A number when divided by a divisor leaves a remainder of 24. 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 24. 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 + 24 (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 + 24) = ld + 11 2kd + 48 = ld + 11 2kd - ld = 11 - 48 (d(2k - l)) = -37
Since both 'k' and 'l' are integers, (2k - l) is also an integer. Let's denote it as 'm'. So, we have:
d * m = -37
Since 'd' (the divisor) must be a positive integer, 'm' must be -1 or 37. But 'm' = 2k - l, which is unlikely to be negative because 'k' and 'l' are quotients of 'a' divided by 'd'. So, 'm' must be 37.
Therefore, the divisor 'd' is 1.
Similar Questions
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?
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?
Two different numbers when divided by a divisor left reminder 11 and 21 respectively. When their sum was divided by the same divisor reminder was 4. what is the divisor?Options28891535
When a number is divided by a certain divisor, the remainder is 46. If another number is divided by same divisor, it leaves remainder 31. If the sum of both the numbers is divided by the same divisor, it gives remainder 19. Find divisor
When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.