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The number 95 can be written as the sum of the squares of 4 different

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Re: The number 95 can be written as the sum of the squares of 4 different [#permalink]
chetan2u wrote:
CRITICAL info - Since the SUM of squares of these 4 integers is ODD, the SUM of these numbers will also be ODD..
ONLY 9 and 15 are ODD in choices...

Thank you for such a time-saving shortcut. I only have one question - where do we derive the aforementioned information from? Thank you!
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The number 95 can be written as the sum of the squares of 4 different [#permalink]

Quote:
Since the SUM of squares of these 4 integers is ODD, the SUM of these numbers will also be ODD.

Quote:
Thank you for such a time-saving shortcut. I only have one question - where do we derive the aforementioned information from? Thank you!

I too am bit confused.
If a number is odd, then its square will be odd.
But odd + Odd = even.
What did I miss here?
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Re: The number 95 can be written as the sum of the squares of 4 different [#permalink]
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Quote:
Since the SUM of squares of these 4 integers is ODD, the SUM of these numbers will also be ODD.

Quote:
Thank you for such a time-saving shortcut. I only have one question - where do we derive the aforementioned information from? Thank you!

I too am bit confused.
If a number is odd, then its square will be odd.
But odd + Odd = even.
What did I miss here?

Hi,

So you agree that a number if squared will have the same property as far as odd and even is concerned. So odd^2 is odd and even^2 is even.

If sum of squares is 95, an odd number, then the sum of these integers will also be odd, whatever be the combination of squares.

Example ..
Three are odd and one even.
That is odd^2+odd^2+odd^2+even^2=odd...
In the same breadth, the sum of integers will be odd+odd+odd+even, which will be odd.
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Re: The number 95 can be written as the sum of the squares of 4 different [#permalink]
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Re: The number 95 can be written as the sum of the squares of 4 different [#permalink]
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