VJesus12 wrote: ↑

Sun Apr 25, 2021 1:26 pm

If \(3 < x < 100,\) for how many values of \(x\) is \(\dfrac{x}3\) the square of a prime number?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine

Answer: B

Source: Official Guide

We want values of x (where 3 < x < 100) such that x/3 is the square of a prime number.
So, let's start checking squares of prime numbers.
Some prime numbers are 2, 3, 5, 7, 11, etc

2² = 4 and (3)(4) = 12. So, x = 12 meets the given conditions.
3² = 9 and (3)(9) = 27. So, x = 27 meets the given condition
5² = 25 and (3)(25) = 75. So, x = 75 meets the given conditions.
7² = 49 and (3)(49) = 147. No good. We need values of x such that 3 < x < 100

So, there are exactly 3 values of x that meet the given conditions.
Answer: B