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(#M40038404) INTERVIEW Numerical Ability question Cubes Keep an EYE

Two MIT math grads bump into each other while shopping. They haven't seen each other in over 20 years. First grad to the second: "How have you been?"
Second: "Great! I got married and I have three daughters now."
First: "Really? How old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
First: "Right, ok... Oh wait... Hmm, I still don't know."
Second: "Oh sorry, the oldest one just started to play the piano."
First: "Wonderful! My oldest is the same age!"
How old was the first grad’s daughter?

Asked In Interview Dikesh Kumar Gumansingh (10 years ago)

Unsolved Read Solution (3)

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Swechchha Agarwal  (10 years ago)

We know there are 3 daughters whose ages multiply to 72. let’s look at the possibilities…

Ages: Sum of ages:
1 1 72 74
1 2 36 39
1 3 24 28
1 4 18 23
1 6 12 19
1 8 9 18
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 4 6 13
after looking at the building number the man still can’t figure out what their ages are, so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter(by "oldest just started to play piano"). that rules out the “2 6 6” possibility since the two oldest would be twins. therefore, the daughters ages must be “3 3 8”.

Is this solution Helpfull? Yes (5) | No   

sunil kumar  (10 years ago)

Sorry in the previous solution by mistake i get it youngest instead of oldest...here is the correct solution...

Possible combinations are

1*1*72 not possible ..common sense
1*2*36 = 39
1*3*24 = 28
1*4*18 = 23
1*6*12 = 19
1*8*9 = 18
2*2*18 = 22
2*3*12 = 17
2*4*9 = 15
2*6*6 = 14
3*3*8= 14
3*4*6 = 13


Since the number of the building is known but still he is askng for another clue..which he has confusion which can only come if the sum of two combination is same n i.e. 14

And lastly he has an oldest daughter that means there cannot be two oldest daughters..
So we get the ages from 3+3+8

And so the answer is 8

Is this solution Helpfull? Yes (2) | No   

sunil kumar  (10 years ago)

Possible combinations are

1*1*72 not possible ..common sense
1*2*36 = 39
1*3*24 = 28
1*4*18 = 23
1*6*12 = 19
1*8*9 = 18
2*2*18 = 22
2*3*12 = 17
2*4*9 = 15
2*6*6 = 14
3*3*8= 14
3*4*6 = 13


Since the number of the building is known but still he is askng for another clue..which he has confusion which can only come if the sum of two combination is same n i.e. 14

And lastly he has an oldest daughter that means there cannot be two oldest daughters..
So we get the ages from 2+6+6

And so the answer is 2

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