It is currently 10 Dec 2018, 09:33

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

Which is greater: 10^7 or 7^10?

Author Message
TAGS:
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 15

Kudos [?]: 49 [0], given: 220

Which is greater: 10^7 or 7^10? [#permalink]  26 Oct 2017, 23:42
00:00

Question Stats:

81% (00:47) correct 18% (00:06) wrong based on 16 sessions
 Quantity A Quantity B 10^7 7^10

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 330 [1] , given: 66

Re: Which is greater: 10^7 or 7^10? [#permalink]  27 Oct 2017, 02:35
1
KUDOS
One way to solve it could be to rewrite $$7^10 = 7^7 7^3$$ and divide both sides by $$7^7$$. Thus, we have to compare $$\frac{10}{7}^7$$ and $$7^3$$. Given that 10/7 is roughly 1.5, it is easy to notice that quantity B is greater. Answer B
GRE Instructor
Joined: 10 Apr 2015
Posts: 1230
Followers: 45

Kudos [?]: 1108 [2] , given: 7

Re: Which is greater: 10^7 or 7^10? [#permalink]  30 Oct 2017, 14:43
2
KUDOS
Expert's post
Bunuel wrote:
 Quantity A Quantity B 10^7 7^10

We can solve this question using matching operations

Given:
Quantity A: 10^7
Quantity B: 7^10

Divide both quantities by 7^7 to get;
Quantity A: (10^7)/(7^7)
Quantity B: (7^10)/(7^7)

Simplify to get;
Quantity A: (10/7)^7
Quantity B: 7^3

ASIDE: If you're wondering how I got (10/7)^7 for Quantity A, I used a nice rule that says (b^x)/c^x) = (b/c)^x

Evaluate 7^3 to get;
Quantity A: (10/7)^7
Quantity B: 343

First recognize that 2^7 = 128
Since 10/7 is LESS THAN 2, we can conclude that (10/7)^7 is some number less than 128
So we have:
Quantity A: some number less than 128
Quantity B: 343

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: Which is greater: 10^7 or 7^10?   [#permalink] 30 Oct 2017, 14:43
Display posts from previous: Sort by