alebra problem

Expert replies

kat187: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Dec 29, 2009 10:21 pm

alebra problem

by kat187 » Fri Mar 19, 2010 2:08 pm

hi I got a simple question for all you gurus out there.

if xy=1

then

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

for this can I substitute x=2 and y=1/2 ?
and rewrite it as

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

Source: Beat The GMAT — Problem Solving | Fri Mar 19, 2010 2:08 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Fri Mar 19, 2010 5:37 pm

No you cannot do that IMO.

Here's how you must do it.

if xy=1, then 2 ^(x+y)^2 / 2 ^(x-y)^2 = ?

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

Numerator --> 2^(x+y)^2. Whenever you face an exponent, Always start simplifying from the topmost exponent.
2^(x+y)^2 = 2^(x^2+y^2+2xy)
xy=1, 2^(x^2+y^2+2*1) = 2^(x^2+y^2+2) = 2^(x^2+y^2) * 2^2 = 2^(x^2+y^2) * 4

Denominator --> 2^(x-y)^2 = 2^(x^2+y^2-2xy) = 2^(x^2+y^2 - 2*1) = 2^(x^2+y^2-2) = 2^(x^2+y^2) * 2^(-2)

Numerator / Denominator = 2^(x^2+y^2) * 4 / 2^(x^2+y^2) * 2^(-2)

2^(x^2+y^2) gets cancelled out.

4 / 2^(-2) = [spoiler]4*4 = 16[/spoiler] IMO

Can you post the OA?

kat187: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Dec 29, 2009 10:21 pm

by kat187 » Fri Mar 19, 2010 6:06 pm

=16

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Fri Mar 19, 2010 9:46 pm

kat187 wrote:hi I got a simple question for all you gurus out there.

if xy=1

then

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

for this can I substitute x=2 and y=1/2 ?
and rewrite it as

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

2 ^(x+y)^2 / 2 ^(x-y)^2=2 ^[(x+y)^2-(x-y)^2]=2^[(X+Y+X-Y)(X+Y-X+Y)]=2^[(2X)(2Y)]=2^4XY=2^4=16

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review