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# If x + y = 7, what is the value of xy(x – y)?

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Math Expert
Joined: 02 Sep 2009
Posts: 50570
If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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09 Oct 2017, 23:36
00:00

Difficulty:

95% (hard)

Question Stats:

27% (02:24) correct 73% (01:55) wrong based on 84 sessions

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If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2

_________________
Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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Updated on: 11 Oct 2017, 00:27
(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving
y^2-7y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0

Sufficient

(2)

x^2=y^2
(x+y)(x-y)=0
Since we know that x+y = 7, then there is only one option for this eqution to hold true x-y=0, thus xy(x-y)=0

Sufficient

Originally posted by Alexey1989x on 10 Oct 2017, 01:04.
Last edited by Alexey1989x on 11 Oct 2017, 00:27, edited 1 time in total.
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Joined: 26 Mar 2013
Posts: 1877
Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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11 Oct 2017, 00:07
1
Alexey1989x wrote:
(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving

y^2-2y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0

Hi,

The highlighted part should be 7y.
Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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11 Oct 2017, 00:28
Mo2men wrote:
Alexey1989x wrote:
(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving

y^2-2y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0

Hi,

The highlighted part should be 7y.

Thank for notice, you're correct!
Manager
Joined: 28 Jul 2016
Posts: 135
Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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12 Dec 2017, 11:52
1
1
Bunuel wrote:
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2

Hi Bunuel
Why answer is B, not D?
Substituting 7*(x+y) = 7*7 = 49 = 4xy (1)
x + y = 7
So, x = 7 - y
Let's put x to equation (1):
4*y*(7-y) = 49
This gives us following results:

y = 3.5 and x = 3.5
So A is sufficient also
Math Expert
Joined: 02 Sep 2009
Posts: 50570
Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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12 Dec 2017, 19:18
LeonidK wrote:
Bunuel wrote:
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2

Hi Bunuel
Why answer is B, not D?
Substituting 7*(x+y) = 7*7 = 49 = 4xy (1)
x + y = 7
So, x = 7 - y
Let's put x to equation (1):
4*y*(7-y) = 49
This gives us following results:

y = 3.5 and x = 3.5
So A is sufficient also

Yes, the OA is D. Edited. Thank you.
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GMAT 1: 700 Q50 V33
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Re: If x + y = 7, what is the value of xy(x – y)?  [#permalink]

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12 Dec 2017, 22:19
Bunuel wrote:
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2

From Stmnt 1: 4xy = 49

(x+y)^2 - (x-y)^2 = 4xy = 49

Which means (x-y)^2 = 0 or x - y = 0 . Hence, Sufficient.

From Stmnt 2:

(x+y)(x-y) = 0

which means x - y = 0.. Sufficient.
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Re: If x + y = 7, what is the value of xy(x – y)? &nbs [#permalink] 12 Dec 2017, 22:19
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