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If r=0.345, s=(0.345)^2, and t=root(0.345), which of the

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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] New post 06 May 2012, 08:47
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Question Stats:

70% (01:38) correct 30% (00:39) wrong based on 123 sessions
If \(r=0.345\), \(s=0.345^2\), and \(t=\sqrt{0.345}\), which of the following is the correct ordering of \(r\), \(s\), and \(t\) ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

If \(x\) is in the range \(0<x<1\) then: \(0<x^2<x<\sqrt{x}<1\).

Consider the simpler example: if \(x=\frac{1}{4}\) then \(0<\frac{1}{16}<\frac{1}{4}<\frac{1}{2}<1\).

So, \(s<r<t\).

Answer: D.
[Reveal] Spoiler: OA

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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] New post 08 Jun 2015, 13:22
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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] New post 10 Jun 2015, 20:24
Expert's post
Hi All,

This prompt showcases some great Number Property rules that you're likely to face (in some way or another) on the Official GMAT.

Regardless of the actual numbers involved, IF you're dealing with a positive fraction (meaning a value that is greater than 0 and less than 1), then there are some rules to remember...

1) Squaring that fraction will make the result SMALLER
2) Square-rooting that fraction will make the result BIGGER

Here are some additional Number Property rules for NEGATIVE fractions (meaning a value that is less than 0 and greater than -1)....

1) Squaring that fraction will make the result BIGGER (since squaring a negative creates a positive) AND the result will be CLOSER to 0.
2) Cubing that fraction will make the result BIGGER (since the result will be closer to 0).

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Rich
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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the   [#permalink] 10 Jun 2015, 20:24
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