Question

If $p$ is a prime number, which of the following could also be a prime number?

• A. $\frac{p}{3}$
• B. $2p$
• C. $p^2$
• D. $p+2$
• E. $2p+2$

Answer 1

Answer: (D)

$p+2$

As the prime numbers are: $2,3,5,7,11,13,17,19,23,\mathrm{29....}$
Plug in a prime number for $p$, and see which of the answers is also prime.
Plug $p=2$ for option A, Then $\frac{p}{3}=\frac{2}{3}$,which is not a prime, plugging any prime for $p$ in option A will not give a prime, as prime numbers are only divisible by itself or $1$.
Option B,C and E will always give an even value which is divisible by $2$, so that can not be a prime as prime numbers are only divisible by itself or $1$.
The only answer remaining is D it must be correct, it could be a prime number.
For example $p=3$ ; $p+2=3+2=5$ is a prime number.
Hence,choice D is correct.