Multiple choice

Find the largest number of four digits such that on dividing by $15,18,21$ and $24$ the remainders are $11,14,17$ and $20$ respectively.

  1. $6557$
  2. $7556$
  3. $5675$
  4. $7664$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The common difference between the divisors (15, 18, 21, 24) and remainders (11, 14, 17, 20) is 4. We find the LCM of 15, 18, 21, 24, which is 2520. The largest 4-digit number is 9999; 9999 divided by 2520 leaves a remainder of 2439. Subtracting 2439 from 9999 gives 7560, and subtracting the common difference 4 gives 7556.

AI explanation

Notice the difference between each divisor and its corresponding remainder is 4 (15 - 11 = 4, 18 - 14 = 4, and so on). Find the least common multiple of 15, 18, 21, and 24, which is 2520. The largest four-digit multiple of 2520 is 2520 multiplied by 3, or 7560. Subtract the common difference of 4 from 7560 to get 7556.

Keep practicing — related questions