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# If q is a positive integer less than 17 and r is the

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Intern
Joined: 30 Aug 2010
Posts: 13
If q is a positive integer less than 17 and r is the  [#permalink]

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13 Sep 2010, 08:37
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Difficulty:

55% (hard)

Question Stats:

55% (01:33) correct 45% (01:43) wrong based on 240 sessions

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If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?

(1) q>10
(2) q=2^k, where k is a positive integer

I have the official answer to this question, but I'm quite sure it's not correct.
Math Expert
Joined: 02 Sep 2009
Posts: 55632
Re: If q is a positive integer less than 17 and r is the...  [#permalink]

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13 Sep 2010, 08:58
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rraggio wrote:
If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?

(1) q>10
(2) q=2^k, where k is a positive integer

I have the official answer to this question, but I'm quite sure it's not correct.

(1) q>10
This means q can be any integer between 11 and 16. So the remainder can be any integer from 6 to 1.
Statement (1) is not sufficient. So it's B or C or E.

(2) q=2^k
This means q can be one of these values: 2, 4, 8, 16. So the remainder can be respectively 15, 13, 9, 1.
Statement (2) is not sufficient. So it's C or E.

(1) and (2)
This means q must be 16, so the remainder is 1.

I don't know why the official answer is B.
Did I miss anything?

Thanks!

Red part is not correct.

For (2):
17 divide by 2 yields remainder of 1;
17 divide by 4 yields remainder of 1;
17 divide by 8 yields remainder of 1;
17 divide by 16 yields remainder of 1;

So when q=2^k then the remainder upon division 17 by q is always 1.

Hope it helps.
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Intern
Joined: 30 Aug 2010
Posts: 13
Re: If q is a positive integer less than 17 and r is the...  [#permalink]

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13 Sep 2010, 08:41
(1) q>10
This means q can be any integer between 11 and 16. So the remainder can be any integer from 6 to 1.
Statement (1) is not sufficient. So it's B or C or E.

(2) q=2^k
This means q can be one of these values: 2, 4, 8, 16. So the remainder can be respectively 15, 13, 9, 1.
Statement (2) is not sufficient. So it's C or E.

(1) and (2)
This means q must be 16, so the remainder is 1.

I don't know why the official answer is B.
Did I miss anything?

Thanks!
Retired Moderator
Joined: 05 Jul 2006
Posts: 1669
Re: If q is a positive integer less than 17 and r is the...  [#permalink]

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13 Sep 2010, 12:56
[quote="rraggio"]If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?

(1) q>10
(2) q=2^k, where k is a positive integer

from one obviously insuff

from 2

17 = 2^3+1 ,
q = 2^k such that k=<3 ( from given q<17) so q can be 0,2,4,16

remainder will always be 1 ............suff

B
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Joined: 02 Mar 2012
Posts: 284
Schools: Schulich '16
Re: If q is a positive integer less than 17 and r is the  [#permalink]

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20 Jun 2016, 05:53
rraggio wrote:
(1) q>10
This means q can be any integer between 11 and 16. So the remainder can be any integer from 6 to 1.
Statement (1) is not sufficient. So it's B or C or E.

(2) q=2^k
This means q can be one of these values: 2, 4, 8, 16. So the remainder can be respectively 15, 13, 9, 1.
Statement (2) is not sufficient. So it's C or E.

(1) and (2)
This means q must be 16, so the remainder is 1.

I don't know why the official answer is B.
Did I miss anything?

Thanks!

this is where you are wrong.
Explanaton for B.
if q=2 the ramainder is not 15 its 1. 17/2=1(remainder)
Same for others.
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Joined: 09 Sep 2013
Posts: 11371
Re: If q is a positive integer less than 17 and r is the  [#permalink]

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17 Jan 2019, 12:47
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Re: If q is a positive integer less than 17 and r is the   [#permalink] 17 Jan 2019, 12:47
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