Hmm, I would've guessed (D)

(1)
The only numbers for X which yield a 2 digit +ve number when raised to the power of 3 are 1,2,3,4. Out of these, only x = 3 satisfied the criteria (3^3 = 27)

(2)
Same applies to this, except the list is now 1,2,3, and again, only 3 satisfies the criteria (3^4 = 81)

A.

2) insuff as (-3)^4 is 81. so x can be 3 or -3.

sharmishtha_goel wrote:A.

2) insuff as (-3)^4 is 81. so x can be 3 or -3.

Ah, can't believe I missed that!

Thanks people....

Hey guys,

It looks like the OA here was C, right? Sharmishtha's explanation of statement 2 is perfect, but why wouldn't statement 1 still work? Since I didn't see that addressed here I figured I'd chime in. Since the question doesn't define x as an integer, statement 1 still has the potential to just be "the cube root of 11" or something like that. As written, the question requires both statements to rule out:

Statement 1: allows for the noninteger cube root of any 2-digit odd integer (or, of course, 3)

Statement 2: allows for -3 or the noninteger fourth root of any 2-digit odd integer (or, of course, 3)

Together, however, -3 is out and the 3rd/4th roots wouldn't match up to both allow for integers when both cubed and ^4th power UNLESS we're talking about x = 3.