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Re: If n is a positive integer, is (10^n)-1 divisible by Q ? [#permalink]
12 Oct 2013, 08:31
If n is a positive integer, is 10^n - 1 divisible by q?
(1) q is not divisible by either 5 or 2 (2) q is not divisible by 9
I must have gotten this one wrong, but here is my reasoning.
Q is not divisible by either 2 or 5 says that 10n is not a multiple of q. But we don't know if 10^n-1 could be because 1 of course is not a multiple of 10. Remember when we If you add (or subtract) two multiples of N, the result is always a multiple of N but If you add two non-multiples of N, the result could be either a multiple of N or a non-multiple of N. So in this case, we don't know
Further more as n has to be a postiive integer than 10 is at least 10, so our possible values are 9,99,999 etc...
Statement 2: If q is not divisible by 9 then IMO 10^n-1 is not divisible by 9 for the reason mentioned above.
Hence IMO answer should be (B)
Experts please advice Cheers
Say n=1. Then 10^n-1=9.
Now, if q=1, then 9 IS divisible by q but if q=7, then 9 is NOT divisible by q.
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