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01 Aug 2021, 05:50
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
85% (01:00) correct
15%
(01:05)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, which of the following expressions always represents an odd integer?
A. n + 5
B. 2n – 4
C. 3n + 3
D. 6n + 3
E. \(n^2 + 1\)
A. n + 5
B. 2n – 4
C. 3n + 3
D. 6n + 3
E. \(n^2 + 1\)
19 Aug 2021, 18:31
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A. n + 5
n=4, gives odd and n=5, gives even
B. 2n – 4
n=4, gives even and n=5, gives even
C. 3n + 3
n=4, gives odd and n=5, gives even
D. 6n + 3
n=4, gives odd and n=5, gives odd
E. \(n^2 + 1\)
n=4, gives odd and n=5, gives even
Hence, OA is (D) which is always odd.
n=4, gives odd and n=5, gives even
B. 2n – 4
n=4, gives even and n=5, gives even
C. 3n + 3
n=4, gives odd and n=5, gives even
D. 6n + 3
n=4, gives odd and n=5, gives odd
E. \(n^2 + 1\)
n=4, gives odd and n=5, gives even
Hence, OA is (D) which is always odd.
20 Aug 2021, 04:09
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Solution:
We are given that n is a positive integer. We have to take cases where n is odd and even.
A. \(n+5\)
If \(n = odd\), then \(Odd+5 = Even\). Because \(Odd+Odd=Even\).
If \(n = even\), then \(Even+5 = Odd\). Because \(Even+Odd=Odd\).
We cannot be sure if \(n+5\) is odd or not.
B. \(2n-4\)
If \(n = odd\), then \(2\times Odd-4 = Even\). Because \(Even-Even=Even\).
If \(n = even\), then \(2\times Even-4 = Even\). Because \(Even-Even=Even\).
We can be sure that \(2n-4\) is Even.
C. \(3n+3\)
If \(n = odd\), then \(3\times Odd+3 = Even\). Because \(Odd+Odd=Even\).
If \(n = even\), then \(3\times Even+3 = Even\). Because \(Even+Odd=Odd\).
We cannot be sure that \(3n+3\) is Even or Odd.
D. \(6n+3\)
If \(n = odd\), then \(6\times Odd+3 = Odd\). Because \(Even+Odd=Odd\).
If \(n = even\), then \(6\times Even+3 = Odd\). Because \(Even+Odd=Odd\).
We can be sure that \(6n+3\) is always Odd.
Hence the right answer is Option D.
We are given that n is a positive integer. We have to take cases where n is odd and even.
A. \(n+5\)
If \(n = odd\), then \(Odd+5 = Even\). Because \(Odd+Odd=Even\).
If \(n = even\), then \(Even+5 = Odd\). Because \(Even+Odd=Odd\).
We cannot be sure if \(n+5\) is odd or not.
B. \(2n-4\)
If \(n = odd\), then \(2\times Odd-4 = Even\). Because \(Even-Even=Even\).
If \(n = even\), then \(2\times Even-4 = Even\). Because \(Even-Even=Even\).
We can be sure that \(2n-4\) is Even.
C. \(3n+3\)
If \(n = odd\), then \(3\times Odd+3 = Even\). Because \(Odd+Odd=Even\).
If \(n = even\), then \(3\times Even+3 = Even\). Because \(Even+Odd=Odd\).
We cannot be sure that \(3n+3\) is Even or Odd.
D. \(6n+3\)
If \(n = odd\), then \(6\times Odd+3 = Odd\). Because \(Even+Odd=Odd\).
If \(n = even\), then \(6\times Even+3 = Odd\). Because \(Even+Odd=Odd\).
We can be sure that \(6n+3\) is always Odd.
Hence the right answer is Option D.
