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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]

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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]

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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink]

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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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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink]

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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink]

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New post 01 Dec 2016, 10:08
Bunuel wrote:
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


Let \(r = 0.36\) ; \(s = 0.36^2\) & \(t = \sqrt{0.36}\)

So, \(r = 0.36 , s ≈ 0.13\) & \(t = 0.60\)

Thus, \(s < r < t = 0.13 < 0.36 < 0.60\)

Hence, answer will be (D) \(s < r < t\)
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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the   [#permalink] 01 Dec 2016, 10:08
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