metallicafan wrote:If y is a positive integer, is square root of y an integer?
(1) square root of 4y is not an integer.
(2) square root of 5y is an integer.
The question is easy. However, in statement #2, I have a doubt: How can we be so sure that the only possible value of y is 5?
If it is true that √y = integer, then y = (integer)².
Question rephrased: Is y a perfect square?
A perfect square has an EVEN number of prime factors:
9 = 3*3
100 = 2*2*5*5
etc.
Statement 1: √(4y) is not an integer
√(4y) = 2√y.
Since 2√y is not an integer, √y is not an integer.
SUFFICIENT.
Statement 2: √(5y) = integer.
Thus, 5y = (integer)², implying that 5y is a perfect square.
Since 5y is a perfect square, it has an even number of prime factors.
Since y has one fewer prime factor than 5y, y must have an ODD number of prime factors.
Thus, y is not a perfect square.
SUFFICIENT.
The correct answer is
D.
An infinite number of values for y will satisfy statement 2:
5, 20, 45, 500, etc.
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