Data Sufficiency

If x is positive integer, is root x an integer.

1) root(4x) is an integer
2) root(3x) is not an integer.

I thought answer is E, but OA is A

Please help

If you simplify statement 1 you will get 2 root x. Since 2 is an integer root x must also be for the product of these numbers to be an integer.

You might be thinking, what if root x were to equal yyy.5 ? The answer to this is that there is no way to take a root of an integer and get .5 as the decimal.

.5 x .5 = .25 so you will always have this as the decimal when multiplying 2 numbers with .5 at the end.

svd.kumar wrote:If x is positive integer, is root x an integer.

1) root(4x) is an integer
2) root(3x) is not an integer.

I thought answer is E, but OA is A

Please help

1)For the first case, x has to be a perfect square.Since 4 would come out of the root sign and only x will be left. Now that x has to be a perfect square to make the entire thing an integer.
2) Take an example of 3x=27 and 3x=12. Here in both the cases x is a perfect square. but 3x is not.
On the other hand if 3x=15. Here x is not a perfect square and neither is 3x.
hence this statement alone is Insufff.
Hence correct asnwer is A.