matrix:
Four Total Categories
I’ve filled in the given information from both statements, and the parenthetical information is inferred. This clearly lays out the 4 combinations of options. If we sum vertically, we can infer that there are 60 total children with colds. Because there are 70 total children, this also means that 10 do NOT have colds. The bottom-right quadrant cannot be found because we do not know how those 10 children get divided between the two empty boxes. Choice E – together the statements are insufficient...

Categories : Venn Diagrams

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.

The correct answer is D.

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