If my understanding is correct, then the question asks whether the function p(x)/q(x) is a real number, for all real numbers 'x'.

Stmt 1 -

We know only the values of the expression p(x) for x = 2 and x = 3.Hence insufficient

Stmt2 -

We know only the values of expression q(x) for x = 0 and x = 1.Hence insufficinet

Stmt 1 and Stmt 2 taken together -

The values of the expression p(x) and q(x) are known only for x = 2 , x = 3 and x = 0 , x = 1 respectively.
These values alone are not sufficient.

Hence IMO E

Stmt2 -

We know that the values of expression q(x) for x = 0 and x = 1 are zero.in other words, q(x) can be 0 as the denominator of p(x)/q(x) when this fraction doesnot exist...

so sufficient.

choose B？

But q(x) can hold a valid value for other values of 'x', say x = 2, 3, 4 ...
I believe the question asks for 'each real number x' and not a specific real number.

as q(x) cannot hold a valid value for each value of 'x', we can say that the function p(x)/q(x), is not a real number for each real number x but rather for some real numbers(at least when x=0 or 1, q(x) makes the function p(x)/q(x) invalid)

hmm...interesting argument....
can we have the OA pls?

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i've no idea the OA...so i posted it here