A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits.…
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C?
18
16
15
Cannot be determined due to insufficient data
Solution
37DD is a 4-digit number of the form 3700 + 11D. We need ABC times D = 3700 + 11D with all digits distinct and non-zero. Trying D = 4: 37DD = 3744, and $3744 / 4 = 936$; ABC = 936, with digits 9, 3, 6 and D = 4 all distinct and non-zero. So A + B + C = 9 + 3 + 6 = 18.