Question

The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied together give $24,$ while the other two multiply to $30.$ What is the sum of the ages of Jonie's four cousins?

$21$

$22$

$23$

$24$

$25$

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Written solution:

Since the last two are multiplied to $30$ and both are single-digit numbers, one of them must be $5,$ making the other person $6.$ The first two are of ages that multiply to $24.$ The only pair of single-digit numbers whose product is $24$ and none of them are $4$ or $6$ is the pair $3,8.$ Thus, the ages are $3,5,6,8,$ making their sum $22.$

Thus, the answer is B .

2021 AMC 10B Spring Problem 5

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Problem 5 in Other Years