What is the remainder when 121212.......(300) digits is divided by 99.

a. 18
b. 36
c. 72
d. 0

Thank You...

• 1stly see the example------------
  What is the remainder when the number 1234567 is divided by 99?
  
  The we first start from the right hand side of the number taking two digits at a time and find their sum.
  
  So, we get: 67 + 45 + 23 + 01 = 136.
  
  Now, when 136 is divided by 99, the remainder is 37.
  
  So, the remainder when 1234567 is divided by 99, the remainder is 37.
  now ......
  We use the similar method for finding the remainder when the number 121212......300 times is divided by 99.
  
  Note that if we take two digits at a time, starting from the right hand side, then everytime we will get the number 12 and since the given number is a 300 digit number, 12 will be added 150 times and so the sum obtained will be (12) * (150) = 1800 and this number, when divided by 99, the remainder will be 18, which is the required remainder.
  
  Hence, when the number 1212121212 ............. 121212 (300 times) is divided by 99, the remainder is 18.
• 10 years agoHelpfull: Yes(85) No(0)
• 12/99=12
  1212/99=24
  121212/99=36
  .
  .
  .
  121212...(300)/99=(12*300)%99=36
  
  if they say 300 digits then (12*150)%99=18
• 10 years agoHelpfull: Yes(48) No(9)
• Ans is :36
  12/99=12 ---->(12*1)/99
  1212/99=24----->(12*2)/99
  121212/=36----->(12*3)/99
  .......
  .......
  .......
  1212121212..upto300--->(12*300)/99
  (12*300)/99=3600/99=Remainder 36
  
  
• 10 years agoHelpfull: Yes(14) No(16)
• ans is 18
  121212......(300)times we can write this as
  as 2+10+200+1000+20000+100000.........+1000(290 zeros)/%99
  ===>2+10+2+10+2+10+2+10 upto 2's 150 times and 10's 150 times because 2%99=200%99=2000%99=2 and 10%99=1000%99=100000%99=10
  so 150(2+10)%99=1800%99=18
• 10 years agoHelpfull: Yes(5) No(1)
• no. is 1212121.... 300digits.
  it means for this no. to be divisible by 99,it has to be divisible by 11 and 9 both.
  lets check first for divisibility by 11.
  here we see U-L will be 0 as adding atlernatly.. 1+2+1+2.... will be U and same will be L.
  
  now for divisibility by 9..
  1+2+1+2+1+... is divisible by 9 completely.
  so the remainder is 0.
• 10 years agoHelpfull: Yes(5) No(5)
• there are 150 pairs of 12 so 12*150/99
• 10 years agoHelpfull: Yes(3) No(3)
• 18
  12+12+12.......150times
  12(150)=1800
  18+00=18
  
• 10 years agoHelpfull: Yes(2) No(0)
• Take first two digits...take their sum 1+2=3....
  
  taking two digits at a time, we get 150 sets, i.e. 2x150
  so sum of all digits is 450
  450 is divisible by 9 and so divisible by 11 also..hence by 99
  
  remainder is 0
• 10 years agoHelpfull: Yes(2) No(0)
• ANS:72
  
  1 and 2 are individually repeating 150 times each so total sum is 450
  now
  12121212..... /(9*11)
  =121212.......12/11 (as numerator(whose sum is 450) is totally divisible by 9 )
  and as 2 is in the last digit of numerator ,,the last digit in the quotient when divided by 9 is 8 (as 9*8=72) which when divided by 11 gives remainder 8.
  
  As we used 9 already to divide the no. so 8 is multiplied by 9
  hense gives the remainder 72..ans.
• 10 years agoHelpfull: Yes(1) No(5)
• remainder 0,, rule of remender 11,,,12100/11= 0(rem)ans also 9 zero rem
  
• 10 years agoHelpfull: Yes(1) No(3)
• 12*150/99 there are 12 pairs of 150
• 10 years agoHelpfull: Yes(1) No(3)
• 18
  
  12*300 divided by 99 remainder is 18
• 10 years agoHelpfull: Yes(0) No(1)
• The ans is 18..
  
• 10 years agoHelpfull: Yes(0) No(0)
• its 18
  99*x+18=1212
  
• 10 years agoHelpfull: Yes(0) No(0)
• first find the digital sum of 99 i.e.,9+9=18.
  1+8=9...
  now check the options which has sum 9..that is the ans..i.e 18
• 10 years agoHelpfull: Yes(0) No(1)
• 12*150/99=7
• 10 years agoHelpfull: Yes(0) No(0)
• 1212*75
  1212/99=24
  24*75=1800
  1800/99 reminder 18 ans
• 10 years agoHelpfull: Yes(0) No(0)
• 12 repeated 150 times;
  so R(12*150)/99= 18.
  answer is 18.
• 10 years agoHelpfull: Yes(0) No(0)
• to satisfy the divisibility it has to satisfy for 11 & 9,,,,,for 9 i got as 1 remainder and for 11 got as 8 how can i conclude the answer is 18?if any one know can u please explain?
• 10 years agoHelpfull: Yes(0) No(0)
• 18
  12+12+12.......150times
  12(150)=1800
  18+00=18
• 10 years agoHelpfull: Yes(0) No(0)