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

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Joined: 02 Sep 2009
Posts: 47903
If P and Q are positive integers, and if P > 1, does P = Q?  [#permalink]

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24 Jul 2018, 01:56
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Difficulty:

35% (medium)

Question Stats:

76% (00:37) correct 24% (01:48) wrong based on 42 sessions

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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

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Re: If P and Q are positive integers, and if P > 1, does P = Q?  [#permalink]

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24 Jul 2018, 02:08
To find whether P = Q

P > 1

Statement 1

P is a factor of Q

=> P $$\leq$$ Q

=> P can be 2 and Q can be 4 and P $$\neq$$ Q

=> P can be 4 and Q can be 4 and P = Q

Statement 1 is not sufficient

Statement 2

P is a multiple of Q => P $$\geq$$ Q

=> P can be 8 and Q can be 4 and P $$\neq$$ Q

=> P can be 8 and Q can be 8 and P = Q

Statement 2 is not sufficient

Combining statements 1 and 2

We have P $$\leq$$ Q and P $$\geq$$ Q

=> P = Q

Statements 1 and 2 together are sufficient

Hence option C
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Re: If P and Q are positive integers, and if P > 1, does P = Q?  [#permalink]

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24 Jul 2018, 12:16
1
If P and Q are positive integers, and if P > 1, does P = Q?

(1) P is a factor of Q
(P, Q) can be (2,2) or (2,4) or...
Here P< or = Q
NOT SUFFICIENT

(2) P is a multiple of Q
(P, Q) can be (2,2) or (4,2) or...
Here P> or = Q
NOT SUFFICIENT

Combining , we get P = Q
SUFFICIENT

POINT TO REMEMBER: If Any Number P is both factor and multiple of other number Q. This means, both numbers P & Q are equal.

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Re: If P and Q are positive integers, and if P > 1, does P = Q? &nbs [#permalink] 24 Jul 2018, 12:16
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