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# Collection of remainder problems in GMAT

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Intern
Joined: 01 May 2017
Posts: 32
Collection of remainder problems in GMAT [#permalink]

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01 Jul 2017, 04:53
peraspera

if you see the "power cycle of 3" i.e 3^1, 3^2, 3^3, 3^4, 3^5, 3^6, 3^7, 3^8, 3^9, 3^10,...... the units digit is 3,9,7,1,3,9,7,1,3,9 and so on. SO you see the 3,9,7,1 pattern continues.

In the given question when m=1, we get 3^(4n+2+1)=3^(4n+3) . From the "power cycle of 3" we can see that every 4th power of 3 will end in 1 and 3 places ahead on the power cycle would have a unit digit of 7.

Remainder when a number is divided by 10 would be the units digit of that number. For the question above as we have solved the units digit would be 7 and hence remainder would be 7.

Hope this helps.

Regards,
Shreya
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Joined: 25 Aug 2017
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Re: Collection of remainder problems in GMAT [#permalink]

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28 Oct 2017, 08:40
when the positive integer x is divided by 9 the remainder is 5 . what is the remainder when 3x is divided by 9?
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Joined: 02 Sep 2009
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Re: Collection of remainder problems in GMAT [#permalink]

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28 Oct 2017, 08:42
SHATHY wrote:
when the positive integer x is divided by 9 the remainder is 5 . what is the remainder when 3x is divided by 9?

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Re: Collection of remainder problems in GMAT   [#permalink] 28 Oct 2017, 08:42

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# Collection of remainder problems in GMAT

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