KapilKapoor wrote:I got this question wrong in Veritas prep test paper; however i'm not satisfied with the solution and answer. The question is

Q. If n and y are different positive integers and n represents the number of different positive factors of y, is y a perfect square?
11. Root(n) is an odd integer
2. y=Root(5^(2(n-1)))

Ans given is A, i think answer should be D
What is others opinion ???

Regards,
Kapil

(1) √n is an odd integer implies that n must also be an odd integer.
Example: √49 = 7, √9 = 3, √121 = 11, but √100 = 10, √64 = 8
Also, all the powers of an odd integer are also odd, viz., 3² = 9, 3^3 = 27, 3^4 = 81 and so on.

It is given that n represents the number of different positive factors of y, which means that the question is asking if n is an odd integer. And it is clear that n is an odd integer; SUFFICIENT.

(2) y = √(5^(2(n-1)))
y = (5^(2(n-1)))^(1/2)
y = 5^(n - 1), but from this we cannot make out whether y is a perfect square or not; NOT sufficient.

The correct answer is A.