Statement 1 by itself isn't enough; j could be, for example, 2, in which case the remainder would be 1. But if J were 14, the remainder would be 11. So just knowing that J is even isn't enough.

Statement 2 by itself is also insufficient. J could be 7, in which case the remainder would be 4, or 8, in which case the remainder would be 1, etc...

Taken together, we know that J could only be 2, 4, 6, or 8. All of those numbers are factors of 24. So 25/2 would be 12 r 1, 25/4 would be 6 r 1, 25/6 would be 4 r 1, and 25/8 would be 3 r 1. So, when we consider the two statements together, we can find an answer. The remainder of 25/j is 1. Therefore, the answer is C.

option1

remainder of 25/2=1
remainder of 25/4=1
remainder of 25/6=1
remainder of 25/8=1
remainder of 25/10=5

insuff

option 2
remainder of 25/2=1
remainder of 25/3=1
remainder of 25/4=1
remainder of 25/5=0

insuff

option 1 and option 2
suff

ans C

C wrote:What is the remainder when 25 is divided by positive integer j?

(1) j is even.

(2) j < 9

Source is MGMAT practice test #2. I don't know the correct answer.

Hope someone can explain their approach to these kind of DS problems.

Thanks.

IMO

C