The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leave the remainders 16, 52, 60 and 68 respectively, is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 16.
let's check for the difference of the divisor and remainder in each case.
36 - 16 = 20
72 - 52 = 20
80 - 60 = 20
88 - 68 = 20
In all cases the difference is constant,
Required number = LCM of (36, 72, 80, 88)k - 20.
LCM of (36, 72, 80, 88) = 7920.
For the least value of the number one should put k = 1.
7920 × 1 - 20 = 7900
Required sum of digits = 7 + 9 + 0 + 0 = 16.