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

[aljumaily.anas]

Hey I would appreciate your help on this question from GMAT Prep:

If xy=1, what is the value of 2(x+y)^2 / 2(x-y)^2 =?

A)2
B)4
C)6
D)16
E)32

I can see that this problem involves the difference of squares but I can't seem to grab a string beyond that. Thanks

[aljumaily.anas]

Figured it out.

For those of you who also didn't know how to solve this one initially, the answer is as follows:

2((x+y)^2)/2((x-y)^2)=
2^(x+y^2)-(x-y^2)=
2^(X^2+2xy+y^2)-(x^2-2xy+y^2)=
2^((x^2-X^2)+(2xy+2xy)+(y^2-y^2)=
2^4xy= (remember xy=1) so
2^4*1=
16

[RonPurewal]

* It seems you've forgotten some exponent symbols in the original problem.

* Since you're just given xy = 1"”and no further restrictions on x and y"”you can just plug in x = 1 and y = 1. (You could also use any other values that multiply to 1, but these are the easiest ones.)
Whatever falls out of the expression with those values is the answer to the problem. No algebra required.

[NL]

Interesting! I also totally forgot the existence of xy=1. Nice!

[RonPurewal]

Whenever a problem starts out with a condition that's relatively easy to satisfy (e.g., "If xy = 1"), the possibility of plugging numbers should always be a prime consideration.

On a problem like this one, even if you're the fastest algebra wiz in the entire world, number-plugging knocks the socks off of algebra in terms of pure efficiency.

(It's best, of course, to be able to do both, equally comfortably.)