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If x is a prime number greater than 2, which of the following could be a prime number?

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Re: If x is a prime number greater than 2, which of the following could be a prime number?

by Brent@GMATPrepNow » Sun Mar 08, 2020 6:06 am
BTGmoderatorLU wrote: ↑
Sat Mar 07, 2020 12:38 pm
 Source: GMAT Paper Tests

If x is a prime number greater than 2, which of the following could be a prime number?

A. x^2
B. x/2
C. 3x
D. x−4
E. x^2+1

The OA is D
Check the answer choices.....

D) If x = 7, then x - 4 is also prime.
Similarly, if x = 11, then x - 4 is prime.
And if x = 23, then x - 4 is prime.

Answer: D

Aside: Let's see why answer choice E can never be prime.

First of all, let's recognize that if x is a prime number greater than 2, then x is ODD
Any odd number can be written in the form 2k + 1, where k is an integer
For example, 13 = 2(6) + 1, and 37 = 2(18) + 1

E) x² + 1
Replace x with 2k + 1 to get: (2k + 1)² + 1
Expand to get: 4k² + 4k + 1 + 1
Simplify: 4k² + 4k + 2
Factor: 2(2k² + 2k + 1)
This tells us that we can write x² + 1 as a multiple of 2, which means x² + 1 is EVEN, which means it cannot be prime

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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