If an integer is not perfect square, then the number of different positive factors of that integer is always even. And if it is a perfect integer, then the number of different positive factors of that integer is always odd.Ramit88 wrote:If n and y are positive integers and n represents the no. of different positive factors of y , is y a perfect square?
1. √n is an odd int
2. y = √[5^{2(n-1)}]
Statement 1: √n is an odd integer.
Hence n is also an odd integer. Thus y must be a perfect square.
Sufficient
Statement 2: y = √[5^{2(n-1)}] = 5^(n - 1)
For y to be a perfect square, √y must be an integer.
Thus, √(5^(n - 1)) must be an integer. Which is only possible when (n - 1) is even. But we don't know anything about n.
Not sufficient
The correct answer is A.
