Question

When asked for his taxi number, the driver replied, “If you divide the number of my taxi by 2, 3, 4, 5, 6 each time you will find a remainder of one. But if you divide it by 11, the remainder is zero.” What is the taxi number?

• A. 121
• B. 1001
• C. 1881
• D. 781

Hint:

Translate "remainder 1 on division" into LCM logic and solve using congruence with constraints.

Answer 1

The Correct Option is D

We are told:
- Number leaves remainder 1 when divided by 2, 3, 4, 5, and 6
- It is divisible by 11
Let’s denote the taxi number as \( N \).
If \( N \equiv 1 \pmod{2,3,4,5,6} \), then \( N - 1 \) is divisible by LCM of 2,3,4,5,6.
LCM(2,3,4,5,6) = 60 So \( N = 60k + 1 \), and also \( N \equiv 0 \pmod{11} \) Try multiples of 60 plus 1 that are divisible by 11: \[ k = 13 \Rightarrow N = 60 \cdot 13 + 1 = 781 \Rightarrow \boxed{781} \]