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
