CAT Exam > CAT Questions > A natural number when divided by D leaves rem...
Start Learning for Free
A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as 8. Which of the following can be the value of D? (Given: D is a natural number.)
- a)12
- b)8
- c)6
- d)Both (1) and (2)
- e)Both (2) and (3)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A natural number when divided by D leaves remainder 5. When four times...
Let the number be N.
N = Dk + 5; where k is the quotient. 4N = 4Dk + 20 ...(i)
N = Dk + 5; where k is the quotient. 4N = 4Dk + 20 ...(i)
As we get 8 as the remainder when 4N is divided by D,
4N = Dy+ 8 ...(ii)
From (i) and (ii);
D(y - 4k) =12
L.H.S. is divisible by D ⇒R.H.S. is divisible by D.
⇒ D = 1 or 2 or 3 or 4 or 6 or 12
D should also be greater than 5 and 8.
From the given option only 12 satisfies the condition.
Hence, option 1.
From the given option only 12 satisfies the condition.
Hence, option 1.
Most Upvoted Answer
A natural number when divided by D leaves remainder 5. When four times...
Given information:
- A natural number when divided by D leaves a remainder of 5.
- When four times the number is divided by D, the remainder is 8.
To find: Possible values for D.
Solution:
Let's assume the natural number to be x.
First condition:
When x is divided by D, the remainder is 5.
This can be represented as x ≡ 5 (mod D), where '≡' represents congruence.
Second condition:
When four times x is divided by D, the remainder is 8.
This can be represented as 4x ≡ 8 (mod D).
Using the Chinese Remainder Theorem:
Since x ≡ 5 (mod D), we can express x as x = 5 + kD, where k is a positive integer.
Substituting this value of x in the second condition, we get:
4(5 + kD) ≡ 8 (mod D)
20 + 4kD ≡ 8 (mod D)
20 ≡ 8 (mod D)
Analysis of the second condition:
The equation 20 ≡ 8 (mod D) implies that D divides (20 - 8) = 12.
So, the possible values of D are factors of 12.
Possible values for D:
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Out of these, only D = 12 satisfies the first condition x ≡ 5 (mod D) because any number divisible by 12 will have a remainder of 0 when divided by 12.
Therefore, the only possible value for D is 12 (option A).
- A natural number when divided by D leaves a remainder of 5.
- When four times the number is divided by D, the remainder is 8.
To find: Possible values for D.
Solution:
Let's assume the natural number to be x.
First condition:
When x is divided by D, the remainder is 5.
This can be represented as x ≡ 5 (mod D), where '≡' represents congruence.
Second condition:
When four times x is divided by D, the remainder is 8.
This can be represented as 4x ≡ 8 (mod D).
Using the Chinese Remainder Theorem:
Since x ≡ 5 (mod D), we can express x as x = 5 + kD, where k is a positive integer.
Substituting this value of x in the second condition, we get:
4(5 + kD) ≡ 8 (mod D)
20 + 4kD ≡ 8 (mod D)
20 ≡ 8 (mod D)
Analysis of the second condition:
The equation 20 ≡ 8 (mod D) implies that D divides (20 - 8) = 12.
So, the possible values of D are factors of 12.
Possible values for D:
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Out of these, only D = 12 satisfies the first condition x ≡ 5 (mod D) because any number divisible by 12 will have a remainder of 0 when divided by 12.
Therefore, the only possible value for D is 12 (option A).
Free Test
FREE
| Start Free Test |
Community Answer
A natural number when divided by D leaves remainder 5. When four times...
Correct answer is a . because 6 and 8 can't leave a remainder of 8.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer?
Question Description
A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. 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 natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. 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 natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer?.
A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. 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 natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. 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 natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer?.
Solutions for A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A natural number when divided by D leaves remainder 5. When four times of the number is divided with D, we get remainder as8. Which of the following can be the value of D? (Given: D is a natural number.)a)12b)8c)6d)Both (1) and (2)e)Both (2) and (3)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
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