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Ask iit jee aieee pet cbse icse state board experts Expert Question: please give the explanation how to solve this problem?
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[Post New]7 Apr 2008 12:16:14 IST
    Subject: please give the explanation how to solve this problem?
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bachinarayudu (0)

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1.      Find sum of digits of D.
Let
A= 19991999
B = sum of digits of A
C = sum of digits of B
D = sum of digits of C
(HINT : A = B = C = D (mod 9))
    
[Post New]7 Apr 2008 12:58:03 IST
    Subject: Re:please give the explanation how to solve this problem?
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sboosy (3053)

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\mbox{Lets take any 2 numbers} \\ \\ 23,36 \\ \\ \mbox{Sum of digits of 23 is} \ 2+3=5 \\ \\ \mbox{Sum of digits of 36 is} \ 3+6=9 \\ \\ \mbox{Sum of digits of the product of these two is} \ (5*9 = 45) \ \mbox{is} \ 4+5 = 9 \\ \\ \mbox{Now} \ 23*36 = 828 \\ \\ \mbox{Sum of its digits reduced to single digit is} \ 8+2+8 = 18 , 1+8 = 9 \\ \\ \mbox{This is true for multiplication in general} \\ \\ (1999)^{1999} \\ \\ \mbox{Sum of digits of 1999 is} \ 1+9+9+9 = 1 \ \mbox{(reduced to one digit)} \\ \\ \mbox{Thus the sum of digits of the answer reduced to 1 digit is also 1}
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[Post New]7 Apr 2008 13:21:54 IST
    Subject: Re:please give the explanation how to solve this problem?
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nadeemoidu (1184)

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@sboosy
It's true that if this process goes on , the final digit will be 1 . but how do we know that after 4 operations , the result will be a 1 digit no.?
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[Post New]7 Apr 2008 13:25:51 IST
    Subject: please give the explanation how to solve this problem?
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sboosy (3053)

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ok i shud have mentioned it ...
i meant to say that u ll may b end up getting something like 37(2 digits) or 244(3 digits) ...some number whose sum of digits is 1 ..
i just wanted to give an idea .
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