Multiple choice

By dividing the largest four-digit number by 40 and 52, the remainder in each case is 34. Number is:

  1. $9814$
  2. $9980$
  3. $9914$
  4. $9846$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need N such that N ≡ 34 (mod 40) and N ≡ 34 (mod 52), with N being the largest 4-digit number satisfying this. LCM(40, 52) = 520. Numbers of form 520k + 34 give remainder 34 when divided by both. Largest 4-digit: try k=19 gives 9914. Check: 9914 ÷ 40 = 247 rem 34, 9914 ÷ 52 = 190 rem 34. Correct.

Keep practicing — related questions