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Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 05:08
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Let A=5^30, B=2^70, and C=3^40. Which of the following is true?

A. A<B<C

B. A<C<B

C. B<A<C

D. C<A<B

E. C<B<A

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Last edited by

Bunuel on 10 Oct 2017, 06:39, edited 2 times in total.

Edited the question.

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 05:33
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Please correct the question. There’s a typo error

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:02
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Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:34

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MathRevolution wrote:

Let (CHANGED from what I originally quoted) A=5^30, B=2^70, and C=3^40. Which of the following is true? A. A<B<C B. A<C<B C. B<A<C D. C<A<B E. C<B<A

Make all the exponents the same. They are all multiples of 10.

\(a^{(nm)} = (a^{n})^{m}\)

A = \(5^{30} = (5^3)^{10}\)

B = \(2^{70}\) = \((2^7)^{10}\)

C = \(3^{40}\) = \((3^4)^{10}\)

--------

A= \((125)^{10}\)

B = \((128)^{10}\)

C = \((81)^{10}\)

Now there are manageable bases all to the 10th power.

Answer changed after question was edited C < A < B

ANSWER D

EDITED: my original answer changed after the question was edited. I also changed material in quotations to reflect Bunuel 's edit
Last edited by

genxer123 on 10 Oct 2017, 07:04, edited 3 times in total.

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:40
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Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:44

Bunuel wrote:

genxer123 wrote:

MathRevolution wrote:

Let A=5^30, C=2^70, and B=3^40. Which of the following is true? A. A<B<C B. A<C<B C. B<A<C D. C<A<B E. C<B<A

Hmm. I get Answer C

Make all the exponents the same. They're multiples of 10.

\(a^{(nm)} = (a^{n})^{m}\)

A = \(5^{30} = (5^3)^{10}\)

C = \(2^{70}\) = \((2^7)^{10}\)

B = \(3^{40}\) = \((3^4)^{10}\)

--------

A= \((125)^{10}\)

C = \((128)^{10}\)

B = \((81)^{10}\)

Now there are manageable bases all to the 10th power.

B < A < C

Bunuel , is the OA correct?

There was a typo. The correct ordering is 2^70 > 5^30 > 3^40.

But the signs haven't been changed. They still say "<"

Maybe I'm confused ( wouldn't be the first time) but I think the answer is C

If 2(C) > 5(A) > 3 (B) then

B < A < C

That is ANSWER C... maybe I'm missing something.

Last edited by

genxer123 on 10 Oct 2017, 06:51, edited 1 time in total.

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:49
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Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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10 Oct 2017, 06:52

Bunuel wrote:

genxer123 wrote:

But the signs haven't been changed. They still say "<"

Correct answer: D. C<A<B

(C=3^40) < (A=5^30) < (B=2^70)

Brain fog -- thanks. I kept looking at the prompt as I had quoted it in the original.

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink ]

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12 Oct 2017, 00:46
A=5^30=(5^3)^10=125^10, B=2^70=(2^7)^10=128^10, and C=3^40=(3^4) ^10=81^10.

Since their bases with the exponents 10 are 125, 128 and 81, C < A < B.

Therefore, the answer is D.

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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true?
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12 Oct 2017, 00:46