Let A be the greatest number that will divide 505, 555 and 605, leaving the same remainder in each case. Then the sum of the digits in A is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
If a number leaves the same remainder when it divides two numbers, it divides their difference with no remainder, because the remainders cancel. So A is the HCF of the differences.
555 − 505 = 50, 605 − 555 = 50, 605 − 505 = 100
HCF of 50, 50 and 100 = 50, so A = 50 (each number leaves the remainder 5)
Sum of the digits of 50 = 5 + 0 = 5