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03 Dec 2019, 01:29
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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:
25%
(medium)
Question Stats:
75% (01:56) correct
25%
(01:32)
wrong
based on 91
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Which of the following expressions yields an even integer for any integer n?
A. \(n^2-10n+21\)
B. \(n^2-2n-24\)
C. \(n^2+8n+7\)
D. \(n^2+11n+18\)
E. \(n^2-4n-60\)
A. \(n^2-10n+21\)
B. \(n^2-2n-24\)
C. \(n^2+8n+7\)
D. \(n^2+11n+18\)
E. \(n^2-4n-60\)
03 Dec 2019, 02:32
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Bunuel
Explanation:
Put value of n= 1 & 2 in Every options for checking
U will find odd & Even value except in option D which will be always even value
as
odd^2 + Odd + even will be even
even^2 + even + Even is also even
IMO-D
Please give kudos, if you find my explanation good enough 
03 Dec 2019, 02:49
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Approach to find whether an expression is EVEN or ODD
It is a 3 step process:
1. \(n^x\) has the same Even and Odd nature as a \(n\) itself so always ignore the power it doesn't matter whether power \(x\) = 2, 3, 100 or so no provided that x is a positive integer.
Always ignore/delete the exponent provided that exponent is a positive integer.
2. Ignore/delete the term which u know is an Even number.
3. if the coefficient of n is odd integer, just ignore the coefficient and write it as n only for simplicity, if the coefficient of n is Even, ignore/delete the complete term as it is Even
A. \(n^2-10n+21\)
Delete 10n as it is Even, and ignore exponent 2, the expression is n +21, this can be even or odd when n is odd or even, Not the right answer
B. \(n^2-2n-24\)
Delete 2n and 24 as these are Even, and ignore the exponent, the expression is n , which can be even or odd. Not the right answer
C. \(n^2+8n+7\)
Delete 8n as it is Even, and ignore the exponent, the expression is n+7, this can be even or odd when n is odd or even, Not the right answer
D. \(n^2+11n+18\)
Delete 18 as it is Even, and ignore the exponent, also ignore the odd coefficient 11, the expression is n+n = 2n , which must be even as n is an integer RIGHT ANSWER
E. \(n^2-4n-60\)
Delete 4n and 60 as these are Even, and ignore the exponent, the expression is n , which can be even or odd. Not the right answer
