Question

What is the smallest four-digit number which when divided by 6, leaves a remainder of 5 and when divided by 5 leaves a remainder of 3? Option 1 : 1043 Option 2 : 1073 Option 3 : 1103 Option 4 : None of these Ques

Answer 1

166 * 6 + 5 = 1001 is the smallest 4-digit number gives a remainder of 5 when divided by 6.

So  N = 1001 + 6 * m   for some m.
 so  N = 200 * 5 + 1 + 5 m + m
          =  (200 + m) * 5 + 1+m

So Remainder when N is divided by 5 =   3  given
  =>  remainder when 1+m is divided by 5  = 3 
  =>  remainder when  m is divided by 5  = 2
          Smallest m is 2.

Hence, N = 1001 + 6 * 2 = 1013.

1013 is the answer.