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Sub 505 Level|   Algebra|                        
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Bunuel
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 26 Sep 2016, 05:01
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D
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90% (00:51) correct 10% (01:15) wrong based on 2198 sessions

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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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D
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AnisMURR
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 31 Oct 2016, 12:34
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hello,

Here is the answer, hope it is clear
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Shrivathsan
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 26 Sep 2016, 05:11
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Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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(x+y)^2 = x^2+y^2+2xy
4=2+2xy
xy=1
D
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GMAT Focus 1: 735 Q90 V89 DI81
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 26 Sep 2016, 05:15
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Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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It is based on algebraic formula..
(X+y)^2=x^2+y^2+2xy..
Substitute the values given..
2^2=2+2xy...
2xy=4-2=2.... xy=1
D
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 27 Sep 2016, 05:09
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Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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x^2 + y^2 = 2 - Given

we can write the above equation as \((x+y)^2\) - 2xy = 2

\((2)^2\)-2xy = 2
=> 4 - 2xy = 2 => -2xy = -2 => xy = 1.

Option D.
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 27 Sep 2016, 05:14
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Given
(x+Y) = 2 and X^2 + Y^2 = 2
(x+Y) = 2
Squaring both sides.

X^2 + Y^2 + 2xy = 4

2 + 2xy = 4

Solving for xy = 1

Option D
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 27 Sep 2016, 15:22
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x+y = 2 or x = 2-y

x^2+Y^2=2
(2-Y)^2+Y^2=2
y^2-2Y+1=0
Y=1

X=2-y
X=1

Ans 1 D
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 10 Jan 2017, 13:18
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Shrivathsan
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2

(x+y)^2 = x^2+y^2+2xy
4=2+2xy
xy=1
D
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Nice! Simple question.... How is it possible to see this under 2 min? LOL!?
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Mar 2018, 10:41
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Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself :? ?
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Mar 2018, 11:07
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dave13
Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2


Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself :? ?
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Hi dave13

In the question itself, there is no relationship between the 2 equations except
that they are talking about the same variable x and y.
In questions like these, we are basically given two simultaneous linear equations
and are excepted to find the value of x and y solving these equations.

Some basic formulae you need to remember are \((x+y)^2 | (x-y)^2 | x^2 - y^2\)

Hope this helps!
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Mar 2018, 11:10
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Two equations are given to form a basic algebra equation.

(x+y)^2= x^2+y^2+2xy
Hence value of xy=1


Sent from my iPhone using GMAT Club Forum
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Mar 2018, 11:31
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dave13
Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2


Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself :? ?

Hi dave13

In the question itself, there is no relationship between the 2 equations except
that they are talking about the same variable x and y.
In questions like these, we are basically given two simultaneous linear equations
and are excepted to find the value of x and y solving these equations.

Some basic formulae you need to remember are \((x+y)^2 | (x-y)^2 | x^2 - y^2\)

Hope this helps!
Show more


Hello pushpitkc :)

thanks for your reply :) ok i understand how from this x^2 + y^2 = 2, we do this (x+y) (x+y) = x^2+xy+yx+y^2 = x^2+y^2+2xy = 2 ok now what ?

and what am i to do with x + y = 2 ? there are no roots, powers etc here :-)
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Mar 2018, 12:04
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Hey dave13

We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\)
After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\)

Substituting these values, we get\(2^2 = 2 + 2xy\) -> \(4 - 2 = 2xy\) -> \(xy = \frac{2}{2} = 1\)(Option D)

Hope this helps!
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 16 Mar 2018, 12:05
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pushpitkc
Hey dave13

We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\)
After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\)

Substituting these values, we ge t\(2^2 = 2 + 2xy\) -> \(4 - 2 = 2xy\) -> \(xy = \frac{2}{2} = 1\)(Option D)

Hope this helps!
Show more


pushpitkc many thanks for explanation. yes it helps just partially :) ok from this \(x^2 + y^2 = 2\) we got this \(x^2 + y^2 + 2xy =2\) ok I understand this part so far

now you say we substitute values - which values are you talking about? and in which equation do you substitute ? how do you get this \(2^2 = 2 + 2xy\) also how do you get in it \(2^2\) :?

I would appreciate your detailed explanation for dummies :)

thanks!
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 16 Mar 2018, 12:46
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pushpitkc
Hey dave13

We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\)
After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\)

Substituting these values, we ge t\(2^2 = 2 + 2xy\) -> \(4 - 2 = 2xy\) -> \(xy = \frac{2}{2} = 1\)(Option D)

Hope this helps!


pushpitkc many thanks for explanation. yes it helps just partially :) ok from this \(x^2 + y^2 = 2\) we got this \(x^2 + y^2 + 2xy =2\) ok I understand this part so far

now you say we substitute values - which values are you talking about? and in which equation do you substitute ? how do you get this \(2^2 = 2 + 2xy\) also how do you get in it \(2^2\) :?

I would appreciate your detailed explanation for dummies :)

thanks!
Show more

Hey dave13

So we have an equation \((x+y)^2 = x^2 + y^2 + 2xy\) -> (1)

The question stem has given us the following details:
\(x+y = 2\)
\(x^2 + y^2 = 2\) -> (2)

Because \(x+y = 2\), value of \((x+y)^2 = 2^2 = 4\) -> (3)

Substituting values from (2) and (3) in equation (1)

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

4 = 2 + 2xy
2xy = 4-2 = 2

Therefore, xy = \(\frac{2}{2} = 1\)

Hope it is clear now.
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 15 Sep 2019, 06:35
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Bunuel
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

A. –2
B. –1
C. 0
D. 1
E. 2
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(x+y)^2= x^2+y^2+2xy
4 = 2 + 2xy
xy = 1

IMO D

Posted from my mobile device
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 06 Feb 2024, 10:53
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x+y=2
x^2+y^2=2

replace values of xy from options , that give answer =2 as per equation.

x+y=2 => 1+1=2
x^2+y^2 =>1^2+1^2=2
xy =>1*1=2

So, 1 is the answer
Option D­
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? 18 Feb 2025, 09:17
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