n is a positive integer. What is the value of (-1)n+2 – (-

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Sep 18, 2019 11:57 pm

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[GMAT math practice question]

n is a positive integer. What is the value of (-1)^{n+2} – (-1)^{n-1} +(-1)^{n+1} –(-1)^n

A. -3
B. -2
C. -1
D. 0
E. 1

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Source: Beat The GMAT — Problem Solving | Wed Sep 18, 2019 11:57 pm

Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Sep 22, 2019 5:38 pm

=>

If n is an odd integer, then (-1)^{n+2} – (-1)^{n-1} +(-1)^{n+1} –(-1)^n = (-1) – 1 + 1 – (-1) = 0.

If n is an even integer, then (-1)^{n+2} – (-1)^{n-1} +(-1)^{n+1} –(-1)^n = 1 – (-1) + (-1) – 1 = 0.
Thus it is always 0.

Therefore, D is the answer.
Answer: D

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