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guest27
Posted: Mon Nov 19, 2007 12:27 am
by help
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?
Posted: Mon Nov 19, 2007 12:53 am
by hermanmunster
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
Re: guest27
Posted: Mon Nov 19, 2007 10:45 am
by naga
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.
Unclue Aurthor
Posted: Mon Nov 19, 2007 1:19 pm
by logan
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.
Posted: Tue Nov 20, 2007 8:56 pm
by ittiait
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.