A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Question
A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Solution
Let's denote the original number as 'a' and the divisor as 'd'.
From the problem, we know that:
- a = kd + 25 (where k is some integer)
- 2a = ld + 11 (where l is another integer)
We can substitute the first equation into the second to get:
2(kd + 25) = ld + 11 2kd + 50 = ld + 11 2kd - ld = 11 - 50 d(2k - l) = -39
Since d, 2k, and l are all integers, this means that d must be a divisor of 39. The only divisors of 39 are 1, 3, 13, and 39.
However, since the remainder when a is divided by d is 25, d must be greater than 25. Therefore, the only possible value for d is 39.
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