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Source: — Problem Solving |

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by Brent@GMATPrepNow » Mon May 12, 2014 6:42 am
prernamalhotra wrote:If 3<x< 100, for how many values of x is x/3 the square of a prime number?

A) 2
B) 3
C) 4
D) 5
E) 9
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 condition12
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

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by GMATGuruNY » Mon May 12, 2014 9:24 am
prernamalhotra wrote:If 3<x< 100, for how many values of x is x/3 the square of a prime number?

A) 2
B) 3
C) 4
D) 5
E) 9

Dividing 3 < x < 100 by 3, we get:
1 < x/3 < 33.33.

Since x/3 must be between 1 and 33, x/3 could be equal to the following:
2² = 4
3² = 9
5² = 25.

The correct answer is B.
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by lram2310 » Mon May 12, 2014 10:44 am
B) 3
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