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Manager
Joined: 04 Sep 2006
Posts: 113

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27 Jun 2009, 21:21
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Q : When an integer divided by 35, remainder is 2, when divided by 31, remainder is 3. What is the number?

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Senior Manager
Joined: 04 Jun 2008
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27 Jun 2009, 21:57
number is of form 35K + 2, or 31x + 3

35K + 2 = 31 X + 3
or 31x + 1 is divisible by 35

put values for x as 0,1,2,3, and see for which values it is divisible by 35.

x=9 gives 280 which is divisible by 35.

so the number is 31*9 + 3 = 282

if 282 is not in ans choices, keep adding the LCM of 31 and 35, in this case their product since they are coprime, to the smallest solution ie 282, each number upon adding the LCM to 282 will give the same two remainders respectively.

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Re: REMAINDER   [#permalink] 27 Jun 2009, 21:57
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