Integers and divisibility

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fighting_cax: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Sat Feb 16, 2008 8:07 pm; Location: Philippines; Thanked: 3 times

by fighting_cax » Mon Jan 26, 2009 3:55 pm

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

OA is A

Please explain.

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Source: Beat The GMAT — Problem Solving | Mon Jan 26, 2009 3:55 pm

Zipper: Master | Next Rank: 500 Posts; Posts: 119; Joined: Sun Nov 30, 2008 2:47 am; Thanked: 11 times

by Zipper » Mon Jan 26, 2009 6:05 pm

m/13=q and 2 remainder
m/17=x and 2 remainder

so m-2 is a multiple of 13 and 17
m-2/13=q with no remainder but we don't need it anyway.

so q must be a multiple of 17

hence, A=0

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