2019 · Q78
Let x be the smallest positive integer such that when 14 divides x, the remainder is 7; and when 15 divides x, the remainder is 5. Which one of the following is correct?
Elementary MathematicsNumber System
- A20 < x < 30
- B30 < x < 40
- C40 < x < 50
- Dx > 50
Explanation
We need x ≡ 7 (mod 14) and x ≡ 5 (mod 15). Trying x = 14k + 7: k = 1 gives 21, but 21 mod 15 = 6 ≠ 5; k = 2 gives 35, and 35 mod 15 = 5. ✓ So the smallest such x is 35, which lies strictly between 30 and 40. The answer is (B).