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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
Joined: 16 Aug 2015
Posts: 6629
GMAT 1: 760 Q51 V42
GPA: 3.82
Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true?  [#permalink]

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25 Nov 2018, 23:35
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:21) correct 43% (01:32) wrong based on 35 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?

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

_________________

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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 08 Jan 2013 Posts: 108 Re: Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true? [#permalink] ### Show Tags 26 Nov 2018, 11:34 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 Joined: 16 Aug 2015 Posts: 6629 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] ### Show Tags 28 Nov 2018, 01:09 => $$A = 2^{50} = (2^5)^{10} = (32)^{10}$$ $$B = 3^{30} = (3^3)^{10} = (27)^{10}$$ $$C = 4^{20} = (4^2)^{10} = (16)^{10}$$ Thus, $$(16)^{10} < (27)^{10} < (32)^{10}$$ and $$C < B < A.$$ Therefore, the answer is E. Answer: E _________________ 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"
"Free Resources-30 day online access & Diagnostic Test"
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Re: Let A=2^{50}, B=3^{30}, and C=4^{20}. Which of the following is true? &nbs [#permalink] 28 Nov 2018, 01:09
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