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605-655 (Medium)|   Algebra|      
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Bunuel
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If xy = 7, what is xy(x + y)^2 ? 10 Oct 2017, 00:50
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60% (01:17) correct 40% (01:08) wrong based on 200 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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D
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akanksha.setiya
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If xy = 7, what is xy(x + y)^2 ? 10 Oct 2017, 01:31
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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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If xy = 7, what is xy(x + y)^2 ? 25 Jun 2019, 13:36
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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
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krishhchainani
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If xy = 7, what is xy(x + y)^2 ? 27 Jun 2019, 22:18
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hpnee
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
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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
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If xy = 7, what is xy(x + y)^2 ? 27 Jun 2019, 22:42
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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.

My answer:D

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If xy = 7, what is xy(x + y)^2 ? 11 Aug 2019, 07:22
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It seems that there is an assumption that both X and Y are integers. Where did that assumption come from?
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ueh55406
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If xy = 7, what is xy(x + y)^2 ? 19 May 2021, 08:37
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Bunuel
If xy = 7, what is xy(x + y)^2 ?

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

Argh ! fell into the trap at first.

stem; \(xy(x+y)^2\)= \(xy *x^2*y^2*2xy\)

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

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

we have x^2*y^2, we have xy. clearly suff.

(2) \(x^2 = 1\)

xy=7----> square both side--->x^2y^2=49 ---> x^2=1---> 1*y^2=49

we have \(x^2=1\),\( y^2=7\), \(xy=7\). sufficient as well.
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If xy = 7, what is xy(x + y)^2 ? 20 Aug 2022, 20:55
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Bunuel
If xy = 7, what is xy(x + y)^2 ?

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

\(xy(x + y)^2 = xy(x^2 + y^2 + 2xy)\)
Since the value of \(xy\) is known, we need to know the value of \(x^2 + y^2\).
Question stem, rephrased:
What is the value of \(x^2+y^2\)?

Statement 1:
SUFFICIENT.

Statement 2:
If x=1, then xy=7 requires that y=7, with the result that \(x^2+y^2 = 50\)
If x=-1, then xy=7 requires that y=-7, with the result that \(x^2+y^2 = 50\)
Since the value of \(x^2+y^2\) is the same in each case, SUFFICIENT.

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D
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