Think of a 135 digit number formed by writing the first 72 natural number side by side in a string.(i.e.) 1 2 3………70 71 72. Find the remainder when it is divided by 12.
a. 2
b. 9
c. 0
d. 5

• ans c
  12345678..........7172 is a 135 digit number
  divisibility rule for 12 is :divisible by 4 and divisible by 3
  for divisible by 3 sum is divisible by 3
  for divisible by 4 last two nos should be divisible by 4
  sum of 72 nos is 72*73/2=36*73
  then 36*73/3 and last two digits 72 is divisible by 4 so remainder is zero
• 9 years agoHelpfull: Yes(25) No(1)
• ans 0, because it is divisible by 3 and 4
• 9 years agoHelpfull: Yes(18) No(3)
• Sum of the first 72 natural numbers is =72(72+1)/2=2628
  2628 is divisible by 3,9 (divisibility rule for 3,9)
  123456......7172 is divisible by 4 also as last two digits of this number which is 72 is divisible by 4 (divisibility rule of 4)
  Option:B
• 9 years agoHelpfull: Yes(4) No(11)
• Option: C (sorry)
• 9 years agoHelpfull: Yes(3) No(5)
• option:C,bcz sum of 1st 72 natural no is 72*73/2=2628 and if it is divided by 12 dn remainder is 0
• 9 years agoHelpfull: Yes(1) No(0)
• c.0 to divisible by 12
  last two digits are must divisible by 3 &4
  so result 0
• 9 years agoHelpfull: Yes(1) No(0)
• The 135 th digit in 1,2,3,.....72 is 2.
  so the number is 72
  72/12 remainder is 0.
  option:C
• 9 years agoHelpfull: Yes(0) No(3)
• c....12 is divisible by 4 n 3...........so by divisibility rule of 4 n 3...it is satisfied............so remainder is 0
• 9 years agoHelpfull: Yes(0) No(1)
• divisibility rule for 12: the number should divide by both 3 and 4
  so taking last two digit 72 it is divisible by 4 and while considering their sum by using the fomula n(n+1)/2, it is found that it is divisible by 3 too
  so the remainder is option c) 0
• 5 years agoHelpfull: Yes(0) No(0)