A is the smallest three-digit number which when divided by 3, 4, and 5 leaves remainders 1, 2, and 3 respectively. What is the sum of the digits of A?
Show answer & explanation
Correct answer: C
Explanation
the correct answer is option 3 i.e. 10.
Here the LCM of 3, 4, and 5 is 60.
We need the smallest three-digit number. so we can multiply 60 by 2. So 60 × 2 = 120.
The number is divided by 3, 4, and 5 respectively, and leaves 1, 2, and 3 as a remainder.
So 3 -1 - 2, 4 - 2 = 2,5 - 3 = 2
Hence 120 will be subtracted by 2.
So the smallest three-digit number = A = 120 - 2 = 118
The sum of the digits of A = 1 + 1 + 8 = 10