Multiple choice

N is the largest 4-digit number which when divided by 4, 5, 6, and 7 leaves the remainders of 2, 3, 4, and 5, respectively. What will be the unit digit of the number N?

  1. 0

  2. 3

  3. 7

  4. 8
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D Correct answer
Explanation

Divisors 4, 5, 6, 7 leave remainders 2, 3, 4, 5. The difference between divisor and remainder is constant at 2. LCM(4, 5, 6, 7) = 420. Largest 4-digit multiple of 420 is 9660. N = 9660 - 2 = 9658. The unit digit is 8.

AI explanation

The remainders show a consistent difference of 2, meaning N plus 2 is divisible by 4, 5, 6, and 7. The least common multiple of these numbers is 420, so N can be expressed as 420k minus 2. The largest 4-digit number occurs when k is 23, yielding 9658, and its unit digit is 8.

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