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07 Feb 2019, 07:56
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A
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% (01:18) correct
15%
(01:34)
wrong
based on 122
sessions
History
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Time
Result
Not Attempted Yet
If x is an integer, then which of the following statements about x^2 – x – 1 is true?
A) It is always odd.
B) It is always even.
C) It is always positive.
D) It is even when x is even and odd when x is odd.
E) It is even when x is odd and odd when x is even.
Solution:
A) It is always odd.
B) It is always even.
C) It is always positive.
D) It is even when x is even and odd when x is odd.
E) It is even when x is odd and odd when x is even.
Solution:
A) If x is an Odd#, then x^2 is O#*O# so also O#, then - O# we get an Even#, then -1 (O#) answer becomes an O#
x=3, 9-3-1 = 5
B) If x is an Even#, then x^2 is E#, E#-E# = E#, then -1 (O#) we get an O# again.
x=2, 4-2-1 = 1
So there's no way that the result can be even. B is out.
C) When there's exponents and fractions together this issue always comes up.
x=1/2, 1/4 - 1/2 - 1 = -5/4 so not necessarily positive
Same with x=-1/2, 1/4 + 1/2 - 1 = -1/4
D) and E) restate A) and B) but are only half correct, can check using the same examples
Official explanation:
Because x is an integer, x must be either even or odd. If x is even, then x^2 – x must also be even, and therefore x^2 – x – 1 is always odd. If x is odd, then x^2 – x must be even, and again, x^2 – x – 1 is always odd. You can also solve this problem by Plugging In. After Plugging In several values for x and calculating x^2 – x – 1, you will discover that the result is always odd. The correct answer is (A).
x=3, 9-3-1 = 5
B) If x is an Even#, then x^2 is E#, E#-E# = E#, then -1 (O#) we get an O# again.
x=2, 4-2-1 = 1
So there's no way that the result can be even. B is out.
C) When there's exponents and fractions together this issue always comes up.
x=1/2, 1/4 - 1/2 - 1 = -5/4 so not necessarily positive
Same with x=-1/2, 1/4 + 1/2 - 1 = -1/4
D) and E) restate A) and B) but are only half correct, can check using the same examples
Official explanation:
Because x is an integer, x must be either even or odd. If x is even, then x^2 – x must also be even, and therefore x^2 – x – 1 is always odd. If x is odd, then x^2 – x must be even, and again, x^2 – x – 1 is always odd. You can also solve this problem by Plugging In. After Plugging In several values for x and calculating x^2 – x – 1, you will discover that the result is always odd. The correct answer is (A).
07 Feb 2019, 07:58
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energetics
\(x^2 – x – 1=odd^2-odd-odd=odd-odd-odd=even-odd=odd\).
Answer: A.
22 Jul 2020, 07:06
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