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# Let A=6^20, B=2^60, and C=4^50. Which of the following is true?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Let A=6^20, B=2^60, and C=4^50. Which of the following is true? [#permalink]

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06 Mar 2017, 00:16
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Question Stats:

53% (01:10) correct 47% (01:03) wrong based on 73 sessions

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$$Let A=6^2^0, B=2^6^0, and C=4^5^0.$$

Which of the following is true?

A. A<B<C
B. A<C<B
C. B<A<C
D. B<C<A
E. C<B<A
[Reveal] Spoiler: OA

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Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true? [#permalink]

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06 Mar 2017, 13:27
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A = 6^20, can be written as 3^20 * 2^20
B = 2^60, can be written as 4^20 * 2^20
C = 4^50, can be written as 4^20 * 2^60

Therefore, A < B < C

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Joined: 17 Oct 2016
Posts: 8
Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true? [#permalink]

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06 Mar 2017, 13:42
OA it's not correct, C > B for sure because 2^60<2^100. The answer is or E or B. Since 6^20=3^20 x 2^20 (A) and 2^20 x 2^80 (C) i believe that 2^80 > 3^20 so to me the correct answer is E.
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true? [#permalink]

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08 Mar 2017, 00:16
==> You can compare the big and small numbers by making the base or the exponent the same. From$$A=6^2^0, B=2^6^0=(2^3)^2^0=8^2^0$$,
you get 6<8, which becomes A<B, and from $$B=2^6^0=(2^2)^3^0=4^3^0, C=4^5^0,$$
you get 30<50, which becomes B<C.

Thus, you get A<B<C. The answer is A.
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Joined: 05 Jan 2017
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Location: India
Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true? [#permalink]

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08 Mar 2017, 00:41
A = 6^20
B = 2^60 = 8^20
C = 4^50 = 2^100

we can see that 6^20<8^20 or A<B
also we can see that 2^60 <2^100 or B<C

hence A<B<C

Option A
Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true?   [#permalink] 08 Mar 2017, 00:41
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