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

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

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06 May 2012, 08:47
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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

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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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10 Jun 2015, 20:24
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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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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** General Discussion Math Expert Joined: 02 Sep 2009 Posts: 52231 If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] Show Tags 08 Jun 2015, 13:22 1 4 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. _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2723 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] Show Tags 20 Jun 2015, 19:53 girikorat 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 CONCEPT:For solving any such question, One must know that 1) If 0<x<1, then the higher powers of x result in smaller numbers and lower powers of x result in a bigger number 2) If x>1, then the higher powers of x result in Bigger numbers and lower powers of x result in a Smaller number Here since 0.345 is between 0 and 1 therefore the number with the highest power i.e. s must be least and the number with the Lowest power i.e. t must be Biggest number therefore s < r < t Answer: Option _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13331 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the [#permalink] Show Tags 07 Jul 2015, 21:06 Hi All, This question is based on a couple of important Number Property rules regarding positive fractions (between 0 and 1): 1) When 'squaring' a positive fraction, the result gets SMALLER (e.g.. (1/2)^2 = 1/4). Since 'square-rooting' is the opposite of 'squaring'.... 2) When 'square-rooting' a positive fraction, the result gets BIGGER. While these rules are not tested that often on the Official GMAT, it's likely that you'll be tested on either or both at least once on Test Day. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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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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01 Dec 2016, 10:08
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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]

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05 Oct 2017, 09:14
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

Since r is a positive decimal between 0 and 1, s = r^2 and t = √r. We see that when r is raised to a power > 1, its value decreases, and when it is raised to a power < 1, its value increases (recall that square root means ½ power). Thus, the correct ordering is 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]

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28 Oct 2018, 12:56

Solution

Given:
• r=0.345
• s=$$0.345^2$$
• t=√0.345

To find:
• The correct order of r, s, and t among the given options.

Approach and Working

For 0< x <1:
• On increasing the power of x, the value of power of x will decrease.
o For example: 0.5 >$$0.5^2$$

• On decreasing the power of x, the value of power of x will increase.
o For example: $$0.5^2$$ < 0.5

Thus, we can conclude that: s< r and r <t
• Hence, s < <r < t

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Re: If r=0.345, s=(0.345)^2, and t=root(0.345), which of the &nbs [#permalink] 28 Oct 2018, 12:56
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