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GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

Prime numbers are always positive.

(1) |23x| is a prime number. Here, x can be 1 or -1

x = 1: |23x| = 23 (a prime number) x = -1: |23x| = |23(-1)| = |-23| = 23 (a prime number) (the mod converts the negative to positive)

(2) 2x^{\frac{1}{2}} is a prime number. Are you sure the actual question doesn't say 2x^{2} is a prime number?
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GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

Actually with the given options, answer must be B, as it would yield x=1.

However for the answer to be E, the statement 2 must have x^2 instead of x^1/2 as karishma pointed out.
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GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

Actually with the given options, answer must be B, as it would yield x=1.

However for the answer to be E, the statement 2 must have x^2 instead of x^1/2 as karishma pointed out.

Actually, I formatted the question and that is exactly what I was thinking when I was doing that.... Or maybe I got confused by the layout..
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GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

Actually with the given options, answer must be B, as it would yield x=1.

However for the answer to be E, the statement 2 must have x^2 instead of x^1/2 as karishma pointed out.

Actually, I formatted the question and that is exactly what I was thinking when I was doing that.... Or maybe I got confused by the layout..

GMAT Club test set the correct answer as (E), as they conclude x could be 1 or -1. But Is prime number can be negative? So my answer would be (D) as x=1

The question reads: 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.

The correct answer is E.

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

(1) |23x| is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) 2\sqrt{x^2} is a prime number. The same here: x=1 or x=-1. Not sufficient.