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If P and Q are positive integers, and if P > 1, does P =

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If P and Q are positive integers, and if P > 1, does P =

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If P and Q are positive integers, and if P > 1, does P = Q?

(1) P is a factor of Q
(2) P is a multiple of Q

OA C

Source: Magoosh

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BTGmoderatorDC wrote:
If P and Q are positive integers, and if P > 1, does P = Q?

(1) P is a factor of Q
(2) P is a multiple of Q
Statement 1:
Case 1: P=2 and Q=2, with the result that P divides evenly into Q
In this case, P=Q, so the answer to the question stem is YES.
Case 2: P=2 and Q=4, with the result that P divides evenly into Q
In this case, P≠Q, so the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
Case 1: P=2 and Q=2, with the result that P is a multiple of Q
In this case, P=Q, so the answer to the question stem is YES.
Case 2: P=4 and Q=2, with with the result that P is a multiple of Q
In this case, P≠Q, so the answer to the question stem is NO.
INSUFFICIENT.

Statements combined:
Statement 1: Q/P = m, where m is a positive integer.
Statement 2: P/Q = n, where n is a positive integer.
Multiplying the two equations, we get:
Q/P * P/Q = mn
1 = mn
Since m and n must be positive integers, m=1 and n=1.
Thus:
P/Q = n = 1, implying that P=Q.
The answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

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