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A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will be
- a)4,1
- b)3,2
- c)2,3
- d)1,2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A number when divided successively by 4 and 5 leaves remainder 1 and 4...
When dividing a positive integer n by another positive integer D (divider), we obtain a quotient Q, which is a non-negative integer and a remainder R, which is an integer such that 0 ≤ R < D. We can write n = DQ + R.
When dividing our number n by 4 we obtain a remainder of 1, so, if the quotient is some integer Q, we can write n = 4Q + 1.
successively divide means quotient Q is divide by 5.
Now, dividing Q by 5, we obtain another quotient say q and remainder 4, thus we can write Q = 5q + 4.
It follows that n = 4(5q + 4) + 1 = 20q + 17.
Since n = 20q + 17 = 5(4q + 3) + 2, it means that when dividing n by 5 first, we get a quotient 4q + 3 and remainder 2.
Then dividing 4q + 3 by 4 we obviously obtain a remainder of 3.
Hence remainder is 2,3 by dividing the no by 5,4.
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When dividing our number n by 4 we obtain a remainder of 1, so, if the quotient is some integer Q, we can write n = 4Q + 1.
successively divide means quotient Q is divide by 5.
Now, dividing Q by 5, we obtain another quotient say q and remainder 4, thus we can write Q = 5q + 4.
It follows that n = 4(5q + 4) + 1 = 20q + 17.
Since n = 20q + 17 = 5(4q + 3) + 2, it means that when dividing n by 5 first, we get a quotient 4q + 3 and remainder 2.
Then dividing 4q + 3 by 4 we obviously obtain a remainder of 3.
Hence remainder is 2,3 by dividing the no by 5,4.
Most Upvoted Answer
A number when divided successively by 4 and 5 leaves remainder 1 and 4...
Given information:
- A number is divided successively by 4 and 5 with remainders 1 and 4 respectively.
- The same number is divided successively by 5 and 4.
To find:
- The respective remainders when the number is divided successively by 5 and 4.
Solution:
Let's assume the number to be x.
When x is divided by 4, the remainder is 1. This can be written as:
x = 4a + 1, where a is some integer.
When x is divided by 5, the remainder is 4. This can be written as:
x = 5b + 4, where b is some integer.
Now, we can equate the two expressions for x and solve for a and b.
4a + 1 = 5b + 4
4a - 5b = 3
We can see that a = 2 and b = 2 is a solution to this equation. So, we can write:
x = 4a + 1 = 9 + 1 = 10
Now, we need to find the remainders when 10 is divided successively by 5 and 4.
When 10 is divided by 5, the remainder is 0. This means that 10 is divisible by 5.
When 10 is divided by 4, the remainder is 2.
Therefore, the respective remainders when the number is divided successively by 5 and 4 are 0 and 2, which corresponds to option (c) 2,3.
Final answer: Option (c) 2,3.
- A number is divided successively by 4 and 5 with remainders 1 and 4 respectively.
- The same number is divided successively by 5 and 4.
To find:
- The respective remainders when the number is divided successively by 5 and 4.
Solution:
Let's assume the number to be x.
When x is divided by 4, the remainder is 1. This can be written as:
x = 4a + 1, where a is some integer.
When x is divided by 5, the remainder is 4. This can be written as:
x = 5b + 4, where b is some integer.
Now, we can equate the two expressions for x and solve for a and b.
4a + 1 = 5b + 4
4a - 5b = 3
We can see that a = 2 and b = 2 is a solution to this equation. So, we can write:
x = 4a + 1 = 9 + 1 = 10
Now, we need to find the remainders when 10 is divided successively by 5 and 4.
When 10 is divided by 5, the remainder is 0. This means that 10 is divisible by 5.
When 10 is divided by 4, the remainder is 2.
Therefore, the respective remainders when the number is divided successively by 5 and 4 are 0 and 2, which corresponds to option (c) 2,3.
Final answer: Option (c) 2,3.
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A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer?
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A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer?.
A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will bea) 4,1 b) 3,2 c) 2,3 d) 1,2 Correct answer is option 'C'. Can you explain this answer?.
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