Class 10 Exam > Class 10 Questions > n2 - 1 is divisible by 8 if n isa)An integerb...
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n2 - 1 is divisible by 8 if n is
- a)An integer
- b)A natural number
- c)An odd integer
- d)An even integer
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
n2 - 1 is divisible by 8 if n isa)An integerb)A natural numberc)An odd...
Option A: If n is integer similarly n²- 1 is not divisible by 8.
Option B: If n is a natural number then it is not possible for n=1,2.
Option C: If n is odd the possible for n is 3,5,7...
Option D: If n is even then it is not possible for n=2.
Option B: If n is a natural number then it is not possible for n=1,2.
Option C: If n is odd the possible for n is 3,5,7...
Option D: If n is even then it is not possible for n=2.
Thus, the option C is correct.
Most Upvoted Answer
n2 - 1 is divisible by 8 if n isa)An integerb)A natural numberc)An odd...
If n is even then it is not possible for n=2. If n is natural number then it is not possible for n=1,2.If n is integer similarly n²- 1 is not divisible by 8.If n is odd the possible for n is 3,5,7. Thus the n is odd number
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Community Answer
n2 - 1 is divisible by 8 if n isa)An integerb)A natural numberc)An odd...
Explanation:
To prove that n2 - 1 is divisible by 8 if n is an odd integer, we need to follow the following steps:
Step 1: Express n2 - 1 as (n + 1)(n - 1).
Step 2: We know that if a product of two integers is even, then at least one of the integers must be even. Hence, either (n + 1) or (n - 1) must be even.
Step 3: If (n + 1) is even, then n is odd, and (n - 1) must be odd. Similarly, if (n - 1) is even, then n is odd, and (n + 1) must be odd.
Step 4: In either case, one of (n + 1) or (n - 1) is divisible by 2, and the other is divisible by 4. Hence, (n + 1)(n - 1) is divisible by 8.
Step 5: Therefore, n2 - 1 is divisible by 8 if n is an odd integer.
Conclusion:
Hence, the correct option is 'C' i.e., An odd integer.
To prove that n2 - 1 is divisible by 8 if n is an odd integer, we need to follow the following steps:
Step 1: Express n2 - 1 as (n + 1)(n - 1).
Step 2: We know that if a product of two integers is even, then at least one of the integers must be even. Hence, either (n + 1) or (n - 1) must be even.
Step 3: If (n + 1) is even, then n is odd, and (n - 1) must be odd. Similarly, if (n - 1) is even, then n is odd, and (n + 1) must be odd.
Step 4: In either case, one of (n + 1) or (n - 1) is divisible by 2, and the other is divisible by 4. Hence, (n + 1)(n - 1) is divisible by 8.
Step 5: Therefore, n2 - 1 is divisible by 8 if n is an odd integer.
Conclusion:
Hence, the correct option is 'C' i.e., An odd integer.
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n2 - 1 is divisible by 8 if n isa)An integerb)A natural numberc)An odd integerd)An even integerCorrect answer is option 'C'. Can you explain this answer?
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