Mechmeera wrote:Source: Veritas
If x and y are integers and 2 < x < y, does y = 16 ?
(1) The GCF of X and Y is 2.
(2) The LCM of X and Y is 48.
Statement 1:
It's possible that x=4 and y=6, since the GCF of 4 and 6 is 2.
In this case, the answer to the question stem is NO.
It's possible that x=6 and y=16, since the GCF of 6 and 16 is 2.
In this case, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2:
It's possible that x=6 and y=16, since the LCM of 6 and 16 is 48.
In this case, the answer to the question stem is YES.
It's possible that x=6 and y=48, since the LCM of 6 and 48 is 48.
In this case, the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Rule:
xy = (GCF of x and y)(LCM of x and y).
Statements combined:
xy = (GCF)(LCM) = 2*48 = 96.
Factor pairs for 96 such that the smaller factor is greater than 2:
4*24
6*16
8*12.
Since the GCF of the pairs in red is 4, neither of these pairs satisfies Statement 1.
Thus, the only pair that satisfies both statements is x=6 and y=16.
SUFFICIENT.
The correct answer is
C.
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