adkikani wrote:

If x is a positive integer, is \(\sqrt{x}\) an integer

1. \(\sqrt{36x}\) is an integer.

2. \(\sqrt{3x+4}\) is an integer

is \(\sqrt{x}\) an integer?

1. \(\sqrt{36x}\) is an integer.

\(\sqrt{36x}=\sqrt{6^2x}=6\sqrt{x}\)

Now if \(6\sqrt{x}\) is a n integer and x is a positive integer, \(\sqrt{x}\) has to be an integer

sufficient

2. \(\sqrt{3x+4}\) is an integer

there can be various possiblities....

x = 4, \(\sqrt{3x+4} = \sqrt{3*4+4}\sqrt{16}=4\)

here \(\sqrt{x} =2\) is an integer ...yes

x = 7, \(\sqrt{3x+4} = \sqrt{3*7+4}\sqrt{25}=5\)

here \(\sqrt{5} =2\) is not an integer ...

insuff

A

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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