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# If xy = 3, what is the value of xy(x + y) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 46068
If xy = 3, what is the value of xy(x + y) ? [#permalink]

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02 Oct 2017, 23:56
00:00

Difficulty:

55% (hard)

Question Stats:

49% (01:30) correct 51% (01:00) wrong based on 45 sessions

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If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2
(2) x^2 + y^2 = 10

_________________
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Joined: 30 Jan 2017
Posts: 86
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29
GMAT 2: 660 Q47 V34
GMAT 3: 730 Q49 V40
GPA: 3.9
If xy = 3, what is the value of xy(x + y) ? [#permalink]

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03 Oct 2017, 02:38
Bunuel wrote:
If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2
(2) x^2 + y^2 = 10

I took the conventional way.

We have x=3/y and we need the value of 3(x + y).

S1. x – y = 2
Substitute the equation $$x=3/y$$ in the above equation to get $$y^2+2y-3=0$$
You will get y=1 and x=3 ; y=-3 and x=-1
Both the sets give you different value for 3(x+y)
Not sufficient

S2. $$x^2 + y^2 = 10$$
Again substitute $$x=3/y$$ to obtain $$y^4 - 10y^2 + 9=0$$
The sets you obtain are:
x=3 and y=1
x=-3 and y=-1
x=1 and y=3
x=-1 and y=-3
The above values give you different answers for 3(x+y)
Not sufficient

S1 and S2 combined
Only value common to both condition is x=-1 and y=-3
This gives you -12 as the value of 3(x+y)
Sufficient

I know there has to be a faster way. Please suggest.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1140
Location: India
GPA: 3.82
Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]

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03 Oct 2017, 09:48
3
Bunuel wrote:
If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2
(2) x^2 + y^2 = 10

we need to calculate the value of $$3(x+y)$$. Hence need to know the value of $$(x+y)$$

Statement 1: $$(x+y)^2=(x-y)^2+4xy$$, substitute the values to get

$$(x+y)^2=16$$ or $$x+y=±4$$. Hence no unique value. Insufficient

Statement 2: $$(x+y)^2=x^2+y^2+2xy$$, substitute the values to get

$$(x+y)^2=16$$ or $$x+y=±4$$. Hence no unique value. Insufficient

Combining 1 & 2 we get $$x+y=±4$$. Hence no unique value. Insufficient

Option E
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1140
Location: India
GPA: 3.82
If xy = 3, what is the value of xy(x + y) ? [#permalink]

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03 Oct 2017, 09:53
1
fmik7894 wrote:
Bunuel wrote:
If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2
(2) x^2 + y^2 = 10

I took the conventional way.

We have x=3/y and we need the value of 3(x + y).

S1. x – y = 2
Substitute the equation $$x=3/y$$ in the above equation to get $$y^2+2y-3=0$$
You will get y=1 and x=3 ; y=-3 and x=-1
Both the sets give you different value for 3(x+y)
Not sufficient

S2. $$x^2 + y^2 = 10$$
Again substitute $$x=3/y$$ to obtain $$y^4 - 10y^2 + 9=0$$
The sets you obtain are:
x=3 and y=1
x=-3 and y=-1
x=1 and y=3
x=-1 and y=-3
The above values give you different answers for 3(x+y)
Not sufficient

S1 and S2 combined
Only value common to both condition is x=-1 and y=-3
This gives you -12 as the value of 3(x+y)
Sufficient

I know there has to be a faster way. Please suggest.

Hi fmik7894

Apart from being a lengthy method, you have ignored one common value. See highlighted section. as there is no unique solution, IMO answer should be E
SVP
Joined: 26 Mar 2013
Posts: 1672
Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]

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06 Oct 2017, 00:33
Bunuel wrote:
If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2
(2) x^2 + y^2 = 10

(1) x – y = 2

Let x =-1 , y=-3......... x – y = 2............3 (-4) = -12

Let x= 3 , y= 1......... ..x – y = 2............3 (4) = 12

Two values

Insufficient

(2) x^2 + y^2 = 10

Use same examples above

Insufficient

Combine 1 &b2

Use same examples above

No clear soution

Insufficient

Re: If xy = 3, what is the value of xy(x + y) ?   [#permalink] 06 Oct 2017, 00:33
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