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CAT 2007 — QA Question 21

Number TheoryEasy

How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?

Answer & solution

Correct answer: 3

  • A

    6

  • B

    4

  • C

    7

  • D

    5

  • 3

Solution

1/m + 4/n = 1/12

∴ 1/m = 1/12 – 4/n

∴ m = 12n/(n – 48)

As, m is a positive integer, n should be greater than 48 and moreover since n is a positive odd integer lesser than 60, n can take values 49, 51, 53, 55, 57 and 59.

If n = 49, 51, 57 then m is a positive integer.

If n = 53, 55, 59 then m is not an integer.

∴ 3 pairs of values of m and n satisfy the given equation.

Hence, option (e).

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CAT 2007 QA Q21: How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60? — Solution | TheCATExam