If x 1, is (3x)^1/2 an integer? (1) (x/3)^1/2 is not an integer

Question

If  x > 1 , is  \sqrt{3x}  an integer?

(1)  \sqrt{\frac{x}{3}}  is not an integer

(2)  \frac{x}{\frac{1}{\sqrt{3}}}  is an integer

If x > 1, is \sqrt{(3x)} an integer? 
(1) \sqrt{(x/3)} is not an integer
(2) x/(1/\sqrt{3}) is an integer

gmatophobia · Answer

Statement 1

(1)  \sqrt{\frac{x}{3}}  is not an integer

Case 1 :  x = \frac{4}{3}

\sqrt{(\frac{x}{3})}  is not an integer ⇒  \sqrt{(\frac{4}{9})} = \frac{2}{3}  is not an integer

\sqrt{(3x)}  =  \sqrt{(3*\frac{4}{3})} = 2  is an integer

Case 2 :  x = 7

\sqrt{(\frac{x}{3})}  is not an integer ⇒  \sqrt{(\frac{7}{3})}  is not an integer

\sqrt{(3x)}  =  \sqrt{(3*7)}  is an not integer

As we are getting two contradicting answers, the statement alone is not sufficient. We can eliminate A, and D.

Statement 2

(2)  \frac{x}{\frac{1}{\sqrt{3}}}  is an integer

\sqrt{3}*x  is an integer. Hence, x is not an integer and is in the form  x = \sqrt{3}*y

Therefore  \sqrt{3x}  will not be an integer. The statement is sufficient.

Option B

If x > 1, is (3x)^1/2 an integer? (1) (x/3)^1/2 is not an integer