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

Question

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

(A)  x^2 
(B)  \frac{x}{2} 
(C)  3x 
(D)  x - 4 
(E)  x^2 + 1

energetics · Accepted Answer

A) is the square of a prime, which can't be prime by definition since it has 3 factors
B) all prime numbers besides 2 are odd, so dividing x by 2 results in a non-int
C) a prime x can only have factors of itself and 1, if x is 3 then 3*3=9, perfect square so again, more than 2 factors
D) subtracting an even from an odd number means that the result is odd, which could be prime (e.g. 7-4=3)
E) any prime squared is already not prime, adding 1 just means it will be even and obviously not a prime number

shashaankbhat · Answer

IMO D. As it is “could be” question, plugin x=7, only D holds

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MartyTargetTestPrep · Answer

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

All prime numbers are integers.

The only factors of a prime number are that number and 1.

All prime numbers greater than 2 are odd.

Any even number greater than 2 is not prime.

(A)  x^2

The factors of this number are 1, x, and  x^2 . So this number cannot be prime.

(B)  \frac{x}{2}

Since all prime numbers greater than 2 are odd,  \frac{x}{2}  is not an integer, and therefore will not be prime.

(C)  3x

The factors of this number are 1, 3, x, and 3x. So this number cannot be prime.

(D)  x - 4

An odd prime number minus 4 is an odd number. A odd number could be prime.

Example: 11 - 4 = 7

(E)  x^2 + 1

A prime number greater than 2 is odd. The square of an odd number is an odd number. An odd number + 1 is an even number. An even number greater than 2 is not prime.

The correct answer is (D).

BrentGMATPrepNow · Answer

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

Hasini22 · Answer

How answer d is applicable in all cases
(E.g) prime number is 3
3-4 =-1 ( not prime)
5-4 = 1 (not prime)
61-4 = 57 ( not prime)

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abhi.abhishek95 · Answer

The question stems ask for a could be scenario. In that case, option B,D, and E holds correct. Please explain.

Krunaal · Answer

A prime number greater than 2, will be an odd number.

B.  \frac{x}{2}  => an odd number divided by 2 will always result into a fraction, and  could never  be a prime number.

E.  x^2 + 1  => odd number squared + 1 = even number, since x > 2,  x^2 + 1  > 2, and any even number > 2  could never  be a prime number.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards