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

 It is currently 18 Apr 2019, 12:15

### 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

# If n is a number such that (−8)^(2n) = 2^(8+2n), then n =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54369
If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

01 Jun 2017, 13:09
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:17) correct 19% (02:04) wrong based on 140 sessions

### HideShow timer Statistics

If n is a number such that $$(−8)^{(2n)} = 2^{(8+2n)}$$, then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

_________________
Intern
Joined: 29 Mar 2016
Posts: 5
Location: United States
Schools: Stern '20
GMAT 1: 720 Q48 V41
GPA: 3
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

01 Jun 2017, 13:39
(−8)^(2n)=2^(8+2n)
(-2)^6n= 2^(8+2n)
If positive, negative does not matter
6n = 8+2n
n=4
D
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

01 Jun 2017, 15:58
1
1
Bunuel wrote:
If n is a number such that $$(−8)^{(2n)} = 2^{(8+2n)}$$, then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

$$(−8)^{(2n)} = 2^{(8+2n)}$$
Any number with negative raised to even number exponent will always be positive. Therefore $$(−8)^{(2n)}$$ can be written as $$(8)^{(2n)}$$

$$(8)^{(2n)} = 2^{(8+2n)}$$

$$2^3^{(2n)} = 2^{(8+2n)}$$

$$2^{6n} = 2^{(8+2n)}$$

Therefore;
6n = 8 + 2n
6n - 2n = 8
4n = 8
n = $$\frac{8}{4}$$ = 2
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

02 Jun 2017, 00:02
2
amastu wrote:
(−8)^(2n)=2^(8+2n)
(-2)^6n= 2^(8+2n)
If positive, negative does not matter
6n = 8+2n
n=4
D

Hi

When you wrote 6n=8+2n, you will get
6n-2n = 8 or 4n = 8 or n=2.

Your approach is correct, probably there was a typo so I am pointing that out.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4419
Location: India
GPA: 3.5
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

02 Jun 2017, 09:39
1
Bunuel wrote:
If n is a number such that $$(−8)^{(2n)} = 2^{(8+2n)}$$, then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

$$(−8)^{(2n)} = 2^{(8+2n)}$$

Or, $$(−2)^{(3*2n)} = 2^{(8+2n)}$$

Or, $${(6n)} = {(8+2n)}$$

Or, $$6n = 8 + 2n$$

Or, $$4n = 8$$

Or, $$n = 2$$

So, Answer must be (C) 2
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5772
Location: United States (CA)
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

05 Jun 2017, 15:50
1
Bunuel wrote:
If n is a number such that $$(−8)^{(2n)} = 2^{(8+2n)}$$, then n =

(A) 1/2
(B) 3/2
(C) 2
(D) 4
(E) 5

The negative sign in front of the 8 will be eliminated because we are raising a negative number (-8) to an even power. Note that (-8)^(2n) = [(-8)^2]^n = [8^2]^n = 8^(2n). Then:

8^(2n) = (2^3)^(2n) = 2^(6n) = 2^(8 + 2n)

Since bases are the same, we can equate the exponents:

6n = 8 + 2n

4n = 8

n = 2

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

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

Manager
Joined: 08 Oct 2016
Posts: 203
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE: Engineering (Telecommunications)
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

10 Jun 2017, 06:37
I guess the only thing which is confusing for student here is
(−8)^(2n)=2^(8+2n)
On left there is negative sign but keep in mind since n will need to be multiplied with even number so result is always even which in turn make bracket value positive
_________________
Got Q42,V17
Target#01 Q45,V20--April End
Manager
Joined: 18 Jun 2017
Posts: 59
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =  [#permalink]

### Show Tags

16 Jul 2017, 22:37
(−8)^(2n) will always result into positive number. Hence correct option is C.
Re: If n is a number such that (−8)^(2n) = 2^(8+2n), then n =   [#permalink] 16 Jul 2017, 22:37
Display posts from previous: Sort by

# If n is a number such that (−8)^(2n) = 2^(8+2n), then n =

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.