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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 of solving this GMAT Number Properties Question: 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
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
i.e., a = dx + 24
Step 2 of solving this GMAT Number Properties Question: 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...
To find the value of the divisor, we need to use the concept of remainders. Let's analyze the given information step by step:
Step 1: A number when divided by a divisor leaves a remainder of 24.
Let's denote the number as N and the divisor as D. Based on the given information, we can write the equation:
N = D(Q) + 24, where Q is the quotient.
Step 2: When twice the original number is divided by the same divisor, the remainder is 11.
Twice the original number is 2N, and when it is divided by the divisor D, the remainder is 11. We can write this as:
2N = D(P) + 11, where P is the quotient.
Step 3: Finding the relationship between N and 2N.
Since we know that 2N = D(P) + 11, we can express N in terms of 2N:
N = (D(P) + 11)/2
Step 4: Substituting the value of N in the first equation.
Substituting the value of N in the equation N = D(Q) + 24, we get:
(D(P) + 11)/2 = D(Q) + 24
Step 5: Simplifying the equation.
To simplify the equation, we can multiply both sides by 2 to eliminate the denominator:
D(P) + 11 = 2D(Q) + 48
Step 6: Rearranging the equation.
Rearranging the equation, we get:
2D(Q) - D(P) = 37
Step 7: Factoring out the common factor.
We can factor out D from both terms on the left side of the equation:
D(2Q - P) = 37
Step 8: Analyzing the factors.
The left side of the equation is a product of two factors: D and (2Q - P). The right side of the equation is 37, which is a prime number.
Step 9: Determining the value of D.
Since the right side is a prime number, the left side must be a product of 1 and 37 or -1 and -37. Therefore, the possible values for D are 1, 37, -1, or -37.
Step 10: Considering the divisor.
Since a divisor cannot be negative or equal to 1 (as it would make the remainders in both cases the same), the only possible value for the divisor is 37.
Therefore, the value of the divisor is 37 (option D).
Step 1: A number when divided by a divisor leaves a remainder of 24.
Let's denote the number as N and the divisor as D. Based on the given information, we can write the equation:
N = D(Q) + 24, where Q is the quotient.
Step 2: When twice the original number is divided by the same divisor, the remainder is 11.
Twice the original number is 2N, and when it is divided by the divisor D, the remainder is 11. We can write this as:
2N = D(P) + 11, where P is the quotient.
Step 3: Finding the relationship between N and 2N.
Since we know that 2N = D(P) + 11, we can express N in terms of 2N:
N = (D(P) + 11)/2
Step 4: Substituting the value of N in the first equation.
Substituting the value of N in the equation N = D(Q) + 24, we get:
(D(P) + 11)/2 = D(Q) + 24
Step 5: Simplifying the equation.
To simplify the equation, we can multiply both sides by 2 to eliminate the denominator:
D(P) + 11 = 2D(Q) + 48
Step 6: Rearranging the equation.
Rearranging the equation, we get:
2D(Q) - D(P) = 37
Step 7: Factoring out the common factor.
We can factor out D from both terms on the left side of the equation:
D(2Q - P) = 37
Step 8: Analyzing the factors.
The left side of the equation is a product of two factors: D and (2Q - P). The right side of the equation is 37, which is a prime number.
Step 9: Determining the value of D.
Since the right side is a prime number, the left side must be a product of 1 and 37 or -1 and -37. Therefore, the possible values for D are 1, 37, -1, or -37.
Step 10: Considering the divisor.
Since a divisor cannot be negative or equal to 1 (as it would make the remainders in both cases the same), the only possible value for the divisor is 37.
Therefore, the value of the divisor is 37 (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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