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

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New post 06 Mar 2017, 01:16
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:40) correct 39% (01:49) wrong based on 82 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

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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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New post 06 Mar 2017, 14:27
1
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

Answer: A. A<B<C
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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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New post 06 Mar 2017, 14:42
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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Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true?  [#permalink]

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New post 08 Mar 2017, 01:16
==> 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.
Answer: A
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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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New post 08 Mar 2017, 01:41
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
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Re: Let A=6^20, B=2^60, and C=4^50. Which of the following is true? &nbs [#permalink] 08 Mar 2017, 01:41
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