A maximum number of 3 digit such that when expressedin base 2 or base 3 or base 7 has 1 as the rightmost(last) digit. If a,b,c are the first digits(leftmost) of the base 2, base 3 and base 7 representation of that number. Then sum of a,b,c

• given that right most digit is 1.
  means in base system 1 is remainder in each case.
  we have to find greatest 3 digit number, so first we have
  to find the greatest 3 digit number which is divisible by 2,3
  and 7.
  so take lcm of 2,3 and 7.
  LCM(2,3,7)=42.
  Now
  42)999(23
  84
  -----
  159
  126
  -------
  33
  
  so greatest 3 digit number which is divisible by 2,3 and 7 is
  999-33=966
  
  Number which have right most digit is 1 is equal to 966+1=967.
  now express this number in base 2, base 3 and base 7 system
  and find a,b and c.
  
• 9 years agoHelpfull: Yes(9) No(0)
• a=1 , b=1 , c=2 ans is 4
  number is 967
• 10 years agoHelpfull: Yes(4) No(0)
• The number is 967, 2*3*7 = 42, highest 3 digit number = 42*23 = 966 , 966 +1 = 967
  
  Leftmost digit = 2+1+1 = 4
• 10 years agoHelpfull: Yes(3) No(0)
• 2a+1 = 3b+1 = 7c +1
  
  2a=3b
  
  a=3, b=2 : 7
  
  a=6, b=4 : 13
  
  6p + 7
  
  6p + 7 = 7c + 1
  
  6p + 6 = 7c
  
  6 (p+1) / 7 = c
  
  p=6 : 43
  
  p=13 : 85
  
  42d + 43
  
  42(22) + 43 = 967
  
  967 in base 2 = 1111000111
  
  967 in base 3 = 1022211
  
  967 is base 7 = 2551
  
  answer = 1+1+2 = 4
• 9 years agoHelpfull: Yes(3) No(0)
• The answer is 4
  The question says that the number has last digit as 1 in base 2,3,and 7.
  You will see that this true for only those numbers which when divided by 2,3,and 7 leaves remainder 1.
  So the number will be of format (L.C.M of 2,3,7)*n+1.=42n+1
  The highest 3 digit number is 42*23+1=967.
  When you will convert it into base 2,3,and 7 the sum of first digit ie a+b+c will be 4
  Thanks
  
• 9 years agoHelpfull: Yes(3) No(0)
• pls explain in detail
• 10 years agoHelpfull: Yes(2) No(0)
• plzz explain not got the correct answer???????? urgently
• 10 years agoHelpfull: Yes(2) No(0)
• It must be 5
• 10 years agoHelpfull: Yes(0) No(1)
• naveen how did you find that no. ??
• 10 years agoHelpfull: Yes(0) No(1)