Question

A school admits children from the age of 2 to 18 years. A person has all his kids in this school. The product of ages of his kids is 60,060. What is the maximum age of one of the kids?

• A. 13
• B. 14
• C. 15
• D. 21

Answer 1

The correct option is C 15

The product of ages of the kids is given as 60,060.

If we split the number into the product of its prime factors, we can say the factors can be age of the kids.

$60060=2\times 2\times 3\times 5\times 7\times 11\times 13$

Now, since the ages should be less than 18, we arrange the prime factors into groups such that the product obtained in each group is less than 18.

Let's see how:
$2\times (2\times 7)\times (3\times 5)\times 11\times 13$

From the above expression, we can see that any other combination will give ages more than 18 years.

The ages can be written as: $2\times 14\times 15\times 11\times 13$

Hence, the maximum possible age is 15 years.