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CAT 1991 — QA Question 44

Number TheoryEasy

If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is

Answer & solution

Correct answer: 6

  • A

    2

  • B

    5

  • 6

  • D

    12

Solution

 If (2x + 12) is perfectly divisible by x, then (2x + 12)/x has to be an integer.

Now if we divide, the expression simplifies to (2 + 12/x).

The only way in which this expression would be an integer is when 12/x is an integer or if 12 is perfectly divisible by x. [i.e., x is a factor of 12]

This is possible if x takes either of these values : 1, 2, 3, 4, 6, 12. Hence the answer is 6 values.

Hence, option (c).

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CAT 1991 QA Q44: If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values o — Solution | TheCATExam