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CAT 1991 — QA Question 22

Number TheoryEasy

The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is

Answer & solution

Correct answer: 6

  • A

    2

  • B

    4

  • 6

  • D

    8

Solution

Since the sum of reciprocals is 5/12.

The two numbers must have their LCM as 12 and their sum as given will be 10.

Possible numbers are 4 and 6 only.

Alternately,
Let the numbers be a and b.

a + b = 10   ...(1)

1/a + 1/b = 5/12   ...(2)

Solving (1) and (2), we get (a, b) = (4, 6) 

Hence, option (c).

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CAT 1991 QA Q22: The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is — Solution | TheCATExam