Defence Exam > Defence Questions > A is a set of positive integers such that whe...
Start Learning for Free
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?
- a)No integer
- b)One
- c)Two
- d)Three
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A is a set of positive integers such that when divided by 2, 3, 4, 5 a...
We can observe that: The difference in divisor and reminder is same in every case.
(2 – 1) = (3 – 2) = (4 – 3) = (5 – 4) = (6 – 5) = 1
LCM of 2, 3, 4, 5 and 6 = 60
⇒ Required number = 60 – 1 = 59
Set A = [(60 – 1), (120 – 1), (180 – 1), ….] = [59, 119, 179, …..]
Between 0 and 100, only 59 is such integer.
∴ Only one integer between 0 and 100 belongs to the set A.
(2 – 1) = (3 – 2) = (4 – 3) = (5 – 4) = (6 – 5) = 1
LCM of 2, 3, 4, 5 and 6 = 60
⇒ Required number = 60 – 1 = 59
Set A = [(60 – 1), (120 – 1), (180 – 1), ….] = [59, 119, 179, …..]
Between 0 and 100, only 59 is such integer.
∴ Only one integer between 0 and 100 belongs to the set A.
Most Upvoted Answer
A is a set of positive integers such that when divided by 2, 3, 4, 5 a...
Understanding the Problem:
To belong to set A, an integer must leave specific remainders when divided by 2, 3, 4, 5, and 6.
Solving the Problem:
- For an integer to leave a remainder of 1 when divided by 2, it must be odd.
- For an integer to leave a remainder of 2 when divided by 3, it must be 2 more than a multiple of 3.
- For an integer to leave a remainder of 3 when divided by 4, it must be 3 more than a multiple of 4.
- For an integer to leave a remainder of 4 when divided by 5, it must be 4 more than a multiple of 5.
- For an integer to leave a remainder of 5 when divided by 6, it must be 5 more than a multiple of 6.
Finding the Integers:
- The first integer that satisfies all conditions is 59.
- The next integer that satisfies all conditions is 119.
- There are no other integers between 0 and 100 that belong to set A.
Therefore, there is only one integer between 0 and 100 that belongs to the set A.
To belong to set A, an integer must leave specific remainders when divided by 2, 3, 4, 5, and 6.
Solving the Problem:
- For an integer to leave a remainder of 1 when divided by 2, it must be odd.
- For an integer to leave a remainder of 2 when divided by 3, it must be 2 more than a multiple of 3.
- For an integer to leave a remainder of 3 when divided by 4, it must be 3 more than a multiple of 4.
- For an integer to leave a remainder of 4 when divided by 5, it must be 4 more than a multiple of 5.
- For an integer to leave a remainder of 5 when divided by 6, it must be 5 more than a multiple of 6.
Finding the Integers:
- The first integer that satisfies all conditions is 59.
- The next integer that satisfies all conditions is 119.
- There are no other integers between 0 and 100 that belong to set A.
Therefore, there is only one integer between 0 and 100 that belongs to the set A.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer?
Question Description
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer?.
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the reminder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A?a)No integerb)Onec)Twod)ThreeCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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