Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Aug 2005
Posts: 818

When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
Updated on: 29 Jan 2013, 04:16
Question Stats:
69% (01:39) correct 31% (01:52) wrong based on 843 sessions
HideShow timer Statistics
When integer m is divided by 13, the quotient is q and the remainder is 2. When m is divided by 17, the remainder is also 2. What is the remainder when q is divided by 17? A. 0 B. 2 C. 4 D. 9 E. 13
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by seofah on 06 Apr 2009, 13:08.
Last edited by Bunuel on 29 Jan 2013, 04:16, edited 1 time in total.
Renamed the topic and added OA.



Senior Manager
Joined: 01 Mar 2009
Posts: 349
Location: PDX

Re: Remainder [#permalink]
Show Tags
06 Apr 2009, 13:29
So q is 17 because if m = 13q + 2 and m is also 17(z)+2 So when 17 is divided by 17 the remainder is 0. pradeep
_________________
In the land of the night, the chariot of the sun is drawn by the grateful dead



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: Remainder [#permalink]
Show Tags
06 Apr 2009, 16:40
botirvoy wrote: When integer m is divided by 13, the quotient is q and the remainder is 2. When m is divided by 17, the remainder is also 2. What is the remainder when q is divided by 17?
A. 0 B. 2 C. 4 D. 9 E. 13
Detailed explanations please. From the definition of quotients and remainders, we have: m = 13q + 2 m = 17a + 2 (note that the quotient is different in the second case). So we have 13q + 2 = 17a + 2 13q = 17a and since this equation involves only integers, the primes that divide the right side must divide the left, and vice versa. That is, q must be divisible by 17, and a must be divisible by 13. If q is divisible by 17, the remainder is zero when you divide q by 17. Of course, if you can see that q = 17 is one possible value for q here, you can use that to get the answer of zero quickly as well.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Manager
Joined: 02 Mar 2009
Posts: 123

Re: Remainder [#permalink]
Show Tags
06 Apr 2009, 23:59
Got 0 as well but am I right in thinking that 0 is another possible value of q?



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: Remainder [#permalink]
Show Tags
07 Apr 2009, 05:20
shkusira wrote: Got 0 as well but am I right in thinking that 0 is another possible value of q? Yes, perfectly correct  and that makes the question quite easy!
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Director
Joined: 23 May 2008
Posts: 743

Re: Remainder [#permalink]
Show Tags
05 May 2009, 00:22
m13q=2 m17s=2
13q=17s
r=0
A



Manager
Joined: 14 Nov 2008
Posts: 182
Schools: Stanford...Wait, I will come!!!

Re: Remainder [#permalink]
Show Tags
06 May 2009, 00:45
IanStewart wrote: shkusira wrote: Got 0 as well but am I right in thinking that 0 is another possible value of q? Yes, perfectly correct  and that makes the question quite easy! Thanks. Just to add, if q=0, it is divisible by 17.. and hence would not leave any remainder.



Intern
Joined: 10 May 2010
Posts: 1

Re: Remainder [#permalink]
Show Tags
10 May 2010, 23:18
We can solve this using a simple equation and deriving the values: m = 13q + 2  1 m = 17p + 2  2
=> 13q + = 17p + 2 => 13q = 17p => q = 17p/3 Here, 17p is equal to (m2) from eqn 2. Therefore, q = (m2)/3
Now substituting the values in eqn 1: => m = 13(m2)/3 + 2 From here, m = 2.
Now using M, the value of Q can be derived from eqn 1. => 2 = 13q + 2 => q = 0
Now if we divide Q by any number henceforth, the remainder would always be 0.



Manager
Joined: 05 Feb 2007
Posts: 138

Re: Remainder [#permalink]
Show Tags
01 Jun 2011, 08:32
So, I understand how to get to here
m=(13q)+2 m=(17x)+2
13q=17x
But, once I reduce the equation to 13q=17x, I am unable to make any deductions...can someone provide a clear explanation on how to use algebra to derive the values when we still have variables?



