If the number 715(d)423 is divisible by 3 (where d denotes the missing digit), then the smallest whole number value of d is: A. 0 B. 2 C. 5 D. 6

GATE 2018 · General Aptitude · Factors · easy

Answer: The smallest whole number value of d is 2.

1. Sum the six known digits: 7 + 1 + 5 + 4 + 2 + 3 = 22
2. Find the required residue of d modulo 3: 22 = 7*3 + 1, so 22 mod 3 = 1. We need d mod 3 = 2.
3. Pick the smallest valid digit: The candidates are 2, 5, 8. The smallest is d = 2. Verify: 22 + 2 = 24 = 8*3. Divisible by 3.