It is currently 21 Aug 2019, 08:21

### 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

# What is the value of n if

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 [0], given: 7032

What is the value of n if [#permalink]  23 Jan 2019, 16:09
Expert's post
00:00

Question Stats:

86% (01:05) correct 13% (00:31) wrong based on 15 sessions
What is the value of n if $$4^{10} × 64^2 = 16^2 × 4^n$$? ​

A. 6

B. ​10

C. ​12

D. 15

E. 30
[Reveal] Spoiler: OA

_________________
Intern
Joined: 07 Jan 2019
Posts: 38
Followers: 0

Kudos [?]: 21 [1] , given: 11

Re: What is the value of n if [#permalink]  27 Jan 2019, 08:36
1
KUDOS
Solution,

4 ^ 10 * 64 ^ 2 = 16 ^ 2 * 4 ^ n

or, 4 ^ 10 * 4 ^ 3*2 = 4 ^ 2 *2 * 4 ^ n

or, 4 ^ 10+6 = 4 ^ 4+n

or, 10 + 6 = 4 + n

or, n = 16 - 4

or, n = 12

GRE Instructor
Joined: 10 Apr 2015
Posts: 2303
Followers: 72

Kudos [?]: 2190 [1] , given: 26

Re: What is the value of n if [#permalink]  27 Jan 2019, 10:22
1
KUDOS
Expert's post
Carcass wrote:
What is the value of n if $$4^{10} × 64^2 = 16^2 × 4^n$$? ​

A. 6

B. ​10

C. ​12

D. 15

E. 30

Let's rewrite all terms with 4 as the base

GIVEN: $$4^{10} × 64^2 = 16^2 × 4^n$$

Rewrite $$64$$ and $$16$$ as $$4^3$$ and $$4^2$$ to get: $$4^{10} × (4^3)^2 = (4^2)^2 × 4^n$$

Simplify by applying the Power of a Power law: $$4^{10} × 4^6 = 4^4 × 4^n$$

Simplify by applying the Product law: $$4^{16} = 4^{4+n}$$

This means: $$16 = 4+n$$

Solve: $$n = 12$$

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: What is the value of n if   [#permalink] 27 Jan 2019, 10:22
Display posts from previous: Sort by