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What is the largest value of integer n such that 98^98 is divisible by

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Joined: 04 Jul 2017
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Location: India
Concentration: Marketing, General Management
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What is the largest value of integer n such that 98^98 is divisible by [#permalink]

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New post 27 Sep 2017, 09:53
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E

Difficulty:

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Question Stats:

79% (00:55) correct 21% (00:14) wrong based on 28 sessions

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What is the largest value of integer \(n\) such that \(98^{98}\) is divisible by \(7^n\) ?

A. 98
B. 105
C. 148
D. 164
E. 196

Do not have the OA.
The question is from gmatclub itself and appeared in QOTD. However, the discussion link is taking us to another question.
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2017, 10:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Joined: 19 Apr 2016
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Re: What is the largest value of integer n such that 98^98 is divisible by [#permalink]

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New post 27 Sep 2017, 10:09
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98=2*7*7
98^98 =2^98 * (7^2)^98 =2^98 * 7^196

So n =196
Hence Option E is correct

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Re: What is the largest value of integer n such that 98^98 is divisible by [#permalink]

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New post 27 Sep 2017, 10:29
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aashishagarwal2 wrote:
What is the largest value of integer \(n\) such that \(98^{98}\) is divisible by \(7^n\) ?

A. 98
B. 105
C. 148
D. 164
E. 196

Do not have the OA.
The question is from gmatclub itself and appeared in QOTD. However, the discussion link is taking us to another question.


\(98^{98}=(2*49)^{98}=(2*7^2)^{98}=2^{98}*7^{196}\). Therefore the largest value of integer \(n\) such that \(2^{98}*7^{196}\) is sidvisible by \(7^n\) is 196.

Answer: E
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Re: What is the largest value of integer n such that 98^98 is divisible by   [#permalink] 27 Sep 2017, 10:29
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What is the largest value of integer n such that 98^98 is divisible by

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