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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]

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-r-0-345-s ... 32067.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Oct 2017, 02:09, edited 3 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]

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New post 28 Aug 2011, 07:29
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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]

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New post 11 Apr 2012, 01:47
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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]

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New post 07 Nov 2006, 12:26
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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: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of [#permalink]

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New post 26 Apr 2013, 08:16
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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]

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New post 26 Jul 2012, 03:58
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]

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New post 26 Apr 2013, 06:40
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]

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New post 22 May 2014, 04:20
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 JapinderKaur on 22 May 2014, 04:25, 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]

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New post 03 Oct 2017, 02:09
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



OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-r-0-345-s ... 32067.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of   [#permalink] 03 Oct 2017, 02:09
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If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of

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