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n is an integer
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17 Apr 2023, 11:19
17 Apr 2023, 11:19
Expert Reply
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Question Stats:
57% (01:11) correct
42% (01:51) wrong based on 38 sessions
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n is an integer
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\([-1]^{2n+1} \times -1^n\) |
\(1^n \) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: n is an integer
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17 Apr 2023, 17:22
17 Apr 2023, 17:22
Quantity B is always 1
Quantity A
2n + 1 is an odd number. So -1^(2n + 1) is negative
If n is negative whole expression is positive else negative
A is either equal to B or lesser than B. Cannot be Determined
Option D
Quantity A
2n + 1 is an odd number. So -1^(2n + 1) is negative
If n is negative whole expression is positive else negative
A is either equal to B or lesser than B. Cannot be Determined
Option D
Re: n is an integer
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21 Apr 2023, 04:00
21 Apr 2023, 04:00
Expert Reply
OE
Note that −1 and 1, when raised to an integer power, have very limited possibilities. Negative 1 raised to an even power is 1, and −1 raised to an odd power is −1, whereas 1 raised to a power is always 1. Therefore, this is really a problem about odds and evens. So plug in a small even number and a small odd number and try to prove (D). If n = 2, Quantity A is equal to (−1)^5 × (−1)^2, which is −1, and Quantity B is equal to 1. If n = 3, Quantity A is equal to (−1)^7 × (−1)^3, which is 1, and Quantity B is equal to 1. Stop here—the answer is (D).
Note that −1 and 1, when raised to an integer power, have very limited possibilities. Negative 1 raised to an even power is 1, and −1 raised to an odd power is −1, whereas 1 raised to a power is always 1. Therefore, this is really a problem about odds and evens. So plug in a small even number and a small odd number and try to prove (D). If n = 2, Quantity A is equal to (−1)^5 × (−1)^2, which is −1, and Quantity B is equal to 1. If n = 3, Quantity A is equal to (−1)^7 × (−1)^3, which is 1, and Quantity B is equal to 1. Stop here—the answer is (D).
