Gmatprep - Exponents - Hard !

Question

hi all could someone please explain how to solve this ?

Thanks

mNeo · Answer

2 ^ (x + y)^2 
----------------
2 ^ (x - y)^2 

=> 2 ^ { (x + y) ^2 - (x - y) ^2 }
=> 2 ^ { 4xy }

We know that xy = 1

=> 2 ^4
= 16

riverripper · Answer

Since the GMAT is usually very basic testing things and uses intergers a lot of the time, sometimes an easy check once you solve for the XY equations is to use real numbers. Since XY=1 you can assume that its going to be 1 x 1 = 1 Plug those in and its 2 ^(2^2) / 2^(0^2)...so (2^4)/(2^0)...16/1 = 16

Depending how fast you move through the test it helps to check your math...I know most of the mistakes I make in the XY equations are dumb and if I plug in numbers I usually can catch them. If a problem has taken you a long time to figure out already it may be best just to go with what you got if it is one of the available answers.

ywilfred · Answer

2^ 
2^ 
2^ 
2^(4xy)
16

ninomoi · Answer

Yep I got 16. Just remember that (x+y)^2= x^2+2xy+y^2 and (x-y)^2= x^2+2xy-y^2 and you should be fine.

KillerSquirrel · Answer

thanks guys ! I guess it wasn't so hard after all

The OA is 16

Gmatprep - Exponents - Hard !

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