On the GMAT, problems about factors are invariably constrained to POSITIVE INTEGERS.
The problem above should read as follows:
What is the greatest common factor of POSITIVE INTEGERS x and y?
(1) x and y are both divisible by 4
(2) x - y = 4
Statement 1: x and y are both divisible by 4
Options for x and y:
4, 8, 12, 16, 20, 24, 28...
If x=4 and y=4, then the GCF of x and y is 4.
If x=8 and y=8, then the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.
Statement 2: x-y = 4
If x=5 and y=1, then the GCF of x and y is 1.
If x=6 and y=2, then the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.
Statements combined:
Statement 1 yields the following options for x and y:
4, 8, 12, 16, 20, 24, 28...
Statement 2 indicates that the difference between x and y is 4.
Implication:
x and y must be equal to two consecutive values in the list above.
If we select any pair of consecutive values -- 4 and 8, 8 and 12, 12 and 16, 16 and 20 -- the GCF in every case is 4.
SUFFICIENT.
The correct answer is
C.
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