manchester grammar school past peper maths

[Apple33]

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?
Many thanks in advance

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?

[parent2013]

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.

[Apple33]

Yes the answer is 1001