Question

Let n be a prime number. Which of the following statements CAN be true?

A. n is a perfect square
B. n is even
C. n is irrational
D. nis negative
E
n
is divisible by 4

Answer 1

B. n is even

Explanation:

Prime numbers are numbers divisible by only 1 and itself without a remainder. Examples of prime numbers are 2,5,7,11,13,17,19,23,29,31,37,41,43,47,51,53,57,59,etc

Prime numbers from the example above are not perfect squares. Perfect square numbers are 4,9,16,25,36 etc.

Prime factor (n) cannot also be an irrational or negative answers neither can it be divisible by 4 based on the examples given above.

2 is the only even prime number, so, n is even.

Answer 2

The correct option is B.

n is even

Explanation:

Given that n is a prime number. We are required to check which of the following statements CAN be true.

But first, we should know what prime numbers are. They are numbers whose only factors are 1 and itself. Examples are: 2, 3, 5, 7, 11, and so on.

A. n is a perfect square

This is NOT true, a prime number cannot be a square number.

B. n is even

YES. 2 is in this category, and it is a prime number.

C. n is irrational

Prime numbers include only integers, and irrational numbers are no integers.

D. n is negative

Negative numbers are excluded

E. n is divisible by 4

This is also not included. A prime number is only divisible by 1 and itself.