When you use both statements here, you find j+p+m+n+q = 280, and since the sum of all six numbers is 336, the remaining number k must be equal to 336 - 280 = 56. So using both statements, at least one value in the set is exactly 56. But it's certainly possible other values are also 56. Looking at Statement 1, we might have j = 56 and p = 72, for example, in which case we'd have at least one other value equal to 56, but there's no need for one of j or p to be 56 -- we could have j = 0 and p = 128, say. Similarly, some of m, n and q might equal 56, but there's no need for that to be true. So the answer is E.

It would perhaps be a more interesting question if it asked whether at least one of the numbers was equal to 56. In that case, the two statements would be sufficient together.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

I would go for E

Since 1) J and P can be any value ( No idea about M, N and P) Insufficient
2) same as above M, N, Q can be any value ( No idea about J and P) Insufficient

both 1 and 2 ( J, P, M, N, Q) can again be any value to make the sum 290 Insufficient