Multiple choice

A number when divided by 11, 13 and 17 leaves remainders of 7, 9 and 3 respectively. Find the smallest such 4-digit number

  1. 2370

  2. 2470

  3. 2570

  4. 2670

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number n satisfies n = 11a + 7, n = 13b + 9, n = 17c + 3. This is a system of congruences. Solving this, n = 2570 is a solution. Checking: 2570/11 = 233 R 7, 2570/13 = 197 R 9, 2570/17 = 151 R 3.