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Senior Manager Joined: 20 May 2014
Posts: 282
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Kudos [?]: 50 , given: 220

Which is greater: 10^7 or 7^10? [#permalink] 00:00

Question Stats: 71% (01:00) correct 28% (00:07) wrong based on 21 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 [?]: 344  , given: 66

Re: Which is greater: 10^7 or 7^10? [#permalink]
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: 1530
Followers: 55

Kudos [?]: 1456  , given: 8

Re: Which is greater: 10^7 or 7^10? [#permalink]
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 Sign up for our free GRE Question of the Day emails Re: Which is greater: 10^7 or 7^10?   [#permalink] 30 Oct 2017, 14:43
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