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

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

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Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]
niks18 wrote:
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

Not able to understand the highlighted part. Please elaborate.
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Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]
AkshdeepS wrote:
niks18 wrote:
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

Not able to understand the highlighted part. Please elaborate.

Hi AkshdeepS

$$(x+y)^2=(x-y)^2+4xy$$, basically this is a helpful formula. Expand both sides of the equation and you will get the relation.

$$(x+y)^2=x^2+y^2+2xy$$ and

$$(x-y)^2+4xy=x^2+y^2-2xy+4xy=x^2+y^2+2xy$$

why I used this formula because you need to find x+y and the statement gives you x-y. Hence I need a formula that connects the two.
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Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]
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Re: If xy = 3, what is the value of xy(x + y) ? [#permalink]
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