Double-Digit Divisors?

Probability Level 2

The probability that a positive divisor of $60$ is greater than $9$ can be written as $\frac{a}{b}$ , where $a$ and $b$ are coprime positive integers. What is the value of $a+b$ ?

The answer is 3.

1 solution

Arron Kau Staff
May 13, 2014

We have $60 = 2^2\times 3 \times 5$ , thus there are $3 \times 2 \times 2 = 12$ divisors in total. Listing out the divisors less than or equal to $9$ , we have $1, 2, 4, 3, 6, 5$ , which gives $6$ divisors in all. Thus the probability is $\frac{12 - 6}{12} = \frac{1}{2}$ . Hence $a + b = 1 + 2 = 3$ .

Double-Digit Divisors?

The answer is 3.

1 solution

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