Question

Let x be the largest 4 digit number which when divided by 6,7,8,9,10 leaves a remainder 4,5,6,7,8 respectively. Then the sum of digits of x is ?

Answer 1

LCM of 6,7,8,9,10=5040
the remainders when divided by 4 digit number are 4,5,6,7,8
the difference between divisors and remainders is 2
so, subtract 2 from LCM
             5040-2=5038
so,x=5038
sum of digits of x=5+0+3+8
                           =16