Question: 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

“If 3 < x < 100, for how many values of x is x/3 the square”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Approach Solution 1:

We seek x values such that x/3 is the square of a prime number (3 x 100).
So let's begin checking prime number squares.
Few examples are 2, 3, 5, 7, 11 and other prime numbers
2² = 4 and (3)(4) = 12. Therefore, x = 12 fulfills the requirements.
3² = 9 and (3)(9) = 27. Therefore, x = 27 fulfills the requirement.
5² = 25 and (3)(25) = 75. Thus, x = 75 fulfills the requirements.
7² = 49 and (3)(49) = 147. Very bad. We require x values such that 3 x 100.
As a result, there are precisely 3 values of x that satisfy the requirements.

Correct Answer: B

Approach Solution 2:

Setting up the equation as follows:
x/3 should be a square
So, say x/3= a*a
x=3(a*a)
3<3(a*a)<100
If a = 1; the requirement fails
If a = 2; x = 12
If a = 3; x = 27
If a = 5; x = 75
If a = 7; requirement fails
Total number of correct values is Three.

Correct Answer: B

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