k.pankaj.r wrote:If 'r' is the remainder when a positive integer 'n' is divided by 7, what is the value of 'r'?

1) when n is divided by 21, the remainder is an odd integer
2) when n is divided by 28, the remainder is 3

We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:

If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Statement 1:
Possible values of n: 1, 3, 5, 22, 24, 26, . . .
case a: if n=1, then the remainder is 1 when n is divided by 7
case b: if n=3, then the remainder is 3 when n is divided by 7
INSUFFICIENT

Statement 2:
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
SUFFICIENT

Answer = B

Aside: There are more "mathematical" solutions to this question, but in this case, listing the possible values of n should given you a good idea of the sufficiency of the statements.

Cheers,
Brent