2024 · Q89
XYZ is a 3-digit number, where X, Y, Z are distinct non-zero digits. The difference between the two 3-digit numbers XYZ and YXZ is 90. How many possible values exist for the sum (X + Y)?
Elementary MathematicsNumber System
- A9
- B8
- C7
- D6
Explanation
XYZ − YXZ = (100X+10Y+Z) − (100Y+10X+Z) = 90(X−Y) = 90, so X − Y = 1. With distinct non-zero digits, the pairs are (2,1), (3,2), …, (9,8): 8 pairs. The sums X+Y are then 3, 5, 7, 9, 11, 13, 15, 17 — 8 distinct values — option B.