• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If 2^n+2^n-2=5120, then n=?

This topic has 4 expert replies and 0 member replies

GMAT/MBA Expert

If 2^n+2^n-2=5120, then n=?

Post
[GMAT math practice question]

$$If\ \ 2^n+2^{n-2}=5120,\ then\ n=?$$

A. 8
B. 9
C. 10
D. 11
E. 12

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Max@Math Revolution wrote:
[GMAT math practice question]

$$If\ \ 2^n+2^{n-2}=5120,\ then\ n=?$$

A. 8
B. 9
C. 10
D. 11
E. 12
We can PLUG IN THE ANSWERS, which represent the value of n.
When the correct answer is plugged in, the given expression will be equal to 5120.

D: n=11
Plugging n=11 into the given expression, we get:
2¹¹ + 2¹¹¯² = 2¹¹ + 2⁹ = 2⁹(2² + 1) = 512(5) = 2560.
Since the result is too small, the value of n must be GREATER than 11.

The correct answer is D.

To solve algebraically, factor out the SMALLER EXPONENT.
Here, the smaller exponent is n-2:

$$\\2^n+2^{n-2}=5120\\$$
$$\\2^{n-2}(2^2 + 1)=5120\\$$
$$\\2^{n-2}(5)=5120\\$$
$$\\2^{n-2}=1024\\$$
$$\\2^{n-2}=2^{10}\\$$
$$\\n-2=10\\$$
$$\\n=12\\$$

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
Quote:
$$If\ \ 2^n+2^{n-2}=5120,\ then\ n=?$$

A. 8
B. 9
C. 10
D. 11
E. 12
Hi Max@Math Revolution,
Let's take a look at your question.

$$2^n+2^{n-2}=5120$$
$$2^n+2^n.2^{-2}=5120$$

Taking 2^n as a common factor:
$$2^n\left(1+2^{-2}\right)=5120$$
$$2^n\left(1+\frac{1}{2^2}\right)=5120$$
$$2^n\left(1+\frac{1}{4}\right)=5120$$
$$2^n\left(\frac{5}{4}\right)=5120$$
$$2^n=5120\times\frac{4}{5}$$
$$2^n=1024\times4$$
$$2^n=2^{10}\times2^2$$
$$2^n=2^{12}$$
$$n=12$$

Therefore, option E is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2494 messages
Followed by:
32 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>
Factoring yields
2^n+2^{n-2}=2^2^{2n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024.
Therefore,
2^{n-2}=1024=2^{10}
and
n-2 = 10.
It follows that
n = 12.

Therefore, the answer is E.
Answer : E

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[GMAT math practice question]

$$If\ \ 2^n+2^{n-2}=5120,\ then\ n=?$$

A. 8
B. 9
C. 10
D. 11
E. 12
We can simplify the given equation:

2^n + 2^(n-2) = 5120

2^n + 2^n x 2^-2 = 5120

Factoring the common factor of 2^n from both terms on the left side of the equation, we have:

2^n(1 + 2^-2) = 5120

2^n(1 + 1/4) = 5120

2^n(5/4) = 5120

2^n = 5120 x 4/5

2^n = 4096

n = 12

Answer: E

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

Top First Responders*

1 Ian Stewart 43 first replies
2 Brent@GMATPrepNow 35 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 19 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

149 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

53 posts
4 image description Ian Stewart

GMATiX Teacher

52 posts
5 image description GMATGuruNY

The Princeton Review Teacher

32 posts
See More Top Beat The GMAT Experts