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If and and m are positive integers,then what is the remainder of a^m/3

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susheelh
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If and and m are positive integers,then what is the remainder of a^m/3 [#permalink] New post   Updated on: 26 Jun 2016, 00:14
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C
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E

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55% (hard)

Question Stats:

64% (01:44) correct 36% (02:03) wrong based on 14 sessions
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If a and m are positive integers, then what is the remainder of a^m/3 ?

(1) m is even.
(2) a is prime number greater than 9.

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Hello,

I have recently started my GMAT preparation. I am new to this forum. Not sure if this DS question is asked before. Sticking my neck out and asking this question again.

I can see that statement 1 is not sufficient. Statement 2 also does not look sufficient. I have read the section on remainders by Bunuel and understand that the remainder could be 0, 1 or 2. By pure trial and error I think I found the answer.

Can you please suggest what would be the right approach to solve this question?

Thanks in advance!


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Official Answer
C

Originally posted by susheelh on 26 Jun 2016, 00:09.
Last edited by Bunuel on 26 Jun 2016, 00:14, edited 1 time in total.
Edited the question.
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paidlukkha
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Re: If and and m are positive integers,then what is the remainder of a^m/3 [#permalink] New post   26 Jun 2016, 03:03
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Kudos
given a>0 m>0
S1 m = even
1^2 = 1, R 1
3^2 = 9, R O

S2
11/3, R 2
7/3, R 1

Combine
11^2/3 = 1
17^2/3 = 1
Hence C
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Re: If and and m are positive integers,then what is the remainder of a^m/3 [#permalink] New post   26 Jun 2016, 03:47
Hello Paidlukkha!

Thanks for the quick response!

Now when I look closely at it, it looks like

1. Square of any number when divided by 3 gives either a Zero or one as remainder.

2. Any Prime number when divided by 3 gives either 2 or 3 as remainder

3. Square of any prime number when divided by 3 gives one as remainder.

Am I correct in these three generalisations?

If yes - is there any reason why this is so?

PS: Hope this is the right forum to ask clarifications on questions


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Re: If and and m are positive integers,then what is the remainder of a^m/3 [#permalink]
26 Jun 2016, 03:47
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