For algebraic expressionsReplace all 6 with 9 from 1 to 100, What is the algebraic sum of it. I know the ans is 330, but i want the procedure?

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Anurag

  • Dec 9th, 2006
 

Well i think the ans is

first of all by formumla n(n+1)/2 1-100 sum is 5050.  then all 6 are replaced by 9 .that means for series like +0-9 10-19 and so on everytime 3 is added to the normal total(5050)... such case is valid in 9 such series( excluding 60-69).( for now leave the 90-100 series) so to 5050 add 9*3=27. now add 91-99 which comes  to 948( keep in mind to replace 96 by 99) so the final answer is

5050+27+948=6025

(plz verify the figures... logic is correct)

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prabha

  • Dec 11th, 2006
 

hi

am getting the ans as 5380. can any one verify n say me d correct answer?

initial sum s 5050

by replacing the 6's in one's plaCE BY 9 v get the sum increased by 30(3*10)

5050+30=5080

next for ten's place 30*=300. so  the ans s 5380

saggy

  • Dec 11th, 2006
 

answer is 540

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Anmol

  • Dec 14th, 2006
 

 hello everybody mine is same as prabha...

it has got to be 5380

as initial score: 5050

then difference of 3 per 10 that causes 3*9=27 leaving the 60's row

for sixt's row it is difference of 30- i.e. 30*10+3=303 so total diff==303+27=330 added to initial sum=5380

anybodycan contact me at er.akhileshwar@sify.com

Neelakantan G S

  • Jan 1st, 2007
 

n*(n+1)/2 =100*101/2=5050

from 1,2,3,4,5,7,8,9 series we get 3*9=27

From 6 series =10*30=300

So totally =5050+27+300

=5377

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Suman

  • Jan 28th, 2007
 

Sum of first 100 natural numbers = 5050
Now consider the number series 0-10, 11-20, 21-30, 31-40, 41-50, 71-80, 81-90, 91-100.

When 6 is replaced by 9 in all the above series the sum increases by 3 in each one.

So the sum increases by 3*8 = 24

Now consider the series 51-60
Here 56 will become 59 and 60 will become 90.
So the increase in sum is 3 + 30 = 33
Now the last series 61-70
Except for 66 when 6 is replaced by 9 the sum increases by 30 * 8 = 24066 becomes 99.
So the increase is 33
Total = 5050 + 24 + 33 + 240 + 33 = 5380

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raghu

  • Jan 28th, 2007
 

hi frds..the ans is,,,,1+2+3+4+5+6+7+8+9+10=55+3=58;11+12+13+14+15+16+17+`8+19+20=155+3=158.'''''''''''''''''''''and so on..........58+158+258+358+458+588+958+758+858+958=5410...ans 5410

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moumita

  • Feb 26th, 2007
 

ans is 5380

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praveen

  • Mar 19th, 2007
 

ans is 5380

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