If (x + y)^2 = 16 and x^2 - y^2 = 16, what is the value of 2x^2?

Question

(A) 8
(B) 16
(C) 18
(D) 32
(E) 50

Kudos for a correct  solution .

GMATinsight · Answer

(x + y)^2 = 16 
i.e. (x + y) =  + 4

x^2 - y^2 = 16
i.e. (x+y)(x-y) = 16

i.e. @(x+y)=+4, (x-y) = +4 i.e. x=4 and y = 0
and
i.e. @(x+y)=-4, (x-y) = -4 i.e. x=-4 and y = 0

hence x= + 4

i.e. 2x^2 = 2*( + 4)^2 = 32

Answer: Option  D

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Each of the expressions given is equal to 16, so we can set them equal to each other. Note that we have the “square of a sum” and the “difference of two squares” special products. We will put them both in distributed form, then simplify:

(x + y)^2 = x^2 - y^2 
 x^2 + 2xy + y^2 = x^2 - y^2 
 2xy + y^2 = -y^2 
 2xy + 2y^2 = 0

Since 2y(x + y) = 0, it must be true that either 2y or (x + y) is equal to 0. However, (x + y) cannot equal 0, since we are told that (x + y)^2 = 16 . So it must be that 2y= 0. Thus y = 0.

If we plug 0 in for y in x^2 – y^2 = 16, we get x^2 = 16. Thus 2x^2 = 2(16) = 32.

The correct answer is D.

msalvi · Answer

(x+y)(x-y) = 16 
&
(x+y)(x+y) = 16

divide the 2 equations.

(x-y)/(x+y) = 1

therefore x+y = x-y . Implies y = 0. Hence x^2 - y^2 = 16 implies x^2 = 16(since y =0) , therefore 2x^2 = 32

LogicGuru1 · Answer

(x + y)^2 = 16 ; --------------> (x+y)(x+y)=16

x^2 - y^2 = 16; --------------> (x+y)(x-y)=16

(x+y)(x+y) = (x+y)(x-y)

(x+y)=(x-y)

y=0

If  y=0  then x can only be  -+4

therefore  2*x^2= 2*16 = 32

ANSWER is D

ScottTargetTestPrep · Answer

Simplifying the second equation, we have:

(x - y)(x + y) = 16

Both equations are equal to 16, so we can set them equal to each other:

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

x - y = x + y

0 = 2y

y = 0

Since y = 0, (x + y)^2 = 16 means x^2 = 16, so 2x^2 = 2(16) = 32.

Answer: D

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If (x + y)^2 = 16 and x^2 - y^2 = 16, what is the value of 2x^2?

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If (x + y)^2 = 16 and x^2 - y^2 = 16, what is the value of 2x^2?

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