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DS remainder and divisibility

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DS remainder and divisibility [#permalink] New post 26 Aug 2004, 14:08
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hi i dont relaly have a official question but i am having trouble with DS with remainders

eg:

is n divisible by 7 or what is the remainder when n is divided by 7

1. when x is dividived by 6 the remainder is 1
2. when x is divided by 10 the remainder is 2

THIS IS JUST A MOCK question (you may not be able to solve it)

just owndeirng what the best approach to solving these type of questions is and if anyone has any examples

thanks
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 [#permalink] New post 26 Aug 2004, 15:19
If i were to attack this problem, i would begin by getting a feel for the numbers...

ssuming n is positive

1. when x is dividived by 6 the remainder is 1
x could be 1, 7, 13, 19, 25, 31, 37 etc... clearly this adds nothing
mathematically, this tells us that x=6K + 1 for some k

2. when x is divided by 10 the remainder is 2
x coule be 2,12,22,32,42,52,62 etc.. clearly this doesn't solve the problem

the union of these sequences tells us however that x will never be divisble by 7, because the union of the sequences is the empty set.

tog
  [#permalink] 26 Aug 2004, 15:19
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