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 Post subject: manchester grammar school past peper mathsPosted: Sun Mar 30, 2014 12:17 am
Hi,
this question is from Manchester Grammar School, I can't explain it in a simple way to my DS, except algebra.
Is there a simple way to explain it?

Q) What is the difference between the sum of all the even numbers up to and including 2002 and the sum of all the odd numbers up to 2002?

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 Post subject: Re: manchester grammar school past peper mathsPosted: Sun Mar 30, 2014 12:49 am

Joined: Mon Aug 12, 2013 9:13 am
Posts: 452
I think it has to do with juggling of numbers rather than algebra.

Let's try doing it for smaller set of numbers say... first 10 numbers

(2+4+6+8+10) - (1+3+5+7+9) which could be re-written as

(2-1) + (4-3) + (6-5) + (8-7) + (10-9)

1 + 1 + 1 + 1 + 1 =5 which is half of 10

I guess the answer is 2002/2 i.e. 1001.

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 Post subject: Re: manchester grammar school past peper mathsPosted: Sun Mar 30, 2014 12:53 am

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