GMAT focus ( quotient and remainders)

[Abdulla]

When integr m 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

[cramya]

Pick numbers

Lcm of 13 and 17 is 221 Add 2 to get 223 (whic gives a remainder of 2 when dividing by 13 and 17)

223/13 = Q= 17 R=2

Q/17 will always give a remainder of 0

[cramya]

Algebrically

m = 13q+2
m = 17q+2

m = lcm(13,17)q+2

= 221q+2

q=0 m=2 m/13 q=0 0/17 remainder 0

q=1 m=223 Show above

q-2 m = 444 Again 444/13 q=34 34/17 remainder 0

[Abdulla]

Great .. Can I apply the LCM approach in all the remainder problems ??

[Abdulla]

Algebrically

m = 13q+2
m = 17q+2

m = lcm(13,17)q+2

= 221q+2

q=0 m=2 m/13 q=0 0/17 remainder 0 (( could you expand your explanation in this part ))
q=1 m=223 Show above

q-2 m = 444 Again 444/13 q=34 34/17 remainder 0

[cramya]

Yes as long as it leaves the same remainders like this problem.