What is the remainder when 7 + 77 + 777 + 7777 +....(till 100 terms) is divided by 8?
a) 0 b) 2 c) 4 d) 6

• ans. sould be 6 bcs whan 7 is divided by 8 reminder is 7 and than whan it is devided by 77 it will be 5 and remaining 98 term leav the remainder 1 so
  7+5+98 is devided by 7 it will give 6 as the reminder.
  
• 12 years agoHelpfull: Yes(20) No(7)
• I think ans will be 0.
  we write the series as.....
  (8-1)+(8-1)(8-1)+(8-1)(8-1)(8-1)+(8-1)(8-1)(8-1)(8-1)+........till 100 terms/8
  =(-1)+(-1)(-1)+(-1)(-1)(-1)+(-1)(-1)(-1)(-1)+.......till 100 terms/8
  =(-1)+(1)+(-1)+(1)+...........till 100 terms/8
  =0 ans.
• 11 years agoHelpfull: Yes(2) No(4)
• Consider the first term 7: when divided by 8, the remainder is 7
  Consider the second term 77: when divided by 8, the remainder is 5.
  Consider the third term 777: when divided by 8, the remainder is 1.
  Consider the fourth term 7777: when divided by 8, the remainder is 1.
  Consider the fifth term 77777: when divided by 8, the remainder is 1.
  .........
  .........
  Consider the tenth term 7777777777: when divided by 8, the remainder is 1.
  .........
  .........
  Therefore, excepting the first two terms, the remainder in all the other cases is 1.
  The remainder for the entire expression will therefore be the remainder left after dividing
  [7 + 5 + 1 + 1 + 1 + (98 times)] by 8.
  That is, (7 + 5 + 98)/8, or 110/8. The remainder when 110 is divided by 8 is 6.
• 10 years agoHelpfull: Yes(1) No(0)
• Answer is a) 0
  
  remainder 7/8 = 7
  remainder 77/8 = 5
  remainder 777/8 =1
  remainder 7777/8 =1
  remainder 7777....100terms/7 = 1
  sum of remainder = 7 + 5 +(1 + 1 + 1+ ..........98 terms)
  = 110
  finally reminder 100/8
  = 0
• 10 years agoHelpfull: Yes(0) No(1)
• Ans d 6
  7%8=7, 77%8=5, 777%8=1, 7777%8=1, 77777%8=1 ........ 1 is remainder from 3rd term to 100th term
  100-3+1=98 98+7+5=110%8=6
  
• 8 years agoHelpfull: Yes(0) No(0)
• We need to figure out which all numbers cause a confusion when reversed : 0, 1, 6, 8, 9.
  1st digit cannot be 0. So, 9 combinations are possible for the 1st digit.
  2 digits are distinct. So, 2nd digit cannot be 1st digit.
  
  Hence, again 9 combinations possible for 2nd digit. So, totally, 9 * 9 = 81 numbers are possible.
  Since 1st digit is not 0, we can neglect confusions caused by 0, as, if a number with 2nd digit 0 is reversed, it will have its 1st digit as 0, and that is not possible, and hence no confusion. i.e. If we reverse 60, we get 09, but since 0 is not the 1st digit, the agency knows 09 is wrong, and hence it causes no confusion.
  The remaining numbers are 1,6,8,9.
  Numbers starting with 1: 16, 18, 19 cause confusion.
  Numbers starting with 6: 61, 68, 69 cause confusion.
  Numbers starting with 8: 81, 86, 89 cause confusion.
  Numbers starting with 9: 91, 96, 98 cause confusion.
  Now if you think again 69 and 96 does not cause confusion when read upside down. 69 when read upside down is 69, and 96 when read upside down is 96! So, only 10 numbers out of 81 cause confusion.
  
  Hence, there are 71 numbers.
• 7 years agoHelpfull: Yes(0) No(0)