Multiple choice

The divisor and quotient of the number $6123$ are same and the remainder is half the divisor. Find the divisor.

  1. $78$
  2. $87$
  3. $15$
  4. $21$
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A Correct answer
Explanation

Let divisor be D and quotient be Q. D = Q. Dividend = D * Q + R = D^2 + R. Given R = D/2. So 6123 = D^2 + D/2. Multiply by 2: 12246 = 2D^2 + D. 2D^2 + D - 12246 = 0. Using quadratic formula: D = (-1 + sqrt(1 + 4*2*12246)) / 4 = (-1 + sqrt(97969)) / 4 = (-1 + 313) / 4 = 312 / 4 = 78.

AI explanation

Using the division algorithm, Dividend equals Divisor times Quotient plus Remainder. Let the divisor and quotient be x, making the remainder x divided by 2, so 6123 equals x times x plus x divided by 2. Multiplying by 2 gives 12246 equals 2x squared plus x, or x times (2x plus 1). Solving 2x squared plus x minus 12246 equals 0 yields x equals 78. Therefore, the divisor is 78.

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