For proving statement 1, x =4 , y=7 , z=9 ---> x^3 > y^2 > z and x < y < z . Thus this statement could be true. ---> eliminate B and D

for proving statement 3, x=7, y =4, z=9 ----> x^3 > y^2 > z and y < x < z. Thus this statement could be true ---> eliminate A and C

Correct answer is E
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The best strategy in such questions is to check one of the conditions with values and eliminate options based on its validity

Given : x^3 > y^2 > z

I. x < y < z is true for x=3, y=4, z=5 i.e. Answers can only be Options A, C or E

II. x < z < y is true for x=3, y=5, z=4 i.e. Answers can only be Options C or E

III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options E

Answer: option E
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800score Official Solution:

Choice I is possible: x = 3, y = 4, z = 5
Choice II is possible: x = 3, y = 5, z = 4
Choice III is possible: x = 4, y = 3, z = 6

The correct answer is E.
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I am finding it difficult to come up with nos for number picking...? any tips..?

Tips:

1) Try the Positive Integer Values starting from the smallest value. Checking Bigger values might make it more difficult for you so check smaller values first.

2) Try the Negative Integer Values starting from the smallest Absolute values i.e. (-1, -2, -3 etc)

3) Try the Values in the range 0 to 1 and pick easier Numbers (e.g. 1/2, 1/3) in case you have to take square root of values then pick numbers like 1/4, 1/9 etc. Check the similar value in the Values of Negative Range i.e. 0 to (-1)

Summary: The values should be checked in the following 4 ranges
Between 0 and 1
Between 0 and -1
Greater than +1
Less than -1
and Don't forget to check at zero if the Scenario requires it.

Practice applying them in questions and in some time you will understand the best values to pick for specific cases

I hope it Helps
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Choosing and comparing values for x, y, z could be easier if we represent the values in the number line as in the attachment.
Clearly option E.

\(x^3\) > \(y^2\) > z

Option I: x < y < z: For x = 3; y = 4 and z = 5 Option I holds[27 > 16 > 5]

Option II: x < z < y: For x = 3; y = 5 and z = 4 Option II holds [27 > 25 > 4]

Option III: y < x < z : For x = 4, y = 3 and z = 5 Option III holds [64 > 9 > 5]

Answer E
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