For which of the following values of n is $(-0.5)^n$ the greatest?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 10, 2020 12:22 am

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For which of the following values of n is $(-0.5)^n$ the greatest?

A. 5
B. 4
C. 3
D. 2
E. 1

Answer: D

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Sep 10, 2020 12:22 am

ravinikhil: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Sep 10, 2020 6:03 am

Re: For which of the following values of n is $(-0.5)^n$ the greatest?

by ravinikhil » Thu Sep 10, 2020 7:01 am

Remember, any value in decimal, when the power is applied its absolute value decreases.
for 0.5 > 0.5^2.
here, because of the negative sign, it gives the question another twist!
now a positive sign will always be greater than negative !!
negative to the power even nos will be positive right!
so here we have to check positive powers as greatest is required,
also with increasing power, the no will be getting smaller.
hence basically we are looking at the smallest even no in the options.
which is 2 which is also the ans.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: For which of the following values of n is $(-0.5)^n$ the greatest?

by Scott@TargetTestPrep » Tue Sep 15, 2020 4:52 am

Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:22 am
For which of the following values of n is $(-0.5)^n$ the greatest?

A. 5
B. 4
C. 3
D. 2
E. 1

Answer: D

Solution:

Notice that -0.5 is negative, thus, if it’s raised to an odd power, it’s still negative; however, if it’s raised to an even power, it will be positive. Therefore, we can see that the correct choice will be either B or D. Finally, since -0.5 has an absolute value less than 1, when it is raised to a larger power, the value actually gets smaller. That is, (-0.5)^4 < (-0.5)^2. Thus, when n = 2, (-0.5)^n has the greatest value.

Answer: D

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