w, x, y and z are integers such that w < x2, x > y2, y2 < z2 and x > z . Which one of the following inequalities must be true?

Answer:

12) D

The easiest way to solve this is to assign values to the integers given in options A, B, C, D and E. However, the inequalities in the question should still be true)

A – This cannot be 100% proven as true.
Let us say x = 10 and w = 20, this cannot be true.
However, w(20) < x² (10² = 100) is true.

B – This cannot be 100% proven as true.
We are only told that w < x² and x > y². We cannot determine the inequality between w and y.

C – Again, we cannot determine the inequality between w and z.

D – This can be proven as correct.
Since x > y², and y² will always be equal to (if y = 1) or greater than y, we can get the inequalities:
x > y² and y² ≥ y, we can determine the inequality x > y.

E – This cannot be proven correct.