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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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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Updated on: 10 Oct 2017, 06:39
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Difficulty:

65% (hard)

Question Stats:

45% (01:39) correct 55% (01:48) wrong based on 83 sessions

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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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 10 Oct 2017, 05:08. Last edited by Bunuel on 10 Oct 2017, 06:39, edited 2 times in total. Edited the question. Senior Manager Joined: 17 Oct 2016 Posts: 321 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 10 Oct 2017, 05:33 1 Please correct the question. There’s a typo error Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks Math Expert Joined: 02 Sep 2009 Posts: 50623 Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 10 Oct 2017, 06:02 Sasindran wrote: Please correct the question. There’s a typo error Posted from my mobile device ________________ Edited. Thank you. _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 2102 Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags Updated on: 10 Oct 2017, 07:04 1 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 Originally posted by generis on 10 Oct 2017, 06:34. Last edited by generis on 10 Oct 2017, 07:04, edited 3 times in total. Math Expert Joined: 02 Sep 2009 Posts: 50623 Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 10 Oct 2017, 06:40 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. _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 2102 Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags Updated on: 10 Oct 2017, 06:51 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. Originally posted by generis on 10 Oct 2017, 06:44. Last edited by generis on 10 Oct 2017, 06:51, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 50623 Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 10 Oct 2017, 06:49 1 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) _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 2102 Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6517 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? [#permalink] ### Show Tags 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Let A=5^30, B=2^70, and C=3^40. Which of the following is true? &nbs [#permalink] 12 Oct 2017, 00:46
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