Q. For a number to be divisible by 11, which of the following must be true?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
B.
The number must be even
C.
The number must end in 1
D.
The sum of the digits must be divisible by 11
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.
Correct Answer:
A
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
Q. What is the rule for determining if a number is divisible by 11?
A.
The sum of the digits must be even
B.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
C.
It must end in 1
D.
It must be a prime number
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
Correct Answer:
B
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
Q. What is the rule for determining if a number is divisible by 7?
A.
The last digit must be 0
B.
Double the last digit and subtract it from the rest of the number
C.
The sum of the digits must be divisible by 7
D.
The number must end in 7
Solution
To check if a number is divisible by 7, you can double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is as well.
Correct Answer:
B
— Double the last digit and subtract it from the rest of the number
Q. Which of the following is a characteristic of numbers divisible by 7?
A.
They end in 0 or 5
B.
The double of the last digit subtracted from the rest of the number is divisible by 7
C.
They are always even
D.
They are always prime
Solution
A common rule for checking divisibility by 7 is to double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is also divisible by 7.
Correct Answer:
B
— The double of the last digit subtracted from the rest of the number is divisible by 7
Q. Which of the following is a correct application of the divisibility rule for 11?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
B.
The last digit must be 1
C.
The number must be even
D.
The sum of the digits must be 11
Solution
For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.
Correct Answer:
A
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
Understanding Divisibility Rules is crucial for students preparing for exams, as it forms the foundation for various mathematical concepts. Mastering these rules not only helps in solving problems quickly but also enhances accuracy in objective questions. Practicing MCQs and important questions on this topic can significantly improve your exam performance and boost your confidence.
What You Will Practise Here
Fundamental concepts of divisibility and its significance in mathematics.
Divisibility rules for numbers 2, 3, 4, 5, 6, 8, 9, and 10.
Application of divisibility rules in simplifying fractions and solving equations.
Identifying prime and composite numbers through divisibility tests.
Common divisibility patterns and their implications in problem-solving.
Practice questions and MCQs to reinforce understanding of divisibility rules.
Real-life applications of divisibility in various mathematical scenarios.
Exam Relevance
Divisibility Rules are frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require quick identification of divisibility, often presented in multiple-choice formats. Understanding these rules can help in tackling problems related to factors, multiples, and simplifications, which are common in both school and competitive exam settings.
Common Mistakes Students Make
Confusing the rules for different numbers, such as those for 2 and 5.
Overlooking the importance of checking all conditions for divisibility.
Relying too heavily on memorization rather than understanding the underlying concepts.
Misapplying rules in complex problems involving multiple operations.
FAQs
Question: What are the basic divisibility rules I should know? Answer: The basic rules include checking if a number is even for 2, summing the digits for 3, and looking at the last digit for 5, among others.
Question: How can I improve my speed in solving divisibility questions? Answer: Regular practice of MCQs and objective questions will help you recognize patterns and apply rules more quickly.
Question: Are divisibility rules important for competitive exams? Answer: Yes, they are essential as they often form the basis for more complex problems in exams like NEET and JEE.
Start solving practice MCQs on Divisibility Rules today to test your understanding and enhance your exam readiness. Every question you tackle brings you one step closer to mastering this important topic!
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