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

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Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 15

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

CAT Tests
Which is greater: 10^7 or 7^10? [#permalink] New post 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
1 KUDOS received
Director
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

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

Re: Which is greater: 10^7 or 7^10? [#permalink] New post 27 Oct 2017, 02:35
1
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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
2 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1230
Followers: 45

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

Re: Which is greater: 10^7 or 7^10? [#permalink] New post 30 Oct 2017, 14:43
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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

Answer: B

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
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Re: Which is greater: 10^7 or 7^10?   [#permalink] 30 Oct 2017, 14:43
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Which is greater: 10^7 or 7^10?

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