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

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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

M04-07

[Reveal] Spoiler:
Now, I get why statement 1 is not sufficient (x could be 1 or -1). But the OA says that in statement 2, x could still be 1 or -1. Is it not the rule that the square root of a number only yields a positive number. Shouldn't x be here. Help.

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