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655-705 (Hard)|   Algebra|      
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Bunuel
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 22 Mar 2023, 09:30
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Difficulty:

55% (hard)

Question Stats:

53% (01:35) correct 47% (01:19) wrong based on 59 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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Rabab36
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 22 Mar 2023, 12:35
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statement 1
x^2+y^2=3
xy(x + y)^2 given

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

xy=7 given

statement 1 sufficient


statement 2 clearly insufficient


option A
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 23 Mar 2023, 06:20
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let's analyse both statement.

given xy=7

St-1
x^2 + y^2 = 3


To find value of xy(x + y)^2

xy(x + y)^2
=7(x^2+y^2+2xy)
=7(3+2*7)
=7(17)
=119

SUFFICIENT

St-2
x^2 = 1
possible value of x =1/-1
we know xy=7
corresponding value of y=7/-7

Case 1
for x=1,y=7
To find value of xy(x + y)^2
put x and y
=7(1+7)^2
=7(64)
=448

Case 2
for x=-1,y=-7
To find value of xy(x + y)^2
put x and y
=7{(-)1+(-)7}^2
=7{-8}^2
=7(64)
=448

SUFFICIENT

Hence Statement 1 & 2 both are independently sufficient.
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 25 Mar 2023, 08:34
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Jitesh8
let's analyse both statement.

given xy=7

St-1
x^2 + y^2 = 3


To find value of xy(x + y)^2

xy(x + y)^2
=7(x^2+y^2+2xy)
=7(3+2*7)
=7(17)
=119

SUFFICIENT

St-2
x^2 = 1
possible value of x =1/-1
we know xy=7
corresponding value of y=7/-7

Case 1
for x=1,y=7
To find value of xy(x + y)^2
put x and y
=7(1+7)^2
=7(64)
=448

Case 2
for x=-1,y=-7
To find value of xy(x + y)^2
put x and y
=7{(-)1+(-)7}^2
=7{-8}^2
=7(64)
=448

SUFFICIENT

Hence Statement 1 & 2 both are independently sufficient.
Show more


OP Both statements give two different answers to the question. I’m confused how both statements can be sufficient.
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TheBipedalHorse
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 26 Mar 2023, 05:36
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If xy = 7, what is xy(x + y)^2 ?

(1) x^2 + y^2 = 3
(2) x^2 = 1

I originally marked (2) is sufficient. But I overlooked a very simple point that I realized later after finding out I marked the wrong answer. You can probably guess why 1 is sufficient. if I know the value of x^2 + y^2 and if I know the value of xy, then I can easily find out the value of (x+y)^2 (Yes, I missed this... I'm capable of being blind to what's in front of me...I am trying to change that)

Why is (2) alone sufficient? If I know x^2 is 1, then either x is 1 or -1. if xy is positive (7), that means either both x and y are negative or both x and y are positive.

x----------y--------xy
(1)-------(7)-------7
(-1)------(-7)------7

if x and y are of the same sign, (x + y)^2 in both cases (x and y both positive, or x and y both negative) will have the same value. I already know what xy is. so I am easily getting a unique value for xy(x + y)^2

So each statement taken independently is sufficient
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 26 Mar 2023, 05:50
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harshimarathe1
Jitesh8
let's analyse both statement.

given xy=7

St-1
x^2 + y^2 = 3


To find value of xy(x + y)^2

xy(x + y)^2
=7(x^2+y^2+2xy)
=7(3+2*7)
=7(17)
=119

SUFFICIENT

St-2
x^2 = 1
possible value of x =1/-1
we know xy=7
corresponding value of y=7/-7

Case 1
for x=1,y=7
To find value of xy(x + y)^2
put x and y
=7(1+7)^2
=7(64)
=448

Case 2
for x=-1,y=-7
To find value of xy(x + y)^2
put x and y
=7{(-)1+(-)7}^2
=7{-8}^2
=7(64)
=448

SUFFICIENT

Hence Statement 1 & 2 both are independently sufficient.


OP Both statements give two different answers to the question. I’m confused how both statements can be sufficient.
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You are right, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. I fixed the first statement so that the statements do not contradict.
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SaquibHGMATWhiz
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GMAT 1: 760 Q51 V40
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 26 Mar 2023, 06:19
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Bunuel
If xy = 7, what is xy(x + y)^2 ?
(1) x^2 + y^2 = 50
(2) x^2 = 1
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Solution:
Pre Analysis:
  • We are given \(xy=7\)
  • We are asked the value of \(xy(x+y)^2\) or the value of \(7(x+y)^2\) or \(7(x^2+y^2+2xy)\) or \(7(x^2+y^2+14)\)
  • Ways to get the answer:
    • If we get the value of \(x^2+y^2\)
    • If we get individual values of x and y
    • If we get value of any one of x or y

Statement 1: \(x^2 + y^2 = 50\)
  • We can simply put this value in \(7(x^2+y^2+14)\) and get the answer
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: \(x^2 = 1\)
  • From this statement, either \(x=1\) or \(x=-1\)
  • If \(x=1\)
    • then \(y=7\) and \(x^2+y^2=1+49=50\)
  • If \(x=-1\)
    • then \(y=-7\) and \(x^2+y^2=1+49=50\)
  • So, the value of \(x^2+y^2\) doesn't change in both the conditions
  • Thus, statement 2 alone is also sufficient


Hence the right answer is Option D
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If xy = 7, what is xy(x + y)^2 ? (1) x^2 + y^2 = 3 (2) x^2 = 1 27 Mar 2023, 10:40
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harshimarathe1
Jitesh8
let's analyse both statement.

given xy=7

St-1
x^2 + y^2 = 3


To find value of xy(x + y)^2

xy(x + y)^2
=7(x^2+y^2+2xy)
=7(3+2*7)
=7(17)
=119

SUFFICIENT

St-2
x^2 = 1
possible value of x =1/-1
we know xy=7
corresponding value of y=7/-7

Case 1
for x=1,y=7
To find value of xy(x + y)^2
put x and y
=7(1+7)^2
=7(64)
=448

Case 2
for x=-1,y=-7
To find value of xy(x + y)^2
put x and y
=7{(-)1+(-)7}^2
=7{-8}^2
=7(64)
=448

SUFFICIENT

Hence Statement 1 & 2 both are independently sufficient.


OP Both statements give two different answers to the question. I’m confused how both statements can be sufficient.
Show more


Please go through the solution again. Not sure why you are so confused.

Also Note that in such questions we only check whether statements are independently sufficient or not. This does NOT mean you will get exact same value after solving


Please Write Your Question Clearly in order to get more detailed solution.

Thanks
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