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Which of the following is always odd?
- a)2n + 2
- b)n2 + n
- c)2n + 1
- d)4n
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which of the following is always odd?a)2n + 2b)n2 + nc)2n + 1d)4nCorre...
The form 2n + 1 always gives an odd number for any integer n.
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Which of the following is always odd?a)2n + 2b)n2 + nc)2n + 1d)4nCorre...
Understanding the Options
To determine which expression is always odd, let's analyze each option provided:
Option A: 2n + 2
- This expression can be factored as 2(n + 1).
- Since n is an integer, (n + 1) is also an integer, making the entire expression even.
Option B: n² + n
- This can be factored as n(n + 1).
- Regardless of whether n is odd or even, one of these factors will always be even, resulting in an even product.
Option C: 2n + 1
- Here, 2n is even (since it is a multiple of 2).
- Adding 1 to an even number always yields an odd number.
- Therefore, this expression is always odd for any integer value of n.
Option D: 4n
- This can be factored as 4 times n.
- Since 4 is even, this expression is also even for any integer n.
Conclusion
Among the options analyzed, only Option C: 2n + 1 is always odd. This is because it consists of an even number (2n) plus one, which guarantees the result will always be odd, regardless of the integer value of n.
Thus, the correct answer is indeed Option C.
To determine which expression is always odd, let's analyze each option provided:
Option A: 2n + 2
- This expression can be factored as 2(n + 1).
- Since n is an integer, (n + 1) is also an integer, making the entire expression even.
Option B: n² + n
- This can be factored as n(n + 1).
- Regardless of whether n is odd or even, one of these factors will always be even, resulting in an even product.
Option C: 2n + 1
- Here, 2n is even (since it is a multiple of 2).
- Adding 1 to an even number always yields an odd number.
- Therefore, this expression is always odd for any integer value of n.
Option D: 4n
- This can be factored as 4 times n.
- Since 4 is even, this expression is also even for any integer n.
Conclusion
Among the options analyzed, only Option C: 2n + 1 is always odd. This is because it consists of an even number (2n) plus one, which guarantees the result will always be odd, regardless of the integer value of n.
Thus, the correct answer is indeed Option C.
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