GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
n is an integer
[#permalink]
17 Apr 2023, 11:19
17 Apr 2023, 11:19
Expert Reply
1
Bookmarks
00:00
Question Stats:
58% (01:11) correct
41% (01:51) wrong based on 39 sessions
Hide Show timer Statistics
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
[#permalink]
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
[#permalink]
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).
