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# If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of

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If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  07 Nov 2006, 10:50
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Apr 2012, 00:40, edited 2 times in total.
Edited the question and added the OA
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[#permalink]  07 Nov 2006, 11:26
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agree D, for simplicity u could just replace the decimal with 1/4

r=1/4
s=r^2=1/8
t=sqrt s=1/2

s<r<t
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Re: r and s [#permalink]  28 Aug 2011, 06:29
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petrifiedbutstanding wrote:
Can someone provide a good solution to this? This problem is pretty straightforward, but I'd definitely be confused if it got a lil more complex on the real GMAT... Any help will be greatly appreciated.

For,
0<x<1; the higher power of x always be smaller than lower power of x.

0<x<1:
$$x^4<x^3<x^2<x^1<x^{\frac{1}{2}}<x^{\frac{1}{4}}$$

x=1;
$$x^1=x^2=x^3=x^{real numbers}=1$$

x>1;
$$x^{\frac{1}{4}}<x^{\frac{1}{2}}<x^1<x^2<x^3<x^4$$

For x<0; it gets subtle because all even powers become +ve. Try some examples and see what you get. But, there too: consider 0>x>-1; x=-1; -1>x as three separate case.
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  11 Apr 2012, 00:47
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dzodzo85 wrote:
I am also in the same boat on this question, can someone give a much better detailed solution to this problem?

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.
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  26 Jul 2012, 02:58
Hi bunuel,

thanks for that example. I had solved it by keeping the fraction itself.

Thanks
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  26 Apr 2013, 05:40
Hi Mr Bunuel....
I did solve this question by replacing .04 to .345...........

Can it be wise to tackle it by replacement theory????
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  26 Apr 2013, 07:16
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Simply follow this rule,

If x < 1, it reduces in value with each power>1.

So for $$x < 1, x>x^2>x^3>x^4..$$ and so on

In the current example,

$$t=sqrt(0.345)$$ (a value less than 1)
$$r = t^2$$
$$s = r^2 = t^4$$

So, as per our above rule, $$t^4<t^2<t$$ implying $$s<r<t$$
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  26 Apr 2013, 22:48
Good way to explain...
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  21 May 2014, 18:36
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  22 May 2014, 03:20
Another similar question for practice:

$$a = -0.283$$
$$b = a^2$$
$$c = a^3$$
$$d = a^4$$

Which of the following options correctly describes the relationship between the 4 numbers?

(A) a<b<c<d
(B) a<c< d<b
(C) c<a<d<b
(D) a<c<b<d
(E) d<c<b<a

SOLUTION

The simplest way to solve the question is this:

Simplify the value of a to -0.3.
So,
b= 0.09
c = -0.027
d = 0.0081

So, the correct order will be Option C:

c<a<d<b

A Tip!

If a had been a difficult number like, say a= -0.784, then instead of simplifying it by rounding it off to -0.8, I suggest you simply take an easier negative decimal, say -0.2, and calculate the relationship between a,b,c,d for it. That relationship would hold true for any negative decimal between 0 and -1. This tip will save you time because calculating the cube and fourth power of 0.8 will be time-consuming.
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Last edited by MavenQ on 22 May 2014, 03:25, edited 1 time in total.
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  20 Jun 2015, 19:17
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If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  20 Jun 2015, 19:53
Expert's post
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
[Reveal] Spoiler:
D

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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  07 Jul 2015, 21:06
Expert's post
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.

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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of   [#permalink] 07 Jul 2015, 21:06
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# If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of

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