number line problem (GMAT prep)

Pugalenthi wrote:This problem tripped me Please explain.

Is y between -2 and 1 on the number line?
(1) y is to the right of -1 on the number line
(2) y is to the left of 2 on the number line

The answer is E.

Here was my logic :

(1) could go beyond 1 and hence not sufficient
(2) could go beyond -2 and hence not sufficient
taken together - y is between -1 and 2 and hence the answer is NO. But, this logic is flawed What am i missing? Please explain.

y is not equal to the entire range.
-1 < y < 2 implies that y could be ANY VALUE between -1 and 2.
If y = 0, then it is between -2 and 1.
If y = 1.5, then it is not between -2 and 1.
Hence, the two statements combined are INSUFFICIENT.

Here are the choices:
(A) statement 1 works but statement 2 does not work
(B) statement 2 works but statement 1 does not work
(C) the statements do NOT work alone, but they DO work together
(D) each statement works by itself
(E) nothing works, not even using them together

You have eliminated choices (a), (b) and (e). I think we can agree that the choices are narrowed down between (c) and (e)

Here is the flaw with (c)
equation 1: If we combine (1) and (2) we get: -1 < y < 2
equation 2: The question asks is -2 < y < 1

Lets substitute some numbers for y:
Choose number = 2: Is -2 < 2 < 1? Absolutely no!!!
Choose number = 1: Is -2 < 1 < 1? Absolutely no!!!
Choose number = 0: Is -2 < 0 < 1? Yes
If we can't get all yeses for the answer, using them together is not helpful.
Therefore answer equals (e)