Bunuel wrote:

Is b an integer?

(1) a^b is an integer

(2) a is an integer

In my view, the answer should be E.

Statement 1 - a^b is an integer.Let say a = 3 and and b = \(\frac{1}{2}\) (which is not an integer). Then \(a^b\) = \(3^\frac{1}{2}\) = \(\sqrt{3}\). In this case \(a^b\) is not an integer.

Consider another value where a = 4 and and b = \(\frac{1}{2}\) (which again is not an integer). Then \(a^b\) = \(4^\frac{1}{2}\) = \(\sqrt{4}\). In this case \(a^b\) is an integer.

Therefore statement 1 is not sufficient.

Statement 2 - a is an integerClearly not sufficient. As in above two examples, we had "a" as an integer so no real value added by the statement.

BOTH statements combined we are still in the same scenario. Therefore none of the statement is sufficient.

Please correct me if I am wrong.

_________________

Ujjwal

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