To count the positive factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)...
Generally, GMAT problems about factors are constrained to POSITIVE factors.
On the GMAT, the posted problem would probably appear as follows:
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x and y are prime numbers, how many POSITIVE factors has x^2y^2?
1) xy=10
2) x+y is odd
Only two cases are possible:
Case 1: x≠y
Here, to determine the number of factors for x²y², we add 1 to each exponent and multiply:
(2+1)(2+1) = 9 factors
Case 2: x=y, with the result that x²y² = x²x ²= x�
Here, to determine the number of factors for x�, we add 1 to the exponent:
4+1 = 5 factors
Implication:
To determine the number of factors, we need to know whether x=y.
Question stem, rephrased:
Does x=y?
Statement 1:
Only one pair of prime numbers has a product of 10:
2 and 5.
Thus, x≠y.
SUFFICIENT.
Statement 2:
Since x+y = odd, either x or y is ODD, while the other value is EVEN.
Thus, x≠y.
SUFFICIENT.
The correct answer is
D.
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