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Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?  [#permalink]

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New post 26 Nov 2018, 00:35
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (01:31) correct 42% (01:27) wrong based on 49 sessions

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[Math Revolution GMAT math practice question]

Let \(A=2^{50}, B=3^{30}\), and \(C=4^{20}.\) Which of the following is true?

\(A. A<B<C\)
\(B. A<C<B\)
\(C. B<A<C\)
\(D. B<C<A\)
\(E. C<B<A\)

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Re: Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?  [#permalink]

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New post 26 Nov 2018, 12:34
3
C = 4^20 = 2^40 = (2^4)^10 = (16)^10
B = 3^30 = (3^3)^10 = (27)^10
A = 2^50 = (2^5)^10 = (32)^10

16 < 27 < 32, therefore (16)^10 < (27)^10 < (32)^10

So, C<B<A.

Answer => E.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7361
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?  [#permalink]

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New post 28 Nov 2018, 02:09
1
=>

\(A = 2^{50} = (2^5)^{10} = (32)^{10}\)
\(B = 3^{30} = (3^3)^{10} = (27)^{10}\)
\(C = 4^{20} = (4^2)^{10} = (16)^{10}\)

Thus, \((16)^{10} < (27)^{10} < (32)^{10}\) and \(C < B < A.\)

Therefore, the answer is E.
Answer: E
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Re: Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?   [#permalink] 28 Nov 2018, 02:09
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Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?

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