GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Sep 2018, 07:47

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Jun 2006
Posts: 108
If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

Updated on: 03 Oct 2017, 02:09
2
21
00:00

Difficulty:

25% (medium)

Question Stats:

64% (00:40) correct 36% (00:42) wrong based on 1191 sessions

### HideShow timer Statistics

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

Originally posted by girikorat on 07 Nov 2006, 11:50.
Last edited by Bunuel on 03 Oct 2017, 02:09, edited 3 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 49320
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

11 Apr 2012, 01:47
5
5
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, $$s<r<t$$.

_________________
Retired Moderator
Joined: 20 Dec 2010
Posts: 1868
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

28 Aug 2011, 07:29
4
4
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.
_________________
##### General Discussion
Senior Manager
Joined: 30 Aug 2006
Posts: 365
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

07 Nov 2006, 12:26
2
1
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
Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 208
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

26 Jul 2012, 03:58
Hi bunuel,

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

Thanks
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Manager
Joined: 26 Feb 2012
Posts: 102
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

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????
Manager
Joined: 08 Apr 2012
Posts: 123
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

26 Apr 2013, 08:16
1

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 $$s<r<t$$
_________________

Shouvik
http://www.Edvento.com

Intern
Joined: 19 May 2014
Posts: 31
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

Updated on: 22 May 2014, 04:25
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.
_________________

Please press Kudos if you were helped by my post!

Originally posted by JapinderKaur on 22 May 2014, 04:20.
Last edited by JapinderKaur on 22 May 2014, 04:25, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 49320
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of  [#permalink]

### Show Tags

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
_________________
Re: If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which of &nbs [#permalink] 03 Oct 2017, 02:09
Display posts from previous: Sort by

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

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.