n mod 7 = ?

1. n mod 21 = odd number

Since we cannot be sure what this odd number is, the corresponding value of r is also not identifiable.

Think of different values of N, such as 22 and 40 that would yield different odd remainders and correspondingly different values of r.

INSUFFICIENT

2. n mod 28 = 3

Since 28 is a multiple of 7, you can be sure that a (multiple of 28) + 3, will produce a number that also has a remainder of 3 when divided by 7.

Thus r = 3

SUFFICIENT

Pick B

for a question like this one, instead of doing algebra think of it like this:

instead of: R is the remainder when positive integer is divided by 7
think like this: N is 3 more than a multiple of 7

now (1) is clearly insufficient.

n is n+odd multiple of 21. clearly insufficient as it could be anything.

(2)

n = 3 more than a multiple of 28

28 itself is a multiple of 7, so we can simply say n = 3 more than a multiple of 7.

therefore R = 3

hence (B).