Problem Solving

BTGmoderatorDC wrote:Number N is randomly selected from a set of consecutive integers between 50 and 69, inclusive. What is the probability that N will have the same number of factors as 89?

a) 1/2
b 1/5
c) 0
d) 1/3
e) 1/4

OA B

Source: Manhattan Prep

The solution to this problem is straightforward if you know your prime numbers.

We need to determine the probability that a number, when randomly selected from the set of integers between 50 and 69, inclusive, will have the same number of factors as 89. Since 89 is prime and thus has only two factors, we need to determine the number of prime numbers between 50 and 69, inclusive. The prime numbers between 50 and 69, inclusive, are:

53, 59, 61, 67

We also know that there are 69 - 50 + 1 = 20 integers from 50 to 69, inclusive; thus, the probability that N will have the same number of factors as 89 is 4/20 = â…•.

Answer: B