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

Question

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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TarunKumar1234 · Answer

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

Stat1: P is a factor of Q
If Q = 6, then P = 2, 3 or 6. Not sufficient

Stat2: P is a multiple of Q
If P = 6, then Q = 2, 3 or 6. Not sufficient

Combining both, P= Q. Sufficient

So, I think C.

Sushil117 · Answer

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

(1) P is a factor of Q
then p must be smaller or equal to q...insufficient

(2) P is a multiple of Q
p must be equal or larger than q...insufficient

with 1 & 2 together,P must be equal Q
IMO C

Jaychoudhary · Answer

KarishmaB 
Please help with this.

RF1010 · Answer

I did not get this, can someone please explain or post the official solution from Magoosh?

Aarya20 · Answer

Statement #1: One of the factors of any positive integer greater than one is that integer itself. For example, one of the factors of 24 is 24. Also, one factor of every positive integer is 1. Thus, one of the factors of 24 is 1. Suppose Q = 24. Then P could be 24, or it could be {2, 3, 4, 6, 8, 12}. Thus, it could be true that P = Q, but doesn't have to be. This statement, alone and by itself, is insufficient.

Statement #2: One of the multiples of any positive integer is that integer itself. Thus, one multiple of 24 is 24. But of course, that's the lowest multiple and the multiple of any positive integer are infinite. Thus, if Q = 24, then P could be 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, etc. Thus, it could be true that P = Q, but doesn't have to be. This statement, alone and by itself, is insufficient.

Combined statements: This gets very interesting now. Again, let's start with the concrete example of 24. All the factors of 24 are smaller than 24, except for 24 itself. All the multiples of 24 are larger than 24, except for 24 itself. The only number on the entire number line that is simultaneously a factor of 24 and a multiple of 24 is 24 itself. More generally, the only number that is both a factor of Q and a multiple of Q at the same time is Q itself. Thus, if P is both a factor of Q and a multiple of Q, it absolutely must be true that P = Q. Thus, we can give a strong affirmative answer to the prompt question. Combined, the statements are sufficient.

Answer = (C)

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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