If 3 < x < 100, for how many values of x is x/3 the square of a prime number?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine
OAB
Please explain.
(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine
OAB
Please explain.
We want values of x (where 3 < x < 100) such that x/3 is the square of a prime number.kamalj wrote:If 3 < x < 100, for how many values of x is x/3 the square of a prime number?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine
OAB
Please explain.
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
Cheers,
Brent
