How many numbers are there between 0 and 1000 which on division by 2, 4, 6, 8 leave remainders 1, 3, 5, 7 respectively?
(a) 21 (b) 40 (c) 41 (d) 39

• ans : 41
  lcm of 2,4,6,8 is 24
  so the num's are 23,47, ..... (41*24)-1
  
  
• 11 years agoHelpfull: Yes(1) No(0)
• ans : 41
  lcm of 2,4,6,8 is 24
  25%24=1 and 27%24= 3 and 29%24=5 and 31%24= 7
  49%24=1 and 51%24= 3 and 53%24=5 and 55% 24 = 7
  ............... ................ .............. ..............
  ............... ................ .............. ..............
  985%24=1 and 987%24 = 3 and 989 %24 = 5 and 991 % 24= 7
  
  all above are AP with difference 24, you can use any of them , lets take a= 29 d=24 l=989
  l= a+(n-1)d
  989= 29+(n-1)24
  (n-1)24= 989-29=> n-1=960/24=> 40
  n=41....ans.
• 7 years agoHelpfull: Yes(0) No(0)