Data Sufficiency

If x > y² > z�, which of the following statements could be true?

I.x > y > z
II. z > y > x
III. x > z > y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

If we CAN find a set of values that satisfies a statement AND yields values such that x > y² > z�, then we'll keep that statement.

Statement I. x > y > z
If x = 2, y = 1, and z = 0, then x > y² > z�
KEEP statement I

Statement II. z > y > x
If x = 1/4, y = 1/3, and z = 1/2, then x > y² > z�
KEEP statement II

Statement III. x > z > y
If x = 2, y = -1, and z = 0, then x > y² > z�
KEEP statement III

Answer: E

Cheers,
Brent

Hi kaudes11114,

Brent has provided a great explanation that TESTS VALUES, so I won't rehash that here.

Instead, I'm going to point out the Number Properties that this question is based on. These are "math rules" that are worth knowing, as Number Properties show up on a variety of questions in the Quant section:

1) ANY positive or negative number, when raised to an EVEN INTEGER power, becomes positive.
2) 0, raised to ANY power, is still 0.
3) Positive fractions, when raised to a POSITIVE power GREATER THAN 1, become SMALLER

Number Properties tend to show up in Roman Numeral questions and in DS questions, so keep an eye out for them (and learn them) during your studies.

GMAT assassins aren't born, they're made,
Rich

Hi Sushant,

The prompt does NOT state the variables are integers, so you have to consider the possibility that some of them might be NON-integers.

X > Y^2

Here are two examples that 'fit' this information.... The first is fairly obvious:

X = 2
Y = 1

2 > (1)^2, so X > Y

The second is not quite so obvious....

X = .3
Y = .5

.3 > (.5)^2
.3 > .25

So X < Y

GMAT assassins aren't born, they're made,
Rich