The key to understanding this problem is to think about units digits. Whenever a question asks "what is the remainder when divided by 10?", it's really asking "what is the units digit?"

In this problem, we're asking about the units digit of 2 raised to some power. The units digits of powers of 2 form the following pattern:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6 (only looking at the units digit here)
2^5 = 2
2^6 = 4
etc.

You can see that the units digit repeats every 4 powers. So, if we know that p is a multiple of 4, we'll know that the units digit is 6. Otherwise, we won't know. Statement (1) tells us that s (and therefore p) is a multiple of 2, but that's not enough. The units digit could be 4 or 6. Statement (2) tells us that p is a multiple of 4, though, so it's sufficient.

For more info, check out these posts on patterns of units digits:
https://www.beatthegmat.com/if-n-and-m-a ... tml#544266
https://www.beatthegmat.com/what-is-the- ... tml#544267

indiheats wrote:Why can T not be zero ? Making this 1/10 - and therefore a different remainder ... ?

O is a positive integer, is it not ?

No, 0 is not a positive integer - it's the only integer that's neither positive nor negative! Without that positive constraint, you're right, the answer here would have been E. But with it, statement (2) is sufficient.