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# M12-02

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Math Expert
Joined: 02 Sep 2009
Posts: 50585

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15 Sep 2014, 23:46
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Difficulty:

65% (hard)

Question Stats:

56% (01:08) correct 44% (01:05) wrong based on 118 sessions

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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.

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15 Sep 2014, 23:46
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Official Solution:

Statements (1) and (2) combined are insufficient. Consider:

$$q = 3$$, $$n = 1$$ - the answer is "yes";

$$q = 7$$, $$n = 1$$ - the answer is "no".

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19 Aug 2015, 07:09
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mhhh, what is wrong with this :

10^n - 1 can be 9, 99, 999, 9999 so it seems to me that if q is not divisible by q then we can assure that it is not divisible by q.
Any help to explain where I am wrong ?
thanks
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19 Aug 2015, 09:10
Barnal wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mhhh, what is wrong with this :

10^n - 1 can be 9, 99, 999, 9999 so it seems to me that if q is not divisible by q then we can assure that it is not divisible by q.
Any help to explain where I am wrong ?
thanks

What do you mean by above? What are you trying to say?
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14 Oct 2015, 10:46
Offtopic question: if a number is divisible by q (and q is not specified) does this mean that q is an integer? Can q be negative? Or a fraction? Basically I would like to know if divisibility by q implies that q is a positive integer even though it is not stated.
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14 Oct 2015, 11:01
Skytail wrote:
Offtopic question: if a number is divisible by q (and q is not specified) does this mean that q is an integer? Can q be negative? Or a fraction? Basically I would like to know if divisibility by q implies that q is a positive integer even though it is not stated.

when the question discusses divisibility, it implies integers only.
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Joined: 29 Oct 2014
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04 Feb 2016, 17:08
Barnal wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mhhh, what is wrong with this :

10^n - 1 can be 9, 99, 999, 9999 so it seems to me that if q is not divisible by q then we can assure that it is not divisible by q.
Any help to explain where I am wrong ?
thanks

I would like to repeat Barnel's question .. 10 ^n - 1 should be 9, 99 (as n > 0 ) etcc which should be a multiple of 9 .. and as per the second option it is given that the Q is not divisible by 9
Then if Q is not divisible by 9 then the number in question (10 ^n - 1) should also be indivisible by Q right ?

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05 Feb 2016, 00:37
anuharidas wrote:
Barnal wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mhhh, what is wrong with this :

10^n - 1 can be 9, 99, 999, 9999 so it seems to me that if q is not divisible by q then we can assure that it is not divisible by q.
Any help to explain where I am wrong ?
thanks

I would like to repeat Barnel's question .. 10 ^n - 1 should be 9, 99 (as n > 0 ) etcc which should be a multiple of 9 .. and as per the second option it is given that the Q is not divisible by 9
Then if Q is not divisible by 9 then the number in question (10 ^n - 1) should also be indivisible by Q right ?

q could be 3 (NOT divisible by 9), but 10^n - 1 will be divisible by q.
q could be 7 (NOT divisible by 9), n could be 1, and 10^n - 1 will NOT be divisible by q.
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23 Jul 2016, 02:10
I think this is a high-quality question and I agree with explanation. This is a great question but must be a 700 level question and not 600 level. Not sure how you classified this as 600
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28 Aug 2018, 23:37
Bunuel wrote:
Barnal wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mhhh, what is wrong with this :

10^n - 1 can be 9, 99, 999, 9999 so it seems to me that if q is not divisible by q then we can assure that it is not divisible by q.
Any help to explain where I am wrong ?
thanks

What do you mean by above? What are you trying to say?

I think, the question he/she is trying to make is that in Statement -2 if q is not divisible by 9 then why St-2 can't be Sufficient.

But here the thing is if q is not divisible by 9 then q could be divisible by 11 or 3. So Statement-2 is clearly Not-Sufficient.
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Hope it's clear.
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M12-02 &nbs [#permalink] 28 Aug 2018, 23:37
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# M12-02

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