Latest TCS Aptitude Question SOLUTION: 121212....upto 300 digits is divided by 90 .what is the remainder?

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(#M40030032) TCS question remainder theorem Keep an EYE

121212....upto 300 digits is divided by 90 .what is the remainder?

Asked In TCS Moitri Paul (10 years ago)

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RAKESH  (10 years ago)

sum of digits of 121212....upto 300 digits=3*150
so 121212....upto 300 digits is divisible by 9
clearly 121212....upto 300 digits/9=13468013468..........13468
13468013468..........13468/10 gives remainder 8
121212....upto 300 digits/(9*10) gives remainder 8
ANS 8

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RAKESH  (10 years ago)

sum of digits of 121212....upto 300 digits=3*150
so 121212....upto 300 digits is divisible by 9
clearly 121212....upto 300 digits/9=13468013468..........13468
13468013468..........13468/10 gives remainder 8
121212....upto 300 digits/(9*10) will give remainder 8*9=72
ANS 72

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saurabh agarwal  (10 years ago)

ans will be zero...

Is this solution Helpfull? Yes (8) | No (9)  

subham  (10 years ago)

12%90=12
1212%90=42
121212%90=72
12121212%90=12.....
so happens in cyclicity of 3...so 6 digits=3 cyclicity,300 digits=150 (12) pairs..150%3=0..so 1212....300 digits%90=72

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kratika jain  (10 years ago)

121212...(300 digit/9)= 134680134680....
(7 digit) 1212121/9= quotient= 134680
calc digit 7*42+6=300
in the end only 6 digit left 121212/9= quotient= 13468
thus 13468/10 then remainder =8

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shilpa nair  (10 years ago)

ans is 0
121212...upto 300 digits =3*150
it is divisible by 9.
which gives us 134680134680.......134680/10 gives rem 0

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Ankit Gupta  (10 years ago)

Saurabh;;
why r u taking only 2 digits..is there any trick to do so..lets take 3 digits ans will be diff...so plz tell ..which is correct

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gaurav  (10 years ago)

sum of all the digits of the series=450
beacuse there is 150 1's and 1502's
now 450/90 leaves the remainder 0

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Ankit Gupta  (10 years ago)

can it be done in any other way

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RAVI SHUKLA  (10 years ago)

how can u say?clearly 121212....upto 300 digits/9=13468013468..........13468...
plz explain

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Sohini Nandi  (10 years ago)

how we check the divisibility of 9 is if the sum of the digit is divisible by 90..
here 121212.... upto 300 term the sum of the digits is 3(taking 2+1)*(300/2)=450
now u can see 450 is divisible by 90..so the answer will be 0 as rem

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