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CAT 1996 | Question: 138

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

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

Hence the answer is 6 values.

Option C is Correct Answer

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