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 Post subject: guest27
PostPosted: Sun Nov 18, 2007 11:27 pm 
Uncle Arthur is completely mad. He adds up all of the even numbers
between 0 and 1000 (including the number 1000), then he adds up all
of the odd numbers between 0 and 1000, and finally he calculates the
difference between the two totals. What answer does he get?


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 Post subject:
PostPosted: Sun Nov 18, 2007 11:53 pm 
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Joined: Fri Sep 15, 2006 8:51 am
Posts: 8112
1) A headache

2) 500

The difference is 5 for every 5 even numbers added up compared with the associated odd numbers :

2+4+6+8+10 =30
1+3+5+7+9 = 25

1000=10*100 therefore the difference is 100*5 = 500. I definitely have a headache now


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 Post subject: Re: guest27
PostPosted: Mon Nov 19, 2007 9:45 am 
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Joined: Thu Oct 11, 2007 11:51 am
Posts: 14
help wrote:
Uncle Arthur is completely mad. He adds up all of the even numbers
between 0 and 1000 (including the number 1000), then he adds up all
of the odd numbers between 0 and 1000, and finally he calculates the
difference between the two totals. What answer does he get?


DEAR GUEST,

THE FORMULA FOR SUM OF EVEN NUMBERS IS N(N+2)/4 SO

WE HAVE TO PUT THE VALUE OF N AS 1000 ,THAT MEANS
1000(1000+2)/4=1000X1002/4=250500 AND
THE SUM OF ODD NUMBERS IS N*N/4

HERE AGAIN N IS 1000

1000*1000/4=1000*250=250000.

THE DIFFERENCE BETWEEN THE TWO TOTALS = 250500-250000=500.


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 Post subject: Unclue Aurthor
PostPosted: Mon Nov 19, 2007 12:19 pm 
this can possibly done as follows;
the first set of even and the odd is 1&2 and the second set is 3&4 and so on. The last set is 999 & 1000. The difference on each is 1(one) and there are 500 such sets. So, is 500.


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 Post subject:
PostPosted: Tue Nov 20, 2007 7:56 pm 
The median of (even) numbers from 2 to 1000 inclusive is 501.
The median of (odd) numbers from 1 to 999 inclusive is 500.
Each sequence contains (1000 / 2 =) 500 numbers ...

... so the difference is [(501 - 500) x 500] 500.


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