Exponent Problem

Expert replies

meh: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Jun 17, 2013 7:04 am

by meh » Sun Jan 05, 2014 12:07 pm

If x is an integer, is 16^x + 16^-x = b
(1) 4^x + 4^-x = âˆš(b+2)
(2) x>0

I know that the answer is A. But my question is, why, when you square on both sides doesn't âˆš(b+2) end up being |b+2|?

Like this post

Source: Beat The GMAT — Quantitative Reasoning | Sun Jan 05, 2014 12:07 pm

dimochka: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Mon May 23, 2011 9:18 amFollowed by: 4 members; Location: NYC; Thanked: 17 times; GMAT Score:770

by dimochka » Mon Jan 06, 2014 10:57 am

That is because the min value of 4^x+4^-x is 2, at x=0. As a result, the smallest value of b is 0 and there is no need for the absolute value. Based on the constraints, the value of sqrt(b+2) cannot be negative for any integer x.

Like this post

sukriti2hats: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Fri May 30, 2014 8:34 am; Thanked: 1 times

by sukriti2hats » Sat May 31, 2014 4:53 am

Yes ideally on squaring, the absolute value is considered and here the value of b is unknown. But you may note that whatever the value of x be the left hand side of the equation that is 16^x + 16^-x will always be positive. You can check for yourself by taking examples, by keeping different values for x, you will find that the answer is always positive.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 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