In a division sum, the remainder was 71. With the same divisor but twice the…
2023
In a division sum, the remainder was 71. With the same divisor but twice the dividend, the remainder is 43. Which one of the following is the divisor ?
- A.
123
- B.
101
- C.
99
- D.
345
Show answer & explanation
Correct answer: C
Step-by-Step Solution
The division algorithm states that Dividend = (Divisor × Quotient) + Remainder. Let's use this to solve the problem.
Set up the first scenario:
Let the divisor be D.
Let the quotient be Q1.
Dividend = N = (D × Q1) + 71.
Set up the second scenario:
When the dividend is doubled (2N), the divisor (D) remains the same.
Let the new quotient be Q2.
2N = (D × Q2) + 43.
Substitute the first equation into the second:
2 × (D × Q1 + 71) = D × Q2 + 43
(2 × D × Q1) + 142 = (D × Q2) + 43
142 - 43 = (D × Q2) - (2 × D × Q1)
99 = D × (Q2 - 2 × Q1)
Interpret the result:
This equation shows that 99 must be a multiple of the divisor D. Since 99 is the result of the division process modification, the divisor D is 99.