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Math Expert V
Joined: 02 Sep 2009
Posts: 59095
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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14 00:00

Difficulty:   5% (low)

Question Stats: 89% (00:49) correct 11% (01:01) wrong based on 751 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

_________________
Manager  P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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4
1
hello,

Here is the answer, hope it is clear
Attachments IMAG0322.jpg [ 860.01 KiB | Viewed 9098 times ]

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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3
dave13 wrote:
pushpitkc wrote:
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!

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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Manager  Joined: 15 Apr 2016
Posts: 55
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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2
1
Bunuel wrote:
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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Math Expert V
Joined: 02 Aug 2009
Posts: 8180
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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1
1
Bunuel wrote:
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

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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Intern  Joined: 23 Jun 2016
Posts: 41
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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1
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
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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1
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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Retired Moderator G
Joined: 26 Nov 2012
Posts: 555
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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1
Bunuel wrote:
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^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.
Manager  Joined: 29 Aug 2008
Posts: 103
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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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
Manager  B
Joined: 09 Aug 2016
Posts: 62
If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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Shrivathsan wrote:
Bunuel wrote:
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

Nice! Simple question.... How is it possible to see this under 2 min? LOL!?
VP  D
Joined: 09 Mar 2016
Posts: 1229
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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Bunuel wrote:
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 ?
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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dave13 wrote:
Bunuel wrote:
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!
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Intern  B
Joined: 30 Nov 2017
Posts: 22
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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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
VP  D
Joined: 09 Mar 2016
Posts: 1229
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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pushpitkc wrote:
dave13 wrote:
Bunuel wrote:
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!

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 VP  D
Joined: 09 Mar 2016
Posts: 1229
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

### Show Tags

pushpitkc wrote:
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!
SVP  P
Joined: 03 Jun 2019
Posts: 1844
Location: India
Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?  [#permalink]

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Bunuel wrote:
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

IMO D

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