Multiple choice

Raman has three daughters. Aman asked him the ages of his daughters. Raman told him that the product of their ages was 36. After thinking, Aman was unable to find the answer and asked for another clue. Raman said that the sum of their ages is equal to his house door number. Aman knew the house number but was unable to answer and asked for another clue. Raman said that his youngest daughter had blue eyes, and suddenly Aman gave the correct answer. How old is the youngest daughter?

  1. 1 year

  2. 2 years

  3. 3 years

  4. 4 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Factors of 36: (1,1,36), (1,2,18), (1,3,12), (1,4,9), (1,6,6), (2,2,9), (2,3,6), (3,3,4). Sums: 38, 21, 16, 14, 13, 13, 11, 10. Since Aman needed another clue, the sum must be 13 (the only duplicate sum). The clue 'youngest daughter' implies there is a single youngest, so (2,2,9) is rejected, leaving (1,6,6). The youngest is 1.

AI explanation

List all possible combinations of three positive integer ages whose product is 36. The combinations and their sums are (1, 1, 36) summing to 38, (1, 2, 18) summing to 21, (1, 3, 12) summing to 16, (1, 4, 9) summing to 14, (1, 6, 6) summing to 13, (2, 2, 9) summing to 13, (2, 3, 6) summing to 11, and (3, 3, 4) summing to 10. Since Aman knew the house number but still needed another clue, the sum must be ambiguous, leaving only the combinations (1, 6, 6) and (2, 2, 9), both of which sum to 13. The final clue specifies that there is a single youngest daughter, which eliminates the (2, 2, 9) combination since it has two youngest children of the same age, leaving the ages as 1, 6, and 6, making the youngest daughter 1 year old.

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