Question

An auto insurance company has 10,000 policyholders. Each policyholder is classified as (i) young or old, (ii) male or female, and (iii) married or single. Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young single males. How many of the company’s policyholders are young, female, and married?

Answer 1

There are 680 young married females.

Explanation:

The company has 10,000 policyholders.

Of which,

According to age:

3,000 are young

10,000 - 3,000 = 7,000 are old

According to gender:

4,600 are male

10,000 - 4,600 = 5,400 are female

According to relationship

7,000 are married

10,000 - 7,000 = 3,000 are single

The problem states that there are 1,320 young males.

There 3,000 young people, of which 1,320 are males. So 3,000 - 1,320 = 1,680 are young females.

There are 3,010 married males. This are 7,000 policyholders married. So there are 7,000 - 3,010 = 3,990 married females.

There are 1,400 young married persons.

600 of the policyholders are young single males. There are 1,320 young males. So there are 1,320 - 600 = 720 young married males.

There 1,400 young married persons, of which 720 are males. So there are 1,400 - 720 = 680 young married females. This is the final answer.