when positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3







OA - (C)

According to me the IMO is A
Possible Values of n=5,8,,11,14,17,20...
Possible Values of T =8,13,18,23,28..

Statement 1: N-2 is Divi 5 is 17-2=15, 32-2=30 in this case all the values of N-2 are multiples of 15 hence the remainder will be 0.

Statement 2: T is divi by the first value is 18,33 and so on if you muliple 18 and 33 with any of the values of N and then divide it by 15 the remainder will vary

Hence IMO A

The answer is C, refer below link
when-positive-integer-n-is-divided-by-3-the-remainder-is-2-t4146.html?hilit=nt%20divided%20by%2015

Now the above thread shows algebraic appraoch. The numerical way could be as "sanyalpritish" started off.

From Q
n= 3K+2 , so n= 5,8,11,14,17,20,23,26,29,32....

t= 5m+3, so t= 8,13,18,23,28,33....

Statement 1:
n-2=5p, n= 7,12,17,22,27,32...
See common values, n = 17,32...

now pick a value of t, say t=8
n*t = 17*8= 136
nt/15= 136/15 remainder=1

take t= 13
nt= 17*13= 221, nt/15= 221/15, remainder = 11.

Pls note we took n=17 and varied value of t bcos we are pretty sure of value of n from Q stem and Statement 1 but for t we might have more info and hence we tried two values of t.

INSUFFICIENT

statement 2:
t= 3q , t= 3,6,9,12,15,18,.....

Combine with Q stem, t= 18, 33, ... etc...

now you can check St.2 like we did for St.1 but dont take values of n like 17, 32 ....from Statement 1, take it from Q stem and it will turn out to be INSUFFICIENT as well

Combine 1 & 2
n= 17, 32....
t= 18, 33...

nt = 17*18 = 306, nt/15 r= 6
nt= 32*33= 1056, nt/15 , r=6.

Answer C.

Hey thanks you two.. I tried searching for this problem however, nothing came up in the search .. very surprising!!

but thanks for your prompt reply .. appreciate it!

I hope the link helps. Please ask if there are additional questions on this problem.

_________________
Ben Ku
Instructor
ManhattanGMAT