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From statement 1, we know that root x is not an integer. Therefore, no matter what sqrt(y) turns out to be, when it gets multiplied by the value of sqrt(x), the product will not be an integer in any case.

From statement 1, we know that root x is not an integer. Therefore, no matter what sqrt(y) turns out to be, when it gets multiplied by the value of sqrt(x), the product will not be an integer in any case.

Same logic for statement 2.

Does anyone see a flaw in this logic ? Thanks !

Your logic will not be valid, since we don't know about "sqrt(y)". It can be an integer or non-integer that will multiply non-integer "sqrt(x)" & make result an integer or non-integer! Say for example...

what if,
sqrt(x) = 1.5 & sqrt(y)=2 ? YES, result is integer AND
sqrt(x) = 1.5 & sqrt(y)=1.5 ? NO, result is not an integer

From statement 1, we know that root x is not an integer. Therefore, no matter what sqrt(y) turns out to be, when it gets multiplied by the value of sqrt(x), the product will not be an integer in any case.

Same logic for statement 2.

Does anyone see a flaw in this logic ? Thanks !

Your logic will not be valid, since we don't know about "sqrt(y)". It can be an integer or non-integer that will multiply non-integer "sqrt(x)" & make result an integer or non-integer! Say for example...

what if, sqrt(x) = 1.5 & sqrt(y)=2 ? YES, result is integer AND sqrt(x) = 1.5 & sqrt(y)=1.5 ? NO, result is not an integer

It should be 'E'!

Vivek, in your first example, sqrt of (1.5 x 2) is still not an integer. What I am saying is that if we know already that ONE of the roots is not an integer, it wont matter if the other root comes out to an integer or not, since the root of the PRODUCT wont be an integer, and thats what the question is asking. Right ?

From statement 1, we know that root x is not an integer. Therefore, no matter what sqrt(y) turns out to be, when it gets multiplied by the value of sqrt(x), the product will not be an integer in any case.

Same logic for statement 2.

Does anyone see a flaw in this logic ? Thanks !

Your logic will not be valid, since we don't know about "sqrt(y)". It can be an integer or non-integer that will multiply non-integer "sqrt(x)" & make result an integer or non-integer! Say for example...

what if, sqrt(x) = 1.5 & sqrt(y)=2 ? YES, result is integer AND sqrt(x) = 1.5 & sqrt(y)=1.5 ? NO, result is not an integer

It should be 'E'!

Vivek, in your first example, sqrt of (1.5 x 2) is still not an integer. What I am saying is that if we know already that ONE of the roots is not an integer, it wont matter if the other root comes out to an integer or not, since the root of the PRODUCT wont be an integer, and thats what the question is asking. Right ?

pmenon, I think you are mistaking it...
You are taking sqrt of (1.5 x 2) again?

I said, sqrt(x) = 1.5 & sqrt(y)=2
&
sqrt(x*y) = sqrt(x)*sqrt(y) = 1.5x2 = 3.
is this correct?