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Remainder Problems

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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.
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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
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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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