GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 06:34 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 2^n+2^n-2=5120, then n=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

1
1 00:00

Difficulty:   25% (medium)

Question Stats: 77% (01:51) correct 23% (02:05) wrong based on 70 sessions

### HideShow timer Statistics

[GMAT math practice question]

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

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

_________________
Manager  S
Joined: 08 Sep 2008
Posts: 131
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

### Show Tags

E
2^n-2=5120/5
n-2=10
n=12

Sent from my ASUS_Z010D using GMAT Club Forum mobile app
Senior Manager  G
Joined: 17 Oct 2016
Posts: 305
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

### Show Tags

E

Method 1:

2^10 = 1024. This cannot be the value of n. So A, B and C are out.

When n=11, 2^11= 2048 and 2^9=512. Hence n cannot be 11. So E is the only possible value.

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

2^n*(1+1/4) =5120
2^n*(5/4) = 5120
2^n =1096*4
2^n =2^12
n = 12

Posted from my mobile device

Posted from my mobile device
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

### Show Tags

=>
Factoring yields
$$2^n+2^{n-2}=2^22^{n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024.$$
Therefore,
$$2^{n-2}=1024=2^{10}$$
and
$$n-2 = 10.$$
It follows that
$$n = 12.$$

_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

### Show Tags

1
MathRevolution wrote:

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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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

Non-Human User Joined: 09 Sep 2013
Posts: 13722
Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If 2^n+2^n-2=5120, then n=?   [#permalink] 23 Mar 2019, 14:47
Display posts from previous: Sort by

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