Question

Find the greatest number of five digits which when divided by 4, 6, 14 and 20 leaves respectively 1, 3, 11 and 17 as remainders. 

(a) 99930 

(b) 99960 

(c) 99997 

(d) 99957

Answer 1

Answer is: (d) 99957.

Common difference between divisors and respective remainders 

= (4 – 1) = (6 – 3) = (14 – 11) = (20 – 17) = 3 LCM of (4, 6, 14, 20) = 2 × 2 × 3 × 7 × 5 = 420.

Greatest number of five digits = 99999 

Dividing 99999 by 420 and subtracting the remainder 39 from 99999, 

we get 99999 – 39 = 99960

∴ The required number = 99960 – 3 = 99957.