Question

11. The Smiths have 3 children. The product of their ages is 200, and the two youngest are

What is the age of their oldest child?

Answer 1

Therefore, the age of the oldest child is 5.

Explanation:

Let the ages of the three children be x, y, and z, where x ≤ y ≤ z. We are given that:

x * y * z = 200 and x ≤ y

We need to find the age of the oldest child, which is z.

Since 200 has only two prime factors, which are 2 and 5, and the product of the ages is 200, we can deduce that the ages of the children are 2, 5, and 20 (in some order).

If the youngest two are 2 and 5, then the product of their ages is 10, and the product of all three ages cannot be 200. Therefore, the youngest two children must be 2 and 20, and the age of the oldest child is 5.