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Mathematics 21 Online
Parth (parthkohli):

OwlKid's kiddy problem! Find the unit's digit of 11 + 22 + 33 + 44.... + 1010 + 1111 + 1212 + ...... 9797 + 9898 + 9999

OpenStudy (shubhamsrg):

5?

Parth (parthkohli):

Nope

ganeshie8 (ganeshie8):

0, right ?

Parth (parthkohli):

How did you get that one? I just added the OwlKid challenging problem to make it interesting :P I knew the last one though

OpenStudy (anonymous):

0 is the answer i guess?

ganeshie8 (ganeshie8):

sequence is in thr form : 11x

Parth (parthkohli):

I got 0 too, but I am not sure.

ganeshie8 (ganeshie8):

11x = (10+1)x x = [1, 909]

OpenStudy (shubhamsrg):

11(1+2..909) = 11* (909)(910)/2 = ..........5 ??

OpenStudy (anonymous):

I think it's either 5 or 0

OpenStudy (anonymous):

I will go with 5

Parth (parthkohli):

I first got the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 and then multiplied that by 9. I then got the unit digit 0.

Parth (parthkohli):

5 isn't in the choices.

OpenStudy (anonymous):

since we want the unit digit, we can shorten our operation to the units digit of all the terms, sum of units digit from 11 to 99 is 45. and the same unit digit repets in this series only a hundred times, so the unit digits sum will be 45*100, and well, the unit digit of dis term 4500 is 0 only, ( the rest 450 will go as carry on to the tens digit, so the answer is 0 :)

ganeshie8 (ganeshie8):

so total 910 numbers are there to be added. we can exclude the 10x component, ad the units digit will be "0" for that anyway now we need to find whats the units digit of sequence "1 + 2+ 3... " cancel out 9s... answer is 0

Parth (parthkohli):

Oh @dg123 i had the same method but I wasn't sure :p

OpenStudy (anonymous):

now u may be rest in peace, i m sure of dis method :)

Parth (parthkohli):

lol

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