srujani wrote:

If x is an integer, what is the value of x?

(1) |23x| is a prime number

(2) \(2*\sqrt{x^2}\) is a prime number

What you are saying is exactly correct : Square root of a number will always be a non-negative entity. The question doesn't wrestle that point.

\(\sqrt{x^2} = |x| \geq{0}.\). However, as you can see, both x = 1 and x = -1 are valid as because |1| = |-1| = 1.

So basically, \((-1)^2 = (1)^2 = 1\), but \(\sqrt{1}\) = 1.

From F. S 1, we know that |23x| is a prime number for both x =1 and x=-1. Thus,no unique value of x is present. Insufficient

From F.S 2, \(2*\sqrt{x^2}\) can be a prime no only if \(x^2 = 1\). Again, \(x^2 = 1\) \(\to\) \(x = \pm1\). Just as above, we get 2 values of x, hence Insufficient.

Even after combining both the fact statements, no unique value of x can be found.

E.

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