If x is a positive integer, is x/4 an integer?

What we need to check is whether x is a multiple of 4 ?

Statement1: x is a factor of 72
X can be 4 / 3/9 / 2/1/ 72

If x is 4/8 then answer is yes

However if x is 1/9/2 etc, the answer is no

Hence the statement is insufficient.

Statement2: x is a factor of 81

Thus x can be 3/9/27/1/81

In every case x/4 is not an integer.

Hence statement 2 is sufficient.

The answer is B.


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We need to determine whether x/4 is an integer.

Statement One Alone:

72/x is an integer.

In order for 72/x to be an integer, x must be a factor of 72. That is, x is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 or 72. However, we cannot determine whether x/4 is an integer. For instance, if x = 1, then x/4 is NOT an integer, however, if x = 4, then x/4 is an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

81/x is an integer.

In order for 81/x to be an integer, x must be a factor of 81. That is, x is 1, 3, 9, 27 or 81. Any of these numbers divided by 4 won’t be an integer. Thus using the information in statement two, we can determine that x/4 IS NOT an integer.

Answer: B