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
(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.