A number when divided by a divisor left reminder 23. When twice of the number was divided by the same divisor, reminder was 11. what is the divisor?
Question
A number when divided by a divisor left reminder 23. When twice of the number was divided by the same divisor, reminder was 11. what is the divisor?
Solution
Let's denote the number as 'a' and the divisor as 'd'.
From the problem, we have two equations:
- a = d*q1 + 23 (where q1 is the quotient of the first division)
- 2a = d*q2 + 11 (where q2 is the quotient of the second division)
We can express 'a' from the first equation and substitute it into the second equation:
a = dq1 + 23 2(dq1 + 23) = dq2 + 11 2dq1 + 46 = dq2 + 11 2dq1 - dq2 = 11 - 46 d*(2*q1 - q2) = -35
Since 'd' is a divisor, it must be a positive integer. The only way for 'd' to be positive in the equation above is for (2q1 - q2) to be negative. This means that q2 > 2q1.
The smallest possible values for q1 and q2 that satisfy q2 > 2*q1 are q1 = 1 and q2 = 3. Substituting these values into the equation gives:
d*(21 - 3) = -35 d(-1) = -35 d = 35
So, the divisor is 35.
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