2024 · Q75
The difference of 10³¹ − 5 and 10³⁰ + p is divisible by 3 where p is a digit. How many values of p are possible?
Elementary MathematicsNumber System
- A4
- B3
- C2
- D1
Explanation
The difference is 9×10³⁰ − (5+p), divisible by 3 iff 5+p ≡ 0 (mod 3), i.e. p ≡ 1 (mod 3). Digits p ∈ {1, 4, 7}: 3 values — option B.