2021 AMC 10B Problem 5

Problem 5 of 25EasierAlgebra Number Theory

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?

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Solution

The only pair of single-digit positive integers with product

30

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 .

Tagged: factor · ages