# 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?

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 : Venn Diagrams

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?

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.