If 0

Question

If 0 < x^y < 1, which of the following must be greater than x?

I. y^x
II. xy
III. 2x

A. None
B. I Only
C. III Only 
D. I & III Only
E. II & III Only

chetan2u · Answer

X will be a fraction, and if you realize x can be both positive and negative, you can solve the question quite easily.

Say x=(3) and y=-1, so  3^{-1}=\frac{1}{3} ..
Option I... y^x =(-1)^3=-1, which is less than 3
Option II...xy =3*-1=-3, which is again less than X

Now say x =(-1/2) and y=2
Option III .... 2x=2*-1/2=-1, so less than x

Thus None, and answer is A

Soma2001 · Answer

Option verification
Take x>y(x=0.8, y=0.1) such that x^y satisfies the given condition
Take x=y(x=0.5, y=0.5)
Take x<y(x=-0.5, y=2)

The answer should satisfy all the given conditions
.
Therefore there is no such option.
None is the answer

pmahaja2 · Answer

x cannot be 3, it needs to be between -1 and 1

Bunuel · Answer

Check again. If x = 3 and y = -1, then x^y = 3^(-1) = 1/3, which is indeed greater than 0 and less than 1.

If 0 < x^y < 1, which of the following must be greater than x?