Question

A census taker approaches a house and asks the woman who answers the door, “How many children do you have, and what are their ages?”
Woman: “I have three children, the product of their ages is 36, the sum of their ages is equal to the address of the house next door.”
The census taker walks next door, comes back and says, “I need more information.” The woman replies, “I have to go, my oldest child is sleeping upstairs.” Census taker: “Thank you, I now have everything I need.”
What are the ages of each of the three children?

• A. 9,2,2
• B. 6,6,1
• C. 12,3,1
• D. 6,3,2

Answer 1

The Correct Option is A

The problem involves deducing the ages of three children based on their product, sum, and additional contextual clues. The key steps to solve this are:

1. We start by listing the sets of three ages whose product is 36. These combinations are:

   • 1, 1, 36
   • 1, 2, 18
   • 1, 3, 12
   • 1, 4, 9
   • 1, 6, 6
   • 2, 2, 9
   • 2, 3, 6
   • 3, 3, 4
2. The census taker says they need more information after checking the sum of the ages, which means there are multiple combinations with the same sum. Checking the sums:

   • 1+1+36=38
   • 1+2+18=21
   • 1+3+12=16
   • 1+4+9=14
   • 1+6+6=13
   • 2+2+9=13
   • 2+3=6=11
   • 3+3+4=10

   The sums 13 (from 1, 6, 6 and 2, 2, 9) are the same, leading to the need for further clues.
3. The woman states she has an "oldest" child, implying not all ages are the same. Therefore, the set 1, 6, 6 does not work, since there is no distinct oldest child. This leaves us with the combination 2, 2, 9.

Thus, the ages of the children are 9, 2, and 2.