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# Let A=2^50, B=3^30, and C=5^20. Which of the following is true?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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20 Feb 2018, 00:38
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45% (medium)

Question Stats:

58% (01:28) correct 42% (01:50) wrong based on 99 sessions

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[GMAT math practice question]

Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Community Reply Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 03:48 5 1 1 MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. A<B<C B. A<C<B C. C<A<B D. B<C<A E. C<B<A HCF of $$50$$, $$30$$ & $$20$$ is $$10$$, so arrange the numbers to the power of $$10$$ to get a clear picture $$A=2^{50}=(2^5)^{10}=32^{10}$$ $$B=3^{30}=(3^3)^{10}=27^{10}$$ $$C=5^{20}=(5^2)^{10}=25^{10}$$ Clearly, $$A>B>C$$ Option E ##### General Discussion Current Student Joined: 07 Jan 2016 Posts: 1086 Location: India GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 03:46 MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. A<B<C B. A<C<B C. C<A<B D. B<C<A E. C<B<A Unconventional method No of digits in A= 2^50 = 50 log 2 ( here log 2 is of the base 10 ) = 50 x 0.3010 = 15.xx = 15 + 1 = 16 digits No of digits in B = 3^30 = 30 log 3 = 30 x .4771 = 14.xx = 14 +1 = 15 digits No of digits in C = 5^20 = 20 log 5 = 20 x 0.69 = 13.xx = 14 digits Now greater the digits greater the number ( in positive numbers) thus C<B<A / A > B>C (E) imo PS- don't try this on the gmat if you are not sure of Log values I'm sure there are other ways to solve this but this was the only method I could think of Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 03:50 Hatakekakashi wrote: MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. AB. AC. CD. BE. C Unconventional method No of digits in A= 2^50 = 50 log 2 ( here log 2 is of the base 10 ) = 50 x 0.3010 = 15.xx = 15 + 1 = 16 digits No of digits in B = 3^30 = 30 log 3 = 30 x .4771 = 14.xx = 14 +1 = 15 digits No of digits in C = 5^20 = 20 log 5 = 20 x 0.69 = 13.xx = 14 digits Now greater the digits greater the number ( in positive numbers) thus C B>C (E) imo PS- don't try this on the gmat if you are not sure of Log values I'm sure there are other ways to solve this but this was the only method I could think of hi Hatakekakashi Truly unconventional I am sure hardly anyone of us would remember log values at this age Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 03:51 Bunuel :-> Similar Que https://gmatclub.com/forum/let-a-5-30-b ... fl=similar Let A=2^50, B=3^30, and C=5^20. Which of the following is true? A=32^10, B=27^10 & C=25^10 E. C A. AB. AC. CD. BE. C_________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Current Student Joined: 07 Jan 2016 Posts: 1086 Location: India GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 03:54 niks18 wrote: hi Hatakekakashi Truly unconventional I am sure hardly anyone of us would remember log values at this age haha :D well that's true but squares 1-50 cubes 1 - 15 0 is not positive log 1 to 5 1 is not prime i do remember these things most of the times Director Joined: 31 Jul 2017 Posts: 512 Location: Malaysia Schools: INSEAD Jan '19 GMAT 1: 700 Q50 V33 GPA: 3.95 WE: Consulting (Energy and Utilities) Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags Updated on: 20 Feb 2018, 07:55 MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. A<B<C B. A<C<B C. C<A<B D. B<C<A E. C<B<A We can write as - $$A = (1024)^{5}, B = (729)^{5}, C = (625)^{5} Hence, A>B>C$$ _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Originally posted by rahul16singh28 on 20 Feb 2018, 07:47. Last edited by rahul16singh28 on 20 Feb 2018, 07:55, edited 1 time in total. Current Student Joined: 07 Jan 2016 Posts: 1086 Location: India GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 07:50 rahul16singh28 wrote: MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. A<B<C B. A<C<B C. C<A<B D. B<C<A E. C<B<A We can write as - $$A = (1024)^{50}, B = (729)^{5}, C = (625)^{5} Hence, A>B>C$$ 1024^5 you mean? Posted from my mobile device Posted from my mobile device Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 20 Feb 2018, 08:39 Hatakekakashi wrote: rahul16singh28 wrote: MathRevolution wrote: [GMAT math practice question] Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true? A. A<B<C B. A<C<B C. C<A<B D. B<C<A E. C<B<A We can write as - $$A = (1024)^{50}, B = (729)^{5}, C = (625)^{5} Hence, A>B>C$$ 1024^5 you mean? Posted from my mobile device Posted from my mobile device 1024^5 you mean? (2^10)^5=1024^5 _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? [#permalink] ### Show Tags 22 Feb 2018, 02:10 => If we wish to compare these numbers, we need to either make their bases the same or make their exponents the same. In this case, it is easiest to make all exponents the same as follows: $$A=2^{50} = (2^5)^{10} = 32^{10}$$ $$B=3^{30} = (3^3)^{10} = 27^{10}$$ $$C=5^{20} = (5^2)^{10} = 25^{10}$$ Since $$32 > 27 > 25$$, we must have $$A > B > C$$. Therefore, the answer is E. Answer: E _________________ 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$79 for 1 month Online Course"
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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20 Apr 2019, 22:41
MathRevolution wrote:
[GMAT math practice question]

Let $$A=2^{50,} B=3^{30}$$, and $$C=5^{20}$$. Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A

We can write this as (2^5)^10 , (3^3)^10, (5^2)^10 --> A= 32^10, B= 27^10, C= 25^10
From this we can see that C<B<A
Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?   [#permalink] 20 Apr 2019, 22:41
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