A number when divided by 100 leaves a quotient (Q) and a remainder (R). How many three-digit natural numbers are there such that Q + R is divisible by 11?

• it will be like
  
  110 / 100 => Q=1 , R=10
  
  Q+R= 11
  11/11 =0
  
  similarly for 121,132,143,154,165,176,187,198
  
  i.e total 100-200 = 9 numbers
  so in 100-1000 there will be 9*9 = 81 numbers
  
• 12 years agoHelpfull: Yes(39) No(6)
• From 100 to 200. Q would be 1 and reminder(R)need to be 10,
  21,32,43,54,65,76,87,98 again 9 numbers.
  From 200 to 100. Q would be 2 and R need to be
  9,20,31,42,53,64,75,86,97 again 9 numbers.....
  LIKEWISE
  100 to 200----9 numbers
  200 to 300----9 numbers
  300 to 400----9
  400 to 500----9
  500 to 600----9
  600 to 700----9
  700 to 800-----9
  800 to 900-----9
  900 to 1000 ---9
  so total 9x9=81 numbers
• 12 years agoHelpfull: Yes(10) No(6)
• There will be only 9 such numbers...
  
  These numbers are:-
  
  990 =>
  990/100 => Q=9 & R=90
  And, Q+R = 9+90 = 99 is divisible by 11
  
  880 =>
  880/100 => Q=8 & R=80
  And, Q+R = 8+80 = 88 is divisible by 11
  
  770 =>Similarly check for rest of the values
  660 =>
  550 =>
  440 =>
  330 =>
  220 =>
  
  110 =>
  110/100 => Q=1 & R=10
  And, Q+R = 1+10 = 11 is divisible by 11
  
  So, total 9 numbers exists b/w 101 to 999 (i.e in all three-digit natural numbers)
• 12 years agoHelpfull: Yes(7) No(21)
• Sorry guys, mine above shown answer is wrong...plz dont 'like' it
  Correct answer is 81 only.
• 12 years agoHelpfull: Yes(5) No(1)
• because no. is 3 digit we will have to take q=single digit no.(1,2,3,4,5,6,7,8,9)
  when q=1,then we take
  r;
  10
  10*2+1=21
  10*3+2=32
  10*4+3=43
  .
  .
  .
  10*9+8=98
  
  total combinations=9;
  now we take q=2,3,4,5.......9
  every q give 9 combination
  so,3-digit natural numbers=9*9=81ans
• 12 years agoHelpfull: Yes(3) No(0)
• there will be 81 such nos... becoz btween 100 and 200 the nos are 110,121,132,143,154,165,176,187,198 there the q+r is divisible by 11 so similerly between 200,300.........till 900,1000..
• 12 years agoHelpfull: Yes(2) No(1)
• answer is 81
  
  100-200 = 9 numbers
  200-300 =9 numbers
  
  so total 9*9 = 81
• 12 years agoHelpfull: Yes(1) No(7)
• answer would be 9
  it will multiples of 110 up to 9times
  like 110,220,330,440.............,990 if .we divide these no by 100 so Q+R will be definetly divisible by 11
• 12 years agoHelpfull: Yes(1) No(7)
• hii guys correct answer is 81
• 12 years agoHelpfull: Yes(0) No(0)
• answer is 81
  
  N100 =Q+R
  100
• 12 years agoHelpfull: Yes(0) No(2)
• n1=110 and n2=990
  even both extreme three digits numbers divisble by 11.
  so (n2-n1)/11 +1 =81
• 11 years agoHelpfull: Yes(0) No(0)