Question

Puzzle Patel was out looking for a new apartment to rent. The landlord asks him if he has any pets.
Patel: "Three cats"
Landlord: "How old are they?"
Patel: "The product of their ages is 72."
Landlord: "What kind of answer is that!? I need more information."
Patel: "Sorry, that must have been unclear. The sum of the ages of my pets is the same as your house number."
Landlord: "Still not enough information, As we have only 20 houses in this society."
Patel: "My oldest cat is called Gypsy and sum of letters and her age is related as perfect square"
Landlord: "Okay, cool. Now that I know their ages, you can have the house."
What is the sum of the ages of Puzzle Patel's pets?

a) 25
b) 14
c) 44
d) 38

Answer 1

Solution :-

Let ages of three cats be a , b and c .(where c is oldest.)

given that, The product of their ages is 72 .

so,

→ a * b * c = 72

also,

→ (a + b + c) < 20 . { As there are 20 houses in this society.}

now, oldest cat is called Gypsy and sum of letters and her age is related as perfect square .

so,

→ (G + Y + P + S + Y) + c = perfect square

→ (7 + 25 + 16 + 19 + 25) + c = perfect square

→ 92 + c = perfect square.

possible value of c :-

• 92 + 8 = 100 = 10² .
• 92 + 29 = 121 = 11² => But c cant be more than 20.

so, only possible value of c must be 8 .

then,

→ a * b * 8 = 72

→ a * b = 9

Possible values :-

• a = 1 , b = 9 => if b = 9 , c cant be oldest cat.
• a = 3 , b = 3

therefore, we can conclude that,

• a = 3
• b = 3
• c = 8

hence,

→ Sum of their ages = 3 + 3 + 8 = 14 (Ans.) (b)

Learn more :-

Shakuntla Devi, Karl Gauss, Archimedes could do a lot of quick maths since their young ages.

Can you do better and find ...

https://brainly.in/question/37519368