Multiple choice

What is the largest 4 digit number that on being divided “successively” by 11, 12 and 15 leaves remainders 7, 3 and 10 respectively?

  1. 9680

  2. 9280

  3. 7300

  4. 1360

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

Successive division by 11, 12, 15 with remainders 7, 3, 10. Let the number be N. N = 15k + 10. Previous quotient Q1 = 12(15k+10) + 3 = 180k + 123. N = 11(180k + 123) + 7 = 1980k + 1353 + 7 = 1980k + 1360. For largest 4-digit number, 1980k + 1360 <= 9999. 1980k <= 8639. k=4. N = 1980(4) + 1360 = 7920 + 1360 = 9280.