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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

What is value of x?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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 » Tue Mar 05, 2013 4:24 pm
G- Unit30 wrote:Hi,
I had this problem on GMATprep practice exam, so I don't have the full list of anwsers but the question is:

What is the value of x?
2^x - 2^(x-2) = 3(2^13)
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)
So, 2^(x-2)= 2^13
x-2 = 13
[spoiler]x = 15[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Sun Mar 03, 2013 7:10 pm

by G- Unit30 » Tue Mar 05, 2013 4:35 pm
Ahh, thanks that helps. That tricky bit of factoring at the start was the part that was confusing me...I wasn't able to think of how to represent 2^x if I pulled out 2^(x-2) as a factor.

Cheers
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Tue Feb 26, 2013 8:12 am

by neeg » Tue Mar 05, 2013 5:17 pm
I'm unclear about the very fist step of factoring
2^(x-2)[2^2 - 1] = 3(2^13)....how is 2^(x-2)a common factor?

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)
So, 2^(x-2)= 2^13
x-2 = 13
[spoiler]x = 15[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Tue Mar 05, 2013 5:26 pm
neeg wrote:I'm unclear about the very fist step of factoring
2^(x-2)[2^2 - 1] = 3(2^13)....how is 2^(x-2)a common factor?

Good question.
To answer this, let's examine some analogous factoring cases:

k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)

Or how about:
w^x + x^(x+5) = w^x(1 + w^5)

Notice that, each time, the greatest common factor of both terms is the term with the smallest exponent.

So, in the expression 2^x - 2^(x-2), the term with the smallest exponent is 2^(x-2), so we'll factor out 2^(x-2)

Does that help?

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Tue Mar 05, 2013 9:21 pm
Refer the following posts...
https://www.beatthegmat.com/2-x-2-x-2-3- ... tml#577790
https://www.beatthegmat.com/2-x-2-x-2-3- ... tml#577789
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Tue Feb 26, 2013 8:12 am

by neeg » Wed Mar 06, 2013 9:39 am
Brent@GMATPrepNow wrote:
neeg wrote:I'm unclear about the very fist step of factoring
2^(x-2)[2^2 - 1] = 3(2^13)....how is 2^(x-2)a common factor?

Good question.
To answer this, let's examine some analogous factoring cases:

k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)

Or how about:
w^x + x^(x+5) = w^x(1 + w^5)

Notice that, each time, the greatest common factor of both terms is the term with the smallest exponent.

So, in the expression 2^x - 2^(x-2), the term with the smallest exponent is 2^(x-2), so we'll factor out 2^(x-2)

Does that help?

Cheers,
Brent
Thanks Brent.

I understand for the below two as they have common base raised to the same powers and hence can be taken out as the common factor.
k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)

However, for w^x + x^(x+5) = w^x(1 + w^5)-----w^x does not appear in the second term at all so how does it become a common factor?

Similarly for the expression 2^x - 2^(x-2), I understand that smallest exponent is 2^(x-2)but don't see how this is a common factor in the first term which is 2^x?

Neeg
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Tue Feb 26, 2013 8:12 am

by neeg » Wed Mar 06, 2013 9:41 am
Thanks - I follow the different appraoches to solving for x provided in the link.

Neeg
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Wed Mar 06, 2013 10:00 am
neeg wrote: Thanks Brent.

I understand for the below two as they have common base raised to the same powers and hence can be taken out as the common factor.
k^5 - k^3 = k^3(k^2 - 1)
m^19 - m^15 = m^15(m^4 - 1)

However, for w^x + x^(x+5) = w^x(1 + w^5)-----w^x does not appear in the second term at all so how does it become a common factor?

Similarly for the expression 2^x - 2^(x-2), I understand that smallest exponent is 2^(x-2)but don't see how this is a common factor in the first term which is 2^x?
First of all, I made a slight error above. It should read: w^x + w^(x+5) = w^x(1 + w^5)

However, it is still true that 2^x - 2^(x-2) = 2^(x-2)[2^2 - 1]

Students typically have how issues with factoring when the exponents are integers. Things become more complicated when the exponents include variables. Nevertheless, it's important to understand how both types behave.

The basic principle is the same: (x^a)(x^b) = x^(a+b)

(w^3)(w^4) = w^(3+4) = w^7
(w^11)(w^8) = w^(11+8) = w^19
Similarly, (w^x)(w^5) = w^(x+5)
We can also say: w^x(1 + w^5) = w^x + w^(x+5)
Finally, we can say: 2^(x-2)[2^2 - 1] = 2^x - 2^(x-2)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 44
Joined: Tue Mar 12, 2013 2:27 pm
Thanked: 3 times

by J N » Wed Mar 20, 2013 4:21 pm
just an add on for info

does this make sense:

2^10 - 2^6 = whatever

pull out 2^10

2^10 (1 - 1^-4) ????

2^10 (1-1) ??????

=0 ?????


or more relevvant to exapmle

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

pull out 2^x

2^x (1-1^-2)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Wed Mar 20, 2013 5:08 pm
J N wrote:
does this make sense:

2^10 - 2^6 = whatever

pull out 2^10

2^10 (1 - 1^-4) ????

2^10 (1-1) ??????

=0 ?????
The problem occurs in blue.

If you want to factor out 2^10, then 2^10 - 2^6 = 2^10[1 - 2^(-4)]
Notice that (2^10)(1) = 2^10, and (2^10)[2^(-4)] = 2^6
This is no different from saying x^10 - x^6 = x^10[1 - x^(-4)]

Of course, it makes more sense to factor out the 10^6 to get:
2^10 - 2^6 = 2^6(2^4 - 1)
This is the similar to x^10 - x^6 = x^6(x^4 - 1)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1