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If n is a positive integer, is 10^n - 1 divisible by q?

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If n is a positive integer, is 10^n - 1 divisible by q?

Post Fri Dec 15, 2017 7:10 am
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

The OA is E.

Can any expert help me here? I do not know how to explain that none of the statements is enough. Thanks in advanced.

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Post Fri Dec 15, 2017 8:09 am
VJesus12 wrote:
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

The OA is E.

Can any expert help me here? I do not know how to explain that none of the statements is enough. Thanks in advanced.
Statement 1 -
Case 1: n = 1; q = 1. 10^n - 1 = 9; 9 is divisible by 1, so we have a YES
Case 2: n = 1; q = 7 . 10^n - 1 = 9; 9 is not divisible by 7 so we have a NO.
Statement 1 is not sufficient.

Statement 2:
We can use the same cases we used for statement 1, as neither 1 nor 7 is divisible by 9, so we can generate a YES and a NO both for statement 2 and for the statements together, meaning that even together, the statements are not sufficient.

The answer is E

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