Is x > 2y? (1) x > y (2) x^3 > y^2

Is x > 2y?

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

The question is an "IS" question. So, the answer will be Yes or No. A definite Yes or a definite No is what we are looking for.

Statement 1: x > y
Approach: Counter example

Example 1: x = 5 and y = 2.
x > y and x > 2y. Answer Yes.

Example 2: x = 3 and y = 2
x > y. But x is not greater than 2y. Answer No.

We could find a counter example.

Statement 1 alone is not sufficient. Eliminate options A and D.

Statement 2: \(x^3 > y^2\)
Approach: Counter Example

Example 1: x = 5 and y = 2
\(x^3 > y^2\) and x > 2y. Answer Yes.

Example 2: x = 3 and y = 2
\(x^3 > y^2\). But x is not greater than 2y. Answer No.

We could find a counter example.

Statement 2 alone is not sufficient. Eliminate option B.

Combine the two statements:
We used the same numerical examples for statements 1 and 2 independently to establish a counter example.
So, the counter example will hold good when we combine the statements.

Example 1: x = 5 and y = 2
x > y, \(x^3 > y^2\), and x > 2y. Answer Yes.

Example 2: x = 3 and y = 2
x > y, \(x^3 > y^2\), but x < 2y. Answer No.

Because a counter example exists even after combining the statements, the given data is not sufficient.

Choice E is the answer.