2018 · Q5
A five-digit number XY235 is divisible by 3 where x and Y are digits satisfying X + Y ≤ 5. What is the number of possible pairs of values of (X, Y) ?
Elementary MathematicsAlgebra
- A5
- B6
- C7
- D9
Explanation
The digit sum X + Y + 2 + 3 + 5 = X + Y + 10 must be divisible by 3, so X + Y is 2 mod 3. With X + Y <= 5 and X >= 1, we get X + Y = 2 or X + Y = 5. X + Y = 2 gives 2 pairs: (1,1), (2,0); X + Y = 5 gives 5 pairs: (1,4), (2,3), (3,2), (4,1), (5,0). Total = 2 + 5 = 7 pairs. Hence option C.