Multiple choice

If Q is the largest four-digit number in the range 2000 to 9999, the remainder is 3 when Q is divided by 5, 7, 9 and 12. Quantity A: The remainder when Q is divided by 8 Quantity B: 7

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number Q leaves remainder 3 when divided by 5, 7, 9, 12. LCM(5, 7, 9, 12) = 1260. Q = 1260k + 3. For largest 4-digit number, 1260*7 + 3 = 8823. 8823 divided by 8: 8823 = 8 * 1102 + 7. Remainder is 7. Quantity A = 7, Quantity B = 7.

AI explanation

We find the least common multiple of the divisors 5, 7, 9, and 12, which is 1260. The general form of Q is 1260k + 3. The largest four-digit number in this sequence occurs when k equals 7, yielding Q = 1260 times 7 + 3 = 8823. Dividing 8823 by 8 gives 8816 as the quotient with 7 remaining. Therefore, Quantity A is exactly 7, matching Quantity B. The two quantities are equal.

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