Multiple choice

M is the largest 4-digit number which when divided by 4, 5, 6 and 7 leaves remainder 2, 3, 4 and 5, respectively. What will be the remainder when M is divided by 9?

  1. 2

  2. 1

  3. 3

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Divisors are 4, 5, 6, 7. Remainders are 2, 3, 4, 5. The difference is 2 in each case. LCM(4,5,6,7) = 420. M = 420k - 2. Largest 4-digit number: 420*23 = 9660. M = 9660 - 2 = 9658. 9+6+5+8 = 28. 28 mod 9 = 1.

AI explanation

Observe that the difference between each divisor and its corresponding remainder is 2, as 4 - 2 = 2, 5 - 3 = 2, 6 - 4 = 2 and 7 - 5 = 2. The least common multiple of 4, 5, 6 and 7 is 420, so the numbers satisfying the condition are of the form 420k - 2. To find the largest 4-digit number, set 420k - 2 = 9999, which gives k = 23, yielding M = 9658. Dividing 9658 by 9 gives a quotient of 1073 and a remainder of 1.

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