# ISEE Middle Level Quantitative : How to use a Venn Diagram

## Example Questions

### Example Question #1 : How To Use A Venn Diagram

Define:

Universal set  , the set of all natural numbers.

= { |  is a multiple of 3}

= { |  is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

Possible Answers:

Correct answer:

Explanation:

The gray region is the region outside both  and  and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3:  and

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as . Therefore, it is the correct choice.

### Example Question #2 : How To Use A Venn Diagram

Define:

Universal set  , the set of all natural numbers.

= { |  is a multiple of 3}

= { |  is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

Possible Answers:

Correct answer:

Explanation:

The gray region is the region outside both  and  and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3:  and

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as . Therefore, it is the correct choice.

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