BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Value of X - Exponents

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Legendary Member
Posts: 631
Joined: Mon Feb 18, 2008 11:57 pm
Thanked: 29 times
Followed by:3 members

Re: Value of X - Exponents

by netigen » Sat Mar 08, 2008 3:16 pm
adi wrote: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

The answer should be D.
Equate the equation
(2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])] = (2^x) [1 - 1/4] = 3/4 x 2^x

3/4 x 2^x = 3(2^13)

2^(x-2) = (2^13)

x-2 = 13

x= 15
Top
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Mon Jan 07, 2008 12:55 pm
Location: Frisco, Texas

by adi » Sat Mar 08, 2008 3:50 pm
How did you make (2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])]

Also, where did the - go in (2^x) - (2^[x-2])
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Sun Mar 09, 2008 4:12 am

by tony777 » Sun Mar 09, 2008 4:47 am
(2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])]

In netigen's response he/she factored (2^x) - (2^[x-2]) to bring 2^x out.
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Wed Feb 27, 2008 5:55 pm

Shortest Way to Solve

by opengmat » Fri Mar 14, 2008 11:45 pm
The shortest to solve is by plug-in answer choice and equate both sides.

here start with C > LHS < RHS [x=13]
Goto next choice D > LHS = RHS [x=15]

Pls comment,
Top
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 am
Location: Southern California, USA
Thanked: 15 times
Followed by:6 members

backsolving

by resilient » Tue Mar 18, 2008 12:03 am
this is a fairly involved question. I would definintely try to backsolve on this question. It is begging to be back solved. In fact, I dont even see how to equate the equation.
Appetite for 700 and I scraped my plate!
Top
Master | Next Rank: 500 Posts
Posts: 111
Joined: Thu Jan 31, 2008 4:05 pm
Thanked: 18 times
Followed by:1 members

by xilef » Tue Mar 18, 2008 12:44 pm
once you realize that (2^x-2) is 2^x/2^2 then:

2^x-(2^x/2^2)=3(2^13)
2^x(1-1/4)=3(2^13)
2^x(3/4)=3(2^13)
2^x=4(2^13)
2^x=2^2(2^13)
2^x=(2^15)
Top
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Wed Apr 16, 2008 9:01 pm

by hillzheng » Wed Apr 16, 2008 10:29 pm
yes, x=15 or answer be D
Top
Legendary Member
Posts: 1169
Joined: Sun Jul 06, 2008 2:34 am
Thanked: 25 times
Followed by:1 members

by aj5105 » Thu May 07, 2009 10:39 pm
Stuart's reply : https://www.beatthegmat.com/exponent-pro ... 17726.html
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Mon Aug 23, 2010 5:25 pm
GMAT Score:690

by pacogzza » Mon Aug 23, 2010 5:33 pm
Sorry guys, I did not get the process of how you guys went through this problem... Could you go over this prob again and explain it for dummies plz??

Saludos from Mexico (regards from Mexico)
Top
Post new topic Post Reply
• Page 1 of 1