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A man has nine children whose ages are at an exact interval.

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A man has nine children whose ages are at an exact interval. [#permalink] New post   26 Nov 2005, 09:33
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A man has nine children whose ages are at an exact interval. The sum
of the squares of the ages of each is the square of his own age. What
is the age of each child and the man?



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Re: A man has nine children whose ages are at an exact interval. [#permalink] New post   26 Nov 2005, 09:42
GMATT73 wrote:
A man has nine children whose ages are at an exact interval. The sum
of the squares of the ages of each is the square of his own age. What
is the age of each child and the man?


I guess you are in between a question marathon..:) Could you please post the answer choices for the PS????

All i could gather from the above questions are

ages =x,x+y.......= 9x+8y
x^2+(x+y)^2.....= age of the man.

There si something missing..
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Re: A man has nine children whose ages are at an exact interval. [#permalink] New post   26 Nov 2005, 11:03
well, this problem is somewhat similar to the MGMAT posted by me long time ago ..the trick is to skillfully expression the age of each ...realize that 9 is odd. There's possibly a symmetric point, call it t
we have the age of 9 children are
(t-4a), (t-3a),(t-2a), (t-a), t, (t+a) , (t+2a),(t+3a),(t+4a)

spread the sum of those 9 squares, those t*a will be cancelled mutually.
the rest is:

9t^2+60a^2= D^2 ( D is the father's age)
--->(D-3t)(D+3t)= 60a^2
since they're all integer ...try to find those integers which satisfy the equation.
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Re: A man has nine children whose ages are at an exact interval. [#permalink] New post   26 Nov 2005, 12:08
laxieqv wrote:
well, this problem is somewhat similar to the MGMAT posted by me long time ago ..the trick is to skillfully expression the age of each ...realize that 9 is odd. There's possibly a symmetric point, call it t
we have the age of 9 children are
(t-4a), (t-3a),(t-2a), (t-a), t, (t+a) , (t+2a),(t+3a),(t+4a)

spread the sum of those 9 squares, those t*a will be cancelled mutually.
the rest is:

9t^2+60a^2= D^2 ( D is the father's age)
--->(D-3t)(D+3t)= 60a^2
since they're all integer ...try to find those integers which satisfy the equation.


but the question says A man has nine children whose ages are at an exact interval.

so how does your formula work then?
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Re: A man has nine children whose ages are at an exact interval. [#permalink] New post   26 Nov 2005, 19:57
nakib77 wrote:
laxieqv wrote:
well, this problem is somewhat similar to the MGMAT posted by me long time ago ..the trick is to skillfully expression the age of each ...realize that 9 is odd. There's possibly a symmetric point, call it t
we have the age of 9 children are
(t-4a), (t-3a),(t-2a), (t-a), t, (t+a) , (t+2a),(t+3a),(t+4a)

spread the sum of those 9 squares, those t*a will be cancelled mutually.
the rest is:

9t^2+60a^2= D^2 ( D is the father's age)
--->(D-3t)(D+3t)= 60a^2
since they're all integer ...try to find those integers which satisfy the equation.



but the question says A man has nine children whose ages are at an exact interval.

so how does your formula work then?


the interval is a :wink: ...add a to the smallest, get the next one, add a to the next one, get the next next one and so forth ..check it, buddy :wink:



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: A man has nine children whose ages are at an exact interval. [#permalink]
26 Nov 2005, 19:57
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