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27 June, 04:08

An auto insurance company has 10,000 policyholders. Each policy is defined as: young or old male or female; and 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 married males. How many of the company's policyholders are young, female, and single?

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  1. 27 June, 06:14
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    880

    Step-by-step explanation:

    This problem a bit annoying, but let's classify the numbers and see where we can get from there:

    Total = 10,000

    Young = 3,000

    Old = 7,000 (not young defined as 10,000 - 3,000)

    Male = 4,600

    Female = 5,400

    Married = 7,000

    Single = 3,000

    Young Males = 1,320

    Young Females = 3,000 (young) - 1,320 = 1,680

    Married Males = 3,010

    Married Females = 7,000 - 3,010 = 2,990

    Young Married = 1,400

    Young Married Males = 600

    Young Married Females = 1,400 - 600 = 800

    Young Female Single = ?

    Young Female = 1,680 from above. But not all of them are single.

    Young Married Females = 800 from above

    Young Female Single = Young Female - Young Married Females = 1,680 - 800 = 880
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