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?

$21$

$22$

$23$

$24$

$25$

Answer: B

Concepts:factor ages

Difficulty rating: 900

Video solution:

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Written solution:

The only pair of single-digit positive integers with product $30$ is $5,6.$ The single-digit factor pairs of $24$ are $3,8$ and $4,6.$ Because all four ages are distinct, the pair $4,6$ would repeat the age $6,$ so the other pair must be $3,8.$ Thus the ages are $3,5,6,8,$ whose sum is $22.$

Thus, the answer is B .

2021 AMC 10B Spring Problem 5

Answer: B

Difficulty rating: 900

Video solution:

Written solution:

Problem 5 in Other Years