Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
In order to find all possible factors of , we need to break the expression down into its prime factors.
First, though, we should deal with the negative exponent in the denominator. Negative exponents indicate the reciprocal of the positive version of the exponent. For example, 
.
The expression (74 + 76)-1 is thus the same as 
. So our original expression can be rewritten as 
.
Dividing by a fraction is the same as multiplying by its reciprocal. Thus,
.
The expression 65 – 63 can be factored as follows:
The expression 74 + 76 can be factored as follows:
Thus it must be true that
The question asks which of the choices is not a factor of this expression.
10 = 2 × 5. The original expression contains both 2 and 5 as factors. Therefore 10 must be one of its factors. Eliminate A.
16 = 2 × 2 × 2 × 2 = 24. The original expression contains 24. Therefore 16 must be one of its factors. Eliminate B.
27 = 3 × 3 × 3 = 33. The original expression contains 33. Therefore 27 must be one of its factors. Eliminate C.
99 = 3 × 3 × 11 = 32 × 11. The original expression contains 32 but not 11. Therefore 99 CANNOT be one of its factors. CORRECT.
125 = 5 × 5 × 5 = 53. The original expression contains 53. Therefore 125 must be one of its factors.
The correct answer is D.
