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# M02-14

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Math Expert
Joined: 02 Sep 2009
Posts: 47967

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16 Sep 2014, 00:17
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Difficulty:

5% (low)

Question Stats:

78% (00:50) correct 23% (00:44) wrong based on 160 sessions

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If $$x$$ and $$y$$ are positive integers and $$x \gt y$$, then what is the value of $$xy^2 + yx^2$$?

(1) $$xy = 6$$

(2) $$x$$ is a prime number

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:17
Official Solution:

$$xy^2+ yx^2 = xy(x+y)$$

Statement (1) by itself is insufficient. We know that $$xy=6$$, but we do not know what $$x+y$$ equals.

Statement (2) by itself is insufficient. We know that $$x$$ is a prime number, but there is no information about $$y$$.

Statements (1) and (2) combined are sufficient. If $$xy=6$$, then the possible values of $$x$$ and $$y$$ are either 1 and 6 or 2 and 3. If $$x$$ is a prime number and $$x \gt y$$, then $$x=3$$ and $$y=2$$.

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Joined: 07 Sep 2014
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23 Sep 2014, 09:47
I'm unclear as to why Statement (1) is insufficient...

Factoring the provided equation leaves us with xy(x+y). As such, we need to figure out what "xy" is equal to, and what "(x+y)" is equal to.

Statement (1) tells us that xy=6. Hence, possibilities: x=2 and y=3, x=3 and y=2, or their negative counterparts. HOWEVER, we are also told by the prompt that both x and y are positive integers, and that x >y. Thus, x MUST be 3 and y MUST be 2. This provides us with sufficient information.

What am I missing?
Math Expert
Joined: 02 Sep 2009
Posts: 47967

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23 Sep 2014, 09:57
bartone89 wrote:
I'm unclear as to why Statement (1) is insufficient...

Factoring the provided equation leaves us with xy(x+y). As such, we need to figure out what "xy" is equal to, and what "(x+y)" is equal to.

Statement (1) tells us that xy=6. Hence, possibilities: x=2 and y=3, x=3 and y=2, or their negative counterparts. HOWEVER, we are also told by the prompt that both x and y are positive integers, and that x >y. Thus, x MUST be 3 and y MUST be 2. This provides us with sufficient information.

What am I missing?

What about a case when x = 6 and y = 1 ?
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Joined: 12 Jan 2015
Posts: 16
Concentration: Entrepreneurship, Human Resources
GMAT Date: 06-27-2015

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01 Apr 2015, 07:04
What if x=1 and y=6? Please explain.
Math Expert
Joined: 02 Sep 2009
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01 Apr 2015, 07:41
SonaliT wrote:
What if x=1 and y=6? Please explain.

This case is not possible for 2 reasons:
1. We are told that x > y.
2. We are told that x is prime, while 1 is NOT a prime number.

Does this make sense?
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Joined: 06 Jun 2017
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25 Sep 2017, 18:54
Given that xy = 6, why can't we just plug 6 in for both (xy)^2 and (yx)^2 to get 6^2+6^2 for Statement 1?

Thanks!
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25 Sep 2017, 20:47
Gmatfrog3 wrote:
Given that xy = 6, why can't we just plug 6 in for both (xy)^2 and (yx)^2 to get 6^2+6^2 for Statement 1?

Thanks!

Because it's not (xy)^2 + (yx)^2 but x*y^2 + y*x^2. If it were (xy)^2 + (yx)^2 it would have been written that way (in brackets), without them xy^2 ALWAYS means x*y^2.
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Re: M02-14 &nbs [#permalink] 25 Sep 2017, 20:47
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# M02-14

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