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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?  [#permalink]

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Updated on: 12 Oct 2013, 09:28
1
2
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Difficulty:

55% (hard)

Question Stats:

65% (02:00) correct 35% (01:27) wrong based on 126 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

My query :
From statement 1-Q can be either 3,7,9. insufficient.
From statement 2-Q can be either 3,7 insufficient(cannot be 9).

combined we know Q can be either 3 or 7, hence answer to this question is C-NO.

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Quant 47-Striving for 50
Verbal 34-Striving for 40

Originally posted by bblast on 17 Jun 2011, 23:27.
Last edited by Bunuel on 12 Oct 2013, 09:28, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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18 Jun 2011, 01:25
1
bblast wrote:
could not find this discussed anywhere :

If n is a positive integer, is (10^n)-1 divisible by Q ?

Q is not divisible by either 5 or 2.
Q is not divisible by 9.

OA is .

My query :

From statement 1-Q can be either 3,7,9. insufficient.
From statement 2-Q can be either 3,7 insufficient(cannot be 9).

combined we know Q can be either 3 or 7, hence answer to this question is C-NO.

Not sure how you got C .
Im getting E
st.1 Q is not divisible by 5 or 2
so Q can be 3,7,9,13,17,.............. not sufficient

st2: Q is not divisible by 9
Q can be 2,3,4,5,6,7,8,13,17......... not sufficient

1 and 2 together

3,7,13,17....

10^n-1 is divisible by 3 but not by 7
hence insufficient . E

Note: where is question its mentioned that Q is a single digit Integer? U can take any number
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18 Jun 2011, 01:28
Oops:

I need to hammer my skull to get things aligned.

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Quant 47-Striving for 50
Verbal 34-Striving for 40
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Re: If n is a positive integer, is (10^n)-1 divisible by Q ?  [#permalink]

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Updated on: 08 Feb 2014, 07:40
bblast wrote:
could not find this discussed anywhere :

If n is a positive integer, is (10^n)-1 divisible by Q ?

Q is not divisible by either 5 or 2.
Q is not divisible by 9.

OA is .

My query :

From statement 1-Q can be either 3,7,9. insufficient.
From statement 2-Q can be either 3,7 insufficient(cannot be 9).

combined we know Q can be either 3 or 7, hence answer to this question is C-NO.

Easier method.

10^n - 1 / q an integer?

So let's say n=1, then we have 9 / q an integer?

Statement 1:

Q not div by 5 or 2, well if q=3 then yes, but if q = 7 the no.
Insuff

Statement 2: q not div by 9

If q = 1 then yes, q = 7 then no
Insuff

Both together

q = 1 then yes, q=7 then no

Hope its clear
Cheers
J

Originally posted by jlgdr on 12 Oct 2013, 07:14.
Last edited by jlgdr on 08 Feb 2014, 07:40, edited 1 time in total.
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Posts: 58453
Re: If n is a positive integer, is (10^n)-1 divisible by Q ?  [#permalink]

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12 Oct 2013, 09:31
jlgdr wrote:
bblast 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

I must have gotten this one wrong, but here is my reasoning.

Statement 1:

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)

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.

Hope it's clear.
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Re: If n is a positive integer, is 10^n - 1 divisible by q?  [#permalink]

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15 Sep 2019, 02:50
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Re: If n is a positive integer, is 10^n - 1 divisible by q?   [#permalink] 15 Sep 2019, 02:50
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