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The remainder when 7^84 is divided by 342 is :

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The remainder when 7^84 is divided by 342 is :  [#permalink]

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New post 26 Feb 2014, 10:03
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Difficulty:

  25% (medium)

Question Stats:

74% (01:58) correct 26% (02:09) wrong based on 64 sessions

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The remainder when 7^84 is divided by 342 is:

A. 0
B. 1
C. 49
D. 51
E. 341

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Re: The remainder when 7^84 is divided by 342 is :  [#permalink]

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New post 26 Feb 2014, 13:38
ankur1901 wrote:
The remainder when 7^84 is divided by 342 is :

1. 0
2. 1
3. 49
4. 341

Dear ankur1901,

First, let me make perfectly clear: this is NOT a GMAT question. This is far too advanced for anything on the GMAT. This is getting into mathematical hot-shot territory.

Step one is to notice that 342 = 343 -1, and of course, 343 = 7^3, so 342 = (7^3) - 1.

Step two is to remember that (a^n - 1) is divisible by (a^m - 1) if n is divisible by m. Obviously, 84 is divisible by 3. Therefore:

[(7^84) - 1] must be divisible by [(7^3) - 1] = 342

If 342 goes evenly into [(7^84) - 1], then it must divide into (7^84) leaving a remainder of 1.

Does all this make sense?

Mike :-)
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Magoosh Test Prep


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Re: The remainder when 7^84 is divided by 342 is :  [#permalink]

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New post 26 Feb 2014, 18:35
ankur1901 wrote:
The remainder when 7^84 is divided by 342 is :

1. 0
2. 1
3. 49
4. 341


Hi Ankur,

For this kind of problems, the best approach is to find the power of the dividend which is closest to divisor(or the multiple of the divisor)

7 cube = 343
Divisor = 342

343/342 => reminder =1
as 7^84 can be written as (7^3)^28 = the result is 1^28 =>1
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Re: The remainder when 7^84 is divided by 342 is :  [#permalink]

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New post 11 Jan 2019, 22:43
7^84/ 342
(7*7*7)^21/342
343^21/342
Acc to remainder theorem n^x/z if n/z gives remainder r then n^x/z gives remainder r

Ans B 1 or 1^21=1

Thanks
GMAT Club Bot
Re: The remainder when 7^84 is divided by 342 is :   [#permalink] 11 Jan 2019, 22:43
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