How to use a Venn Diagram - ISEE Upper Level: Quantitative Reasoning

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Question

Venn

Let the universal set be the set of all positive integers. Define:

Examine the above Venn diagram. If each integer was to be placed in its correct region, which of the following would be placed in the gray area?

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Answer

The grayed portion of the Venn diagram corresponds to those integers which are not in any of , , or . Therefore, we eliminate any choices that are in any of the three sets.

is the set of integers which end in 1 or 6; we can eliminate 166 and 176 immediately.

is the set of perfect square integers; we can eliminate 144, since .

is the set of integers which, when divided by 4, yields remainder 2. Since , we can eliminate 154.

All four choices have been eliminated.

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