akash singhal wrote:If x > y^2 > z^4, which of the following statements could be true?
1. x>y>z
2. z>y>x
3. x>z>y
A. 1 only
B. 1 and 2 only
C. 1 and 3 only
D. 2 and 3 only
E. 1,2 and 3
.
Constraint: x > y² > z�
Statement I: x > y > z
To make x > y > x and x > z�, let x be a large integer and z be a small integer.
Case 1: x=10, y=2 and z=1
In this case, x > y² > z� and x > y > z.
Since statement I is possible, eliminate D.
Statement III: x > z > y
In Case 1, changing the signs of y and z will make z > y.
Case 2: x=10, z=-1 and y=-2
In this case, x > y² > z� and x > z > y.
Since statement III is possible, eliminate A and B.
Statement II: z > y > x
To make z > y > x and x > z�, let x and z be positive fractions, since a positive fraction raised to a power greater than 1 gets SMALLER.
Case 3: z=1/2, y=1/3, x=1/4
In this case, x > y² > z� and z > y > x.
Since statement II is possible, eliminate C.
The correct answer is
E.
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