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A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ?
- a)2, 3
- b)2,1
- c)1,2
- d)3,4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A number when successively divided by 5 and 6 gives remainders 3 and 2...
Let the quotient of last division is 1.
So the number is 5 × (6 × 1 + 2) + 3 = 5 × 8 + 3 = 43
Now when 43 is divided successively by 3 and 4 the remainders are 1 and 2 respectively.
So the number is 5 × (6 × 1 + 2) + 3 = 5 × 8 + 3 = 43
Now when 43 is divided successively by 3 and 4 the remainders are 1 and 2 respectively.
Most Upvoted Answer
A number when successively divided by 5 and 6 gives remainders 3 and 2...
Given:
- A number successively divided by 5 gives a remainder of 3.
- A number successively divided by 6 gives a remainder of 2.
To find:
- The remainders when the number is successively divided by 3 and 4.
Solution:
Let's assume the number as 'x'.
Dividing by 5:
When x is divided by 5, the remainder is 3. Therefore, we can write:
x = 5a + 3, where 'a' is the quotient.
Dividing by 6:
When x is divided by 6, the remainder is 2. Therefore, we can write:
x = 6b + 2, where 'b' is the quotient.
Equating both equations:
Since both equations are equal to x, we can equate them:
5a + 3 = 6b + 2
Finding a relation between a and b:
Rearranging the equation, we get:
5a - 6b = -1
Finding a particular solution:
To find a particular solution, we can assume a = 1 and substitute it in the equation:
5(1) - 6b = -1
5 - 6b = -1
6b = 5 + 1
6b = 6
b = 1
Therefore, when a = 1 and b = 1, the equation holds true.
Finding the general solution:
To find the general solution, we need to find the difference between two particular solutions.
Let's assume a second particular solution where a = 1 + p and b = 1 + q, where p and q are integers.
Substituting these values in the equation, we get:
5(1 + p) - 6(1 + q) = -1
5 + 5p - 6 - 6q = -1
5p - 6q = -1
Finding the remainders:
Now, let's find the remainders when x is successively divided by 3 and 4.
Dividing by 3:
When x is divided by 3, we can write:
x = 3c + r1, where 'c' is the quotient and 'r1' is the remainder.
Dividing by 4:
When x is divided by 4, we can write:
x = 4d + r2, where 'd' is the quotient and 'r2' is the remainder.
Equating both equations:
Since both equations are equal to x, we can equate them:
3c + r1 = 4d + r2
Finding a relation between c and d:
Rearranging the equation, we get:
3c - 4d = r2 - r1
Finding the difference between two remainders:
From the equation 5p - 6q = -1, we can rewrite it as:
5p = 6q - 1
Comparing it with the equation 3c - 4d = r2 - r1, we can conclude that:
- A number successively divided by 5 gives a remainder of 3.
- A number successively divided by 6 gives a remainder of 2.
To find:
- The remainders when the number is successively divided by 3 and 4.
Solution:
Let's assume the number as 'x'.
Dividing by 5:
When x is divided by 5, the remainder is 3. Therefore, we can write:
x = 5a + 3, where 'a' is the quotient.
Dividing by 6:
When x is divided by 6, the remainder is 2. Therefore, we can write:
x = 6b + 2, where 'b' is the quotient.
Equating both equations:
Since both equations are equal to x, we can equate them:
5a + 3 = 6b + 2
Finding a relation between a and b:
Rearranging the equation, we get:
5a - 6b = -1
Finding a particular solution:
To find a particular solution, we can assume a = 1 and substitute it in the equation:
5(1) - 6b = -1
5 - 6b = -1
6b = 5 + 1
6b = 6
b = 1
Therefore, when a = 1 and b = 1, the equation holds true.
Finding the general solution:
To find the general solution, we need to find the difference between two particular solutions.
Let's assume a second particular solution where a = 1 + p and b = 1 + q, where p and q are integers.
Substituting these values in the equation, we get:
5(1 + p) - 6(1 + q) = -1
5 + 5p - 6 - 6q = -1
5p - 6q = -1
Finding the remainders:
Now, let's find the remainders when x is successively divided by 3 and 4.
Dividing by 3:
When x is divided by 3, we can write:
x = 3c + r1, where 'c' is the quotient and 'r1' is the remainder.
Dividing by 4:
When x is divided by 4, we can write:
x = 4d + r2, where 'd' is the quotient and 'r2' is the remainder.
Equating both equations:
Since both equations are equal to x, we can equate them:
3c + r1 = 4d + r2
Finding a relation between c and d:
Rearranging the equation, we get:
3c - 4d = r2 - r1
Finding the difference between two remainders:
From the equation 5p - 6q = -1, we can rewrite it as:
5p = 6q - 1
Comparing it with the equation 3c - 4d = r2 - r1, we can conclude that:
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A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ? a)2, 3 b)2,1 c)1,2 d)3,4Correct answer is option 'C'. Can you explain this answer?
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A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ? a)2, 3 b)2,1 c)1,2 d)3,4Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ? a)2, 3 b)2,1 c)1,2 d)3,4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ? a)2, 3 b)2,1 c)1,2 d)3,4Correct answer is option 'C'. Can you explain this answer?.
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