Mathematical Puzzle for Competitive Exams

Mathematical Puzzle for competitive examinations- Friends this is a maths puzzle. Solving this type of maths puzzle could be very useful for students taking competitive examinations like CAT, GMAT, etc. Please let me clarify the puzzle is complete and no information in missing. For more such puzzle keep checking back WWW.QUICKERMATHS.COM

Mathematics Age Puzzle

At a census there is the following dialog:

Field helper: number of children?

Citizen: three!

Field helper: age of Your children in whole numbers?

Citizen: The product of the years is 36.

Field helper: This not a sufficent answer!

Citizen: The sum of the ages equals the

number of the house of our next neighbour.

(Field helper acquires the number.)

Field helper: That is still not a sufficient answer!

Citizen: Our eldest child plays the piano.

Field helper: (after some mental calculations) – Fine, now I know the age of your three children. But it would not have been possible without the last clue.

How old are the three children?

Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

20 thoughts to “Mathematical Puzzle for Competitive Exams”

  1. @ Maheswari –
    this statement is important to determine that they are twins – “But it would not have been possible without the last clue”

    Last Clue is “Our eldest child plays the piano.”

    This clue is required only when the sum is 13. In case of 13 there are 2 possibilities. 1, 6, 6 and 2, 2, 9.
    First case be rejected based on the last clue as there is only one elder son.

    1. @ Maheshwari: It is clear from the following statement that they are twins : “But it would not have been possible without the last clue.”

      In all the cases where the sum is distinct (and he knows the sum) he can guess the age of al 3.

      Only in case of sum being 13, the last clue is required.

      there are 2 possible cases – 1,6,6 and 2,2,9. From the last clue we know that there is only one eldest son and not 2. Hence the ages are 2, 2 and 9

    2. @ Maheswari –
      this statement is important to determine that they are twins – “But it would not have been possible without the last clue”

      Last Clue is “Our eldest child plays the piano.”

      This clue is required only when the sum is 13. In case of 13 there are 2 possibilities. 1, 6, 6 and 2, 2, 9.
      First case be rejected based on the last clue as there is only one elder son.

  2. Answer –

    36 = 2^2 x 3^2. If one considers also the one year olds, then there are the following combinations:

    1st 2nd 3rd sum
    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

    Only in case of sum 13 there are 2 combinations so we need another hint. But there is an oldest child only if the family has 2 years old twins and a 9 years old child.

    I hope you liked the above puzzle

  3. I guess the ages are 2, 3, & 6.

    It looks like elder child must be atleast five years of age to play the piano.

    What is the right answer then? 2,3,6 or 3,3,4?
    What is the house number of the neighbor?

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