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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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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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Expert's post
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, $$s<r<t$$.

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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]  26 Apr 2013, 07:16
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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: r and s [#permalink]  07 Nov 2006, 11:10
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

As r,s and t are fractions
s<r<t
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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, 04:56
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.
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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]  11 Apr 2012, 00:35
I am also in the same boat on this question, can someone give a much better detailed solution to this problem?
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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, 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.
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of   [#permalink] 22 May 2014, 03:20
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