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n is a positive integer

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Joined: 18 Apr 2015
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GRE 1: Q160 V160
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n is a positive integer [#permalink] New post 20 Jun 2020, 00:08
Expert's post
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Question Stats:

80% (00:24) correct 19% (00:14) wrong based on 52 sessions
n is a positive integer

Quantity A
Quantity B
\((0.9)^n\)
\(\frac{1}{2}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: n is a positive integer [#permalink] New post 20 Jun 2020, 06:07
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Expert's post
Carcass wrote:
n is a positive integer

Quantity A
Quantity B
\((0.9)^n\)
\(\frac{1}{2}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation



Key concept: If \(0 < x < 1\), then the value of \(x^n\) gets closer and closer to \(0\), as \(n\) gets bigger and bigger.

For example:
\((0.9)^1 = 0.9\)
\((0.9)^2 = 0.81\)
\((0.9)^3 = 0.729\)
\((0.9)^4 = 0.6561\)
.
.
.
etc

So, when n = 1, Quantity A is greater
When n = 1000, Quantity B is greater

Answer: D

Cheers,
Brent
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Re: n is a positive integer   [#permalink] 20 Jun 2020, 06:07
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