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# DS remainder and divisibility

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Manager
Joined: 11 Jul 2004
Posts: 119
DS remainder and divisibility [#permalink]

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26 Aug 2004, 15:08
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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
Senior Manager
Joined: 25 Jul 2004
Posts: 273

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26 Aug 2004, 16:19
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
26 Aug 2004, 16:19
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# DS remainder and divisibility

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