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If a number N is divisible by both 2 and 8, then which of the following statements must be true?
I. N is divisible by 4
II. N is divisible by 6
III. N is divisible by 16
- a)I only
- b)II only
- c)III only
- d)I and II only
- e)I and III only
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a number N is divisible by both 2 and 8, then which of the followin...
Solution:
To solve this question, we need to use the concept of the LCM (Least Common Multiple) of the given numbers.
LCM of 2 and 8 is 8.
Therefore, any number that is divisible by both 2 and 8 must be a multiple of 8.
I. N is divisible by 4
If a number is divisible by 8, it is also divisible by 4. Therefore, statement I is true.
II. N is divisible by 6
If a number is divisible by 8, it is not necessarily divisible by 6. Therefore, statement II is false.
III. N is divisible by 16
If a number is divisible by 8, it is not necessarily divisible by 16. Therefore, statement III is false.
Therefore, the only statement that must be true is statement I, and the correct answer is option A.
To solve this question, we need to use the concept of the LCM (Least Common Multiple) of the given numbers.
LCM of 2 and 8 is 8.
Therefore, any number that is divisible by both 2 and 8 must be a multiple of 8.
I. N is divisible by 4
If a number is divisible by 8, it is also divisible by 4. Therefore, statement I is true.
II. N is divisible by 6
If a number is divisible by 8, it is not necessarily divisible by 6. Therefore, statement II is false.
III. N is divisible by 16
If a number is divisible by 8, it is not necessarily divisible by 16. Therefore, statement III is false.
Therefore, the only statement that must be true is statement I, and the correct answer is option A.
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Community Answer
If a number N is divisible by both 2 and 8, then which of the followin...
The correct answer would be A.
Explanation : N is divisible for 4 since 4 is a factor of 8 and the number would be divisible by 8.
For a number to be divisible by 6 it should be divisible by both 2 and 3 hence it would not be divisible by 6.
now if the number is divisible by 2 and 8 it is not necessary to be divisible by 16 .
Explanation : N is divisible for 4 since 4 is a factor of 8 and the number would be divisible by 8.
For a number to be divisible by 6 it should be divisible by both 2 and 3 hence it would not be divisible by 6.
now if the number is divisible by 2 and 8 it is not necessary to be divisible by 16 .
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If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer?.
If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
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If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If a number N is divisible by both 2 and 8, then which of the following statements must be true?I. N is divisible by 4II. N is divisible by 6III. N is divisible by 16a)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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