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a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?

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a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?  [#permalink]

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New post Updated on: 27 Mar 2019, 07:43
4
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A
B
C
D
E

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  65% (hard)

Question Stats:

58% (01:58) correct 42% (02:05) wrong based on 86 sessions

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\(a = 2^4·5^4\), \(b = 3^4·11^2\), and \(c=2^2·5^6\). Which of the following is true?


A. a > b > c

B. b > a > c

C. b > c > a

D. c > b > a

E. c > a > b
Spoiler: OA

Originally posted by anandgoyal on 17 Jul 2016, 20:03.
Last edited by Bunuel on 27 Mar 2019, 07:43, edited 3 times in total.
Renamed the topic and edited the question.
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Re: a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?  [#permalink]

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New post 17 Jul 2016, 21:27
4
anandgoyal wrote:
\(a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6\) Which of the following is true?


a>b>c

b>a>c

b>c>a

c>b>a

c>a>b

dont forget to kudos


It is easy to compare a and c:

\(a = 2^4·5^4 = 2^2 * 5^4 * 4\)

\(c=2^2·5^6 = 2^2 * 5^4 * 25\)

So c > a

Now compare a and b:

a = 16 * 5 * 125 = 80 * 125
b = 3^4·11^2 = 81 * 121

a > b

Answer: c > a > b
(E)
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Re: a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?  [#permalink]

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New post 27 Oct 2016, 10:50
This one isn't too bad doing long hand.

a = 2^4 x 5^4 = 10^4 = 10,000
b = 3^4 x 11^2 = 81 x 121 = 9,801
c = 10^2 x 5^4 = 62,500

c>a>b

E is correct answer.
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Re: a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?  [#permalink]

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New post 27 Oct 2016, 11:20
anandgoyal wrote:
\(a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6\) Which of the following is true?


a>b>c

b>a>c

b>c>a

c>b>a

c>a>b



\(a = 2^4·5^4 = 10^4\) = 10000
\(b = 3^4·11^2 = 81.121\) ~ 9600
\(c=2^2·5^6 = 10.625\) = 62500

Thus we have - 62500 > 10000 > 9600 Or, c>a>b

Hence , answer will be (E) ...

PS : lawiniecke actual calculation for (B) may not be required , approximation is sufficient here, since the other numbers are wide apart..
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Re: a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?  [#permalink]

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New post 22 Feb 2019, 09:39
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Re: a = 2^4·5^4 b = 3^4·11^2 c=2^2·5^6. Which of the following is true?   [#permalink] 22 Feb 2019, 09:39
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