Help me solve this GMAT Quant Question (GMATPrep) #2

Expert replies

EricImasogie: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sat Aug 02, 2014 10:48 amFollowed by: 1 member

by EricImasogie » Fri Dec 12, 2014 5:34 am

I got the answer right but I'm not how to solve this question (I guessed).

exponent questions like these give me a hard time since they contain a variable set that is + or - another variable set. I typically see problems where perhaps 2^x = 3(2^x) ,which is easier to solve but Im not sure how to get this one. Please help!

Last edited by EricImasogie on Fri Dec 12, 2014 5:52 pm, edited 1 time in total.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Dec 12, 2014 5:34 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 12, 2014 6:37 am

If 2^x - 2^(x-2) = 3(2^13), what is the value of x?
a) 9
b) 11
c) 13
d) 15
e) 17

This requires some factoring.
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2 - 1] = 3(2^13)
2^(x-2)[3] = 3(2^13)
Divide both sides by 3 to get: 2^(x-2)= 2^13
So, x-2 = 13
[spoiler]x = 15[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Dec 12, 2014 10:52 am

Hi EricImasogie,

Factoring the equation (as Brent showed) is a useful approach here. You can actually take it a step further by TESTing THE ANSWERS (you might find it easier to manipulate numbers than to manipulate variables). One of those numbers IS the value of X, so you can plug them in, do the necessary math and find the one value that balances out the equation. Here's how to approach it:

Since the "right side" of the equation is greater than 2^14, X must be bigger than 14 (since the "left side" of the equation involves subtraction). So we can eliminate A, B and C.

Let's TEST answer D: 15

If X = 15, then...

2^15 - 2^13 can be factored into...
(2^13)(2^2 - 1) =
(2^13)(3)

This is EXACTLY what's on the "right side" of the equation, so X MUST be 15

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Dec 16, 2014 7:55 am

Alternatively, we can see that a SUBTRACTION is required, so we can use this clue to bring us closer to the answer on the right hand side of the equation:
3 x 2^13 = (4-1) x 2^13 = 4 x 2^13 - 2^13 = 2^15 - 2^13 = 2^n - 2^(n-2)
So n = 15

Like this post

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