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# If xy = 4, what is the value of xy(x – y) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 46216
If xy = 4, what is the value of xy(x – y) ? [#permalink]

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19 Sep 2017, 01:30
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Difficulty:

55% (hard)

Question Stats:

66% (01:43) correct 34% (02:19) wrong based on 47 sessions

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If xy = 4, what is the value of xy(x – y) ?

(1) x^2*y = 16
(2) x + y = 5

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Concentration: Operations, Strategy
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Re: If xy = 4, what is the value of xy(x – y) ? [#permalink]

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19 Sep 2017, 02:09
A

Substitute xy value in x^2*y=16. It will give us x=4&y=1

B doesn't give any specific values.

So option A

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Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: If xy = 4, what is the value of xy(x – y) ? [#permalink]

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19 Sep 2017, 02:27
If xy = 4
Find: xy(x – y)

(1) x^2*y = 16
=> x * xy = 16 => x=4
=> as xy=4 => y =1
so xy(x-y) = 4(4-1) = 4*3 = 12
Sufficient

(2) x + y = 5
xy=4 => $$x=\frac{4}{y}$$
$$\frac{4}{y}+ y= 16$$ => $$y^2-5y+4 = 0$$ => y=1 or 4
as xy=4 => x=4 or 1.
As we have 2 values of x and y we get 2 values for xy(x – y)
Insufficient

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Re: If xy = 4, what is the value of xy(x – y) ? [#permalink]

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23 Sep 2017, 22:24
Bunuel wrote:
If xy = 4, what is the value of xy(x – y) ?

(1) x^2*y = 16
(2) x + y = 5

hi

statement 1 states that x is equal to 4, and y is equal to 1, hence sufficient..

statement 2, however, provides 2 options
either
x = 1
y = 4
or
x = 4
y = 1
not sufficient ...

thanks ..
Re: If xy = 4, what is the value of xy(x – y) ?   [#permalink] 23 Sep 2017, 22:24
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