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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

If 2^x−2^(x−2)=3∗2^(13) what is the value of x?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members
Thanked: 1 times
by M7MBA » Fri Apr 20, 2018 2:11 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

$$If\ \ \ 2^x−2^{\left(x-2\right)}=3\cdot2^{13}\ \ ,\ what\ \ \ is\ \ the\ \ value\ \ of\ \ \ x?$$ A. 9
B. 11
C. 13
D. 15
E. 17

The OA is the option D.

What is the best way to solve this PS question? Should I try option by option? I need some help. Thanks in advanced.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times

by Vincen » Fri Apr 20, 2018 2:48 am
Hi M7MBA.

I'd solve this PS question rewriting the expression as follows:

$$2^x-2^{\left(x-2\right)}=3\cdot2^{13}\ \ \ \Rightarrow\ \ \ 2^{x-2}\cdot2^2\ -\ 2^{x-2}=3\cdot2^{13}$$ $$\Rightarrow\ \ 2^{x-2}\left(2^2\ -\ 1\right)=3\cdot2^{13}\ $$ $$\Rightarrow\ \ 2^{x-2}\left(3\right)=3\cdot2^{13}\ $$ $$\Rightarrow\ \ 3\cdot2^{x-2}=3\cdot2^{13}\ $$ $$\Rightarrow\ \ x-2=13$$ $$\Rightarrow\ \ x=15.$$ This way, we get that the correct answer is the option D.

I hope it helps.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:52 pm
M7MBA wrote:$$If\ \ \ 2^x−2^{\left(x-2\right)}=3\cdot2^{13}\ \ ,\ what\ \ \ is\ \ the\ \ value\ \ of\ \ \ x?$$ A. 9
B. 11
C. 13
D. 15
E. 17

From the left side of the equation, we first pull out the common factor 2^(x - 2) from each term. We can then simplify the given equation:

2^(x - 2)[2^2 - 1] = 3 x 2^13

2^(x - 2)[4 - 1] = 3 x 2^13

2^(x - 2)[3] = 3 x 2^13

2^(x - 2) = 2^13

x - 2 = 13

x = 15

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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] » Mon Apr 23, 2018 7:36 pm
Hi All,

While this question might look a bit 'scary', you can solve it with a mix of TESTing THE ANSWERS and Arithmetic.

To start, it's worth noting that the 'right side' of the equation is MORE than 2^13. The 'left side' of the equation is 2^X - (another value), so we know that X MUST be greater than 13. Based on the 'spread' of the Answer choices, the correct answer MUST be either D or E. Since 2^17 is considerably bigger than 2^15, let's TEST Answer D first....

Answer D: 15
IF X = 15.....

2^15 - 2^13..... can be rewritten as...
(2^13)(2^2 - 1) =
(2^13)(3)

This is an exact match for the 'right side' of the equation, so this MUST be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1