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# If xy = 7, what is xy(x + y)^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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10 Oct 2017, 00:50
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Difficulty:

55% (hard)

Question Stats:

60% (01:20) correct 40% (01:07) wrong based on 104 sessions

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If xy = 7, what is xy(x + y)^2 ?

(1) x^2 + y^2 = 50
(2) x^2 = 1

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Intern
Joined: 10 Jul 2017
Posts: 26
Re: If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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10 Oct 2017, 01:31
1
If xy = 7, what is xy(x + y)^2 ?

(1) x^2 + y^2 = 50
(2) x^2 = 1

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

Statement 1: given x^2 + y^2 = 50.
Substitute given values to get the answer.
Sufficient.

Statement 2: x^2 = 1.
now given that xy=7.
x^2.y^2=49
y^2 = 49/ x^2 = 49/ 1 = 49.
Now, substitute all values in the equation to get the final result.
Sufficient.

Hence, the correct answer is D. Each statement alone is sufficient.

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Intern
Joined: 11 May 2007
Posts: 1
Re: If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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25 Jun 2019, 13:36
Sorry but I dont understand the explanation correctly.
In case of second statement
y could be +7 or -7
similarly x could be +1 or -1
how can then it be then sufficient
Intern
Joined: 14 Jun 2019
Posts: 1
Re: If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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27 Jun 2019, 22:18
1
hpnee wrote:
Sorry but I dont understand the explanation correctly.
In case of second statement
y could be +7 or -7
similarly x could be +1 or -1
how can then it be then sufficient

Hi,
because xy=7, both x and y need to be positive or both negative and we don't need the value of only x or y, we need the squares of both, so the signs don't matter
Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
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WE: Analyst (Commercial Banking)
If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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27 Jun 2019, 22:42
xy(x + y)^2= xy(x^2 + y^2 + 2xy)
Since the value of xy (=7) is KNOWN, we only need the value of (x^2 + y^2) to find out the value of above expression.

Now the question becomes (x^2 + y^2)=?

Statement 1: x^2 + y^2)=50 SUFFICIENT.

Statement 2: x^2=1
=> x =1 or x=-1.

Since xy=7,
(1) if x=1, then y=7,
So, x^2 + y^2=1^2 + 7^2=50.

Or
(2) if x=-1, then y=-7,
So, x^2 + y^2=(-1)^2 + (-7)^2=50.

In both cases, x^2+y^2=50.
SUFFICIENT.

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Intern
Joined: 15 Jul 2019
Posts: 12
Re: If xy = 7, what is xy(x + y)^2 ?  [#permalink]

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11 Aug 2019, 07:22
It seems that there is an assumption that both X and Y are integers. Where did that assumption come from?
Re: If xy = 7, what is xy(x + y)^2 ?   [#permalink] 11 Aug 2019, 07:22
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