Data Sufficiency

If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.

light_speed wrote:If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.

The answer is (e) because you forgot about positive fractions, which get smaller as you raise them to a higher exponent.

For example, (1/2)^2 = 1/4, which is less than 1/2.

The answer is E. Say x=-2, y=-3

cjiang16 wrote:The answer is E. Say x=-2, y=-3

The stem says "if x and y are positive", so those numbers don't count!

Stuart Kovinsky wrote:

light_speed wrote:If x and y are positive, is x^3> y?
(1)sqrt x> y
(2) x > y

The answer is showing as E, none, . I selected D

My logic:-
For the first option, if you square root a number, it becomes smaller, hence if the square root of x is larger than y, does that not mean x >y?

If x>y, and is positive, should not x^3 also be the same?.

The answer is (e) because you forgot about positive fractions, which get smaller as you raise them to a higher exponent.

For example, (1/2)^2 = 1/4, which is less than 1/2.

Stuart , can you elaborate on case (1). I see your point about positive fractions related to x>y but not for x^2>y. if x^2>y, doesn't that mean that x is larger than 1 and its not a fraction between 0 and 1. thanks