Prime Number

Question

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

(1) |23x| is a prime number.

(2)  2x^{\frac{1}{2}}  is a prime number.

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

KarishmaB · Answer

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?

Vips0000 · Answer

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.

MacFauz · Answer

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.. :oops:

Vips0000 · Answer

Lol.. <img src="{SMILIES_PATH}/icon_twisted.gif" alt=":twisted:" title="Twisted Evil" />

guhabiswasavijit · Answer

Yes, the question says 2* \sqrt{x}  is a prime number. Got it, Thanks.

Bunuel · Answer

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.

(1)+(2) x could be 1 or -1. Not sufficient.

Answer: E.

Prime Number

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