UPSC Exam > UPSC Questions > When a particular positive number is divided ...
Start Learning for Free
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.
- a)34
- b)19
- c)49
- d)64
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
When a particular positive number is divided by 3, the remainder is 1....
Let the quotients when this number is divided by 3 and 5 be x and y respectively.
(Note that x will be greater than y as 3 is smaller than 5).
Number = 3x + 1 = 5y + 4
Given that, x – y = 3
On solving both equation we get, x = 6, y=3
Thus the number is 5 × 3 + 4= 19.
Free Test
FREE
| Start Free Test |
Community Answer
When a particular positive number is divided by 3, the remainder is 1....
To solve this problem, we will use the concept of modular arithmetic.
Let's assume the positive number we are looking for is represented by 'x'.
When 'x' is divided by 3, the remainder is 1. This can be written as:
x ≡ 1 (mod 3)
Similarly, when 'x' is divided by 5, the remainder is 4. This can be written as:
x ≡ 4 (mod 5)
Now, we are given that the difference between the quotients of the division is 3.
We can represent this as:
(x/3) - (x/5) = 3
To simplify this equation, we can find a common denominator:
(5x - 3x) / (3*5) = 3
2x / 15 = 3
Cross-multiplying gives us:
2x = 45
Dividing both sides by 2 gives us the value of 'x':
x = 22.5
However, we are given that 'x' is a positive number. So, 'x' cannot be 22.5.
Therefore, our assumption that 'x' is a decimal number is incorrect.
To find the correct value of 'x', we can substitute the given options into the equations and check which one satisfies both conditions.
Let's start with option B: x = 19
When we divide 19 by 3, the remainder is indeed 1.
Similarly, when we divide 19 by 5, the remainder is 4.
Therefore, option B (19) is the correct answer.
Let's assume the positive number we are looking for is represented by 'x'.
When 'x' is divided by 3, the remainder is 1. This can be written as:
x ≡ 1 (mod 3)
Similarly, when 'x' is divided by 5, the remainder is 4. This can be written as:
x ≡ 4 (mod 5)
Now, we are given that the difference between the quotients of the division is 3.
We can represent this as:
(x/3) - (x/5) = 3
To simplify this equation, we can find a common denominator:
(5x - 3x) / (3*5) = 3
2x / 15 = 3
Cross-multiplying gives us:
2x = 45
Dividing both sides by 2 gives us the value of 'x':
x = 22.5
However, we are given that 'x' is a positive number. So, 'x' cannot be 22.5.
Therefore, our assumption that 'x' is a decimal number is incorrect.
To find the correct value of 'x', we can substitute the given options into the equations and check which one satisfies both conditions.
Let's start with option B: x = 19
When we divide 19 by 3, the remainder is indeed 1.
Similarly, when we divide 19 by 5, the remainder is 4.
Therefore, option B (19) is the correct answer.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?
Question Description
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?.
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?.
Solutions for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?, a detailed solution for When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.a)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup