Remainder Problems

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kartikshah: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sun Jul 15, 2012 12:03 pmFollowed by: 1 member; Location: New York, USA; Thanked: 34 times

by kartikshah » Thu Jul 19, 2012 8:50 am

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

Note: This problem has already been posted on BTG earlier but the solutions provided by users at that time are too brief to be understood by me. Hence I am reposting the question and hope to receive a step by step solution to this problem.
Thanks

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Source: Beat The GMAT — Problem Solving | Thu Jul 19, 2012 8:50 am

imskpwr: Master | Next Rank: 500 Posts; Posts: 377; Joined: Wed Sep 14, 2011 10:45 amFollowed by: 1 member; Thanked: 10 times

by imskpwr » Thu Jul 19, 2012 9:20 am

kartikshah 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?

I hope you are able to frame these equations
m = 13*q + 2...............................1

m = 17*k + 2...............................2

Now you see that (M-2)= 13* q = 17* k
since 13 and 17 are prime to each other ie Coprime. This shows that q must be a multiple of 17.
hence remainder is 0 when q is divided by 17.
ans a
Reply if you need further explanation.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 19, 2012 11:37 am

kartikshah 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

Plug in a value for m that satisfies the given conditions:
When integer m is divided by 13, the remainder is 2.
In other words, m is 2 more than a multiple of 13.
When m is divided by 17, the remainder is also 2.
In other words, m is 2 more than a multiple of 17.
Let m = (13*17) + 2 = 223.

Determine the value of q:
m/13 = 223/13 = 17 R2.
Thus, the quotient q = 17.

Answer the question stem:
When q=17 is divided by 17, the remainder is 0.

The correct answer is A.

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