2025 · Q58
The unit digit of (3 × 1 + 4 × 2 × 1 + 5 × 3 × 2 × 1 + ... + 20 × 18 × 17 × ⋯ × 2 × 1) is
general-mental-abilityquantitative-aptitude
- A2
- B3
- C4
- D5
Explanation
The series is 3x1 + 4x2x1 + 5x3x2x1 + ... + 20x18x17x...x2x1, i.e. term m = m x (m-2)!. The first terms are 3 (unit 3), 8 (unit 8), 30 (unit 0) and 144 (unit 4). Every later term contains both 5 and 2 as factors (for m >= 7, (m-2)! contains 5), so each ends in 0. The unit digit of the total is therefore the unit digit of 3+8+30+144 = 185, which is 5.