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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?
- a)13
- b)59
- c)35
- d)37
- e)12
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number when divided by a divisor leaves a remainder of 24. When twic...
Step 1: Decode "A number when divided by a divisor leaves a remainder of 24"
Let the original number be 'a'.
Let the divisor be 'd'.
Let the quotient of dividing 'a' by 'd' be 'x'.
Therefore, we can write the division as a/d = x and the remainder is 24.
i.e., a = dx + 24
Let the divisor be 'd'.
Let the quotient of dividing 'a' by 'd' be 'x'.
Therefore, we can write the division as a/d = x and the remainder is 24.
i.e., a = dx + 24
Step 2: Decode "When twice the original number is divided by the same divisor, the remainder is 11"
Twice the original number is divided by 'd' means 2a is divided by d.
We know from Step 1 that a = dx + 24.
Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48
We know from Step 1 that a = dx + 24.
Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48
When (2dx + 48) is divided by 'd' the remainder is 11.
2dx is divisible by 'd' and will therefore, not leave a remainder.
The remainder of 11 would be the remainder of dividing 48 by d.
2dx is divisible by 'd' and will therefore, not leave a remainder.
The remainder of 11 would be the remainder of dividing 48 by d.
The question essentially becomes "What number will leave a remainder of 11 when it divides 48?"
When 37 divides 48, the remainder is 11.
When 37 divides 48, the remainder is 11.
Hence, the divisor is 37.
Choice D is the correct answer.
Most Upvoted Answer
A number when divided by a divisor leaves a remainder of 24. When twic...
Given information:
- 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.
Let's assume the original number is x and the divisor is d.
First Condition:
When x is divided by d, the remainder is 24.
This can be written as:
x = qd + 24, where q is the quotient.
Second Condition:
When 2x is divided by d, the remainder is 11.
This can be written as:
2x = pd + 11, where p is the quotient.
To find the value of the divisor, we need to eliminate the unknowns q and p.
Solving the Equations:
We can subtract the first equation from the second equation to eliminate x:
2x - x = pd + 11 - (qd + 24)
x = (p - q)d + (11 - 24)
x = (p - q)d - 13
Since x = (p - q)d - 13, we can substitute this value back into the first equation:
(p - q)d - 13 = qd + 24
Simplifying the equation:
(p - q)d - qd = 24 + 13
pd - qd - qd = 37
(p - 2q)d = 37
Since (p - 2q)d = 37, we know that d is a factor of 37.
Factors of 37: 1 and 37
Since the question asks for the value of the divisor, we can conclude that the value of the divisor is 37. Therefore, the correct answer is option D.
- 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.
Let's assume the original number is x and the divisor is d.
First Condition:
When x is divided by d, the remainder is 24.
This can be written as:
x = qd + 24, where q is the quotient.
Second Condition:
When 2x is divided by d, the remainder is 11.
This can be written as:
2x = pd + 11, where p is the quotient.
To find the value of the divisor, we need to eliminate the unknowns q and p.
Solving the Equations:
We can subtract the first equation from the second equation to eliminate x:
2x - x = pd + 11 - (qd + 24)
x = (p - q)d + (11 - 24)
x = (p - q)d - 13
Since x = (p - q)d - 13, we can substitute this value back into the first equation:
(p - q)d - 13 = qd + 24
Simplifying the equation:
(p - q)d - qd = 24 + 13
pd - qd - qd = 37
(p - 2q)d = 37
Since (p - 2q)d = 37, we know that d is a factor of 37.
Factors of 37: 1 and 37
Since the question asks for the value of the divisor, we can conclude that the value of the divisor is 37. Therefore, the correct answer is option D.
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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?a)13b)59c)35d)37e)12Correct answer is option 'D'. Can you explain this answer?
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