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1140

Re: Remainder [#permalink]
Show Tags
13 Jun 2011, 01:17
13q = 17p lcm = 13 * 17. thus q = 17. hence remainder = 0
_________________
Visit  http://www.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: Remainder [#permalink]
Show Tags
13 Jun 2011, 10:26
amit2k9 wrote: 13q = 17p lcm = 13 * 17.
thus q = 17.
hence remainder = 0 Careful here; if 13q = 17p, all you can say is that q is a multiple of 17, and that p is a multiple of 13. There is no way to find the actual value of q or p, and you certainly cannot be sure that q=17. It could be that q=34 and p=26, for example. In general, if you see an equation like 13q = 17p, and if q and p are integers, then 13q and 17p are *the same number*. So they must have the same divisors. Since 17 is a divisor of 17p, it must be a divisor of 13q, so q must be divisible by 17. Alternatively you can rewrite the equation as p = 13q/17, and since p is an integer, 13q/17 must be an integer, from which again we have that 13q is divisible by 17, so q is divisible by 17.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 18 Dec 2012
Posts: 2

Re: Remainder [#permalink]
Show Tags
29 Jan 2013, 03:08
Can't I just say q=0, so (1) m=13q+2 => m=13*0+2 <=> m=2 (2) m=17k+2 => 2=17k+2 <=> k=0 > 0 divided by 17 will obviously result in a reminder of 0



Intern
Joined: 10 Dec 2012
Posts: 46

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
11 Aug 2015, 12:18
Hi stewart,
Can this be the alternative approach?
m=13q+2 2=13(0)+2 15=13(1)+2 28=13(2)+2
and
m=17p+2 2=17(0)+2 19=17(1)+2 36=17(2)+2
Thus we know p=q and that's 0, so 0/17 = 0.



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
11 Aug 2015, 13:22
jaspreets wrote: Hi stewart,
Can this be the alternative approach?
m=13q+2 2=13(0)+2 15=13(1)+2 28=13(2)+2
and
m=17p+2 2=17(0)+2 19=17(1)+2 36=17(2)+2
Thus we know p=q and that's 0, so 0/17 = 0. Yes, you are correct in your approach. This question can be solved either by algebra as shown by Ian above or by plugging a few values as you have done. The trick here is to realise that you are finding a number that gives a remainder of 2 with both 13 and 17.



Intern
Joined: 10 Dec 2012
Posts: 46

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
11 Aug 2015, 14:49
Thank You Engr2012 for the rapid response. Appreciated



Manager
Joined: 04 Jun 2015
Posts: 85

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
29 Jan 2017, 01:25
seofah wrote: When integer m is divided by 13, the quotient is q and the remainder is 2. When m is divided by 17, the remainder is also 2. What is the remainder when q is divided by 17?
A. 0 B. 2 C. 4 D. 9 E. 13 Here's my take on this We are given \(\frac{m}{13}\) = q (rem 2) and \(\frac{m}{17}\) = _ r 2 One possible value for m that satisfies both the conditions is \(m = 2\). When \(m = 2\), \(q\) will be \(0 (\frac{2}{13}\) gives quotient \(q= 0\) and rem r= 2), which follows \(\frac{0}{17} = 0\)
_________________
Sortem sternit fortem!



VP
Joined: 07 Dec 2014
Posts: 1020

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
29 Jan 2017, 09:46
seofah wrote: When integer m is divided by 13, the quotient is q and the remainder is 2. When m is divided by 17, the remainder is also 2. What is the remainder when q is divided by 17?
A. 0 B. 2 C. 4 D. 9 E. 13 m=2+(13*17)=223 q=223/13=17 17/17 gives remainder of 0 A



Manager
Joined: 06 Jul 2014
Posts: 102
Location: India
Concentration: Finance, Entrepreneurship

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
07 Oct 2017, 01:13
How do we know that when m is divided by 17 the quotient is different?



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: When integer m is divided by 13, the quotient is q and the r [#permalink]
Show Tags
07 Oct 2017, 01:23




Re: When integer m is divided by 13, the quotient is q and the r
[#permalink]
07 Oct 2017, 01:23






