Interesting GMATFix Problem-47

[arora007]

m and n are positive integers and the quotient of m and 5 is the integer q.
What is the remainder when m+n is divided by 15?
1) n-3 is a multiple of 15
2) when q is divided by 3, the remainder is 2.

[neerajkumar1_1]

i fail to understand the statement
the quotient of m and 5 is the integer q.

are u sure u have copied the question right???
I feel something is missing here..

[arora007]

yeah i have copied the question correctly, infact in the answer explanation, the author has explicitly mentioned what he meant by the text "the quotient of m and 5 is the integer q" (m/5) = q
with this input try the question now...

[clock60]

looks like C
what is remainder if m+n=5q+n is divided by 15
(1) insuff as no info about q, only n=15a+3
(2) insuff as no info about n, only q=3b+2
both suff
n+m=5q+n=5(3b+2)+15a+3=15b+10+15a+3=15(a+b)+13
it happens that remainder 13

[arora007]

purrrrfect!

[neerajkumar1_1]

yeah i have copied the question correctly, infact in the answer explanation, the author has explicitly mentioned what he meant by the text "the quotient of m and 5 is the integer q" (m/5) = q
with this input try the question now...

ah thats better... so q is a multiple of 5
or m = 5q
so m could be 5, 10, 15 ,20 anything...

statement 1)
n-3 is a multiple of 15 means
n could be 3, 18, 33 and so on...

(5q + n)/15 will give diff remainders 8, 13, 3
try n = 3 with diff multiple of 5
m + n = 5 + 3 = 8 rem(8/15) = 8
m + n = 10 + 3 = 13 rem13/15) = 13

insufficient..

statement 2)
narrows down value of m ..
since q now would be 2, 5, 8 , 11 or so on
m = 5q
could be 10, 25, 40, 55
but we have nothing on n
isufficient..

together

m could be 10, 25, 40, 55
and n could be 3, 18, 33

m + n = 10 + 3 = 13 Rem(13/15) = 13
or
m + n = 25 + 3 = 28 Rem(28/15) = 13

remainder is constant at 13
sufficient...
ofcourse the logic behind it is..
since n is dislpaced by 3 from the multiple of 15 and m by 10
their remainder will always be 13...