Statement 1

p and x are consecutive integers this means that either p + 1 = x OR p - 1 = x. In other words, p is either the integer before x or the integer after x. We don't know for sure.

So x could be 5, and p could be either 4 or 6. But x could also be 6, and p could be either 5 or 7. There are a lot of options here. Insufficient.

Statement 2

If p - 4 is divisible by 5, this means that (# divisible by 5) + 4 = p. However, we know nothing about how p and x relate without Statement 1. x could be 5, 1, 20037, etc. Insufficient.

Both

If (# divisible by 5) + 4 = p and x is the integer after p, (# divisible by 5) + 5 = x, making x divisible by 5. However, we established that x could also be the integer before p. This would make (# divisible by 5) + 3 = x, which would make x indivisible by 5. Since we cannot determine for sure whether x is or isn't divisible by 5, both statements together are insufficient.

Hi M7MBA,

We're told that P and X are integers. We're asked if X is divisible by 5. This is a YES/NO question. We can answer this question by TESTing VALUES.

1) P and X are consecutive integers.
IF...
P=4, X=5 then the answer to the question is YES.
P=4, X=3 then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) (P - 4) is divisible by 5.
IF...
P=4, X=5 then the answer to the question is YES.
P=4, X=3 then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that 'fit' both Facts (and produce different answers - one YES and one NO).
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich