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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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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Intern  Joined: 27 Apr 2016
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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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4 00:00

Difficulty:   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

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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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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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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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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_________________ 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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