It is currently 22 Feb 2018, 03:03

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If r is between –1 and 0, then which of the following is true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43862
If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 01 Oct 2017, 23:36
1
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

35% (00:58) correct 65% (00:46) wrong based on 84 sessions

HideShow timer Statistics

If r is between –1 and 0, then which of the following is true?

A. \(r^5 < r^6 < r^7\)

B. \(r^5 < 0 < r^7\)

C. \(r^7 < r^6 < r^5\)

D. \(r^7 < r^5 < r^6\)

E. \(r^3 < r^7 < r^6\)
[Reveal] Spoiler: OA

_________________

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

1 KUDOS received
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2063
Location: India
GPA: 3.12
Premium Member CAT Tests
If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 01:26
1
This post received
KUDOS
1
This post was
BOOKMARKED
The best way is to choose a number and look at the various options.
If r = -\(\frac{1}{2}

r^5 = -\frac{1}{32} = - 0.03125, r^3 = -\frac{1}{8} = -0.125\) and \(r^7 = -\frac{1}{128} = -0.007\)
However, r^even is always positive

Options A,B and C are eliminated because, we have a even power
in between two odd powers and the positive term will always be the biggest.
\(r^7\) is greater than \(r^5\), so Option D cannot be the answer.

Therefore, \(r^3 < r^7 < r^6\)(Option E) is the answer option that is always true!
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Intern
Intern
User avatar
B
Joined: 10 Apr 2017
Posts: 37
Schools: Kelley '20
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 08:02
The best way is to choose a number and look at the various options.
If r = -12,r5=−132=−0.03125,r3=−18=−0.12512,r5=−132=−0.03125,r3=−18=−0.125 and r7=−1128=−0.007r7=−1128=−0.007
However, r^even is always positive

Options A,B and C are eliminated because, we have a even power
in between two odd powers and the positive term will always be the biggest.
r7r7 is greater than r5r5, so Option D cannot be the answer.

Therefore, r3<r7<r6r3<r7<r6(Option E) is the answer option that is always true!
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 931
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 09:29
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. \(r^5 < r^6 < r^7\)

B. \(r^5 < 0 < r^7\)

C. \(r^7 < r^6 < r^5\)

D. \(r^7 < r^5 < r^6\)

E. \(r^3 < r^7 < r^6\)


Solving the problem conceptually

we know that \(r\) is negative, hence \(r\) will be greatest when power is even. So choice A, B & C are out

Again as \(r\) is negative and greater than \(-1\) i.e a negative proper fraction, higher powers of \(r\) will be greater than the lower powers, So option D is out.

Answer- E
Intern
Intern
avatar
B
Joined: 28 Dec 2010
Posts: 49
CAT Tests
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 10:22
Others have also solved it perfectly. Some of you might have picked D.

You would have figured out \(r^6\)>0, hence it would be highest. The other 2 would be negative. This rules out A,B,C

Now \(|r^7|< |r^5|\), but since both of these terms are negative, \(r^7> r^5\)
Hence D is wrong.

Answer: E
_________________

_________________________________________
Please Kudos, if you found this post helpful.

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 563
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 11:56
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. \(r^5 < r^6 < r^7\)

B. \(r^5 < 0 < r^7\)

C. \(r^7 < r^6 < r^5\)

D. \(r^7 < r^5 < r^6\)

E. \(r^3 < r^7 < r^6\)


Even power of r will always be greater than odd powers and 0, as even power will result in positive number and odd power will result in -ve number.
Odd power of r will always be less than even power and 0 .

A. Wrong
B. Wrong
C. Wrong

Now between D and E.. we know r^3 <r^5 <r^7 ...

So, r^3 < r^7 <r^6 ..
Answer E

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Intern
Intern
avatar
B
Joined: 07 Sep 2017
Posts: 8
Location: Australia
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 02 Oct 2017, 21:29
Since we know r has to be -ve number, options A, B and C cannot be right. Three of them have a odd number on r, followed by either 0 or an even digit on r.
D or E must be correct.
For D: r^7 < r^5 cannot be right.
E has to be the answer.
Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)
Re: If r is between –1 and 0, then which of the following is true? [#permalink]

Show Tags

New post 04 Oct 2017, 15:37
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. \(r^5 < r^6 < r^7\)

B. \(r^5 < 0 < r^7\)

C. \(r^7 < r^6 < r^5\)

D. \(r^7 < r^5 < r^6\)

E. \(r^3 < r^7 < r^6\)


We know that when a negative number is raised to an odd power, the result is negative, and when a negative number is raised to an even power, the result is positive. Furthermore, if the number is between -1 and 0, raising it to a larger odd power will increase its value since the result will be closer to zero (despite still being negative). Thus, we see that:

r^3 < r^7 < r^6

Notice that r^7 will be larger than r^3, and r^6 will be larger than the prior two because it’s positive.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If r is between –1 and 0, then which of the following is true?   [#permalink] 04 Oct 2017, 15:37
Display posts from previous: Sort by

If r is between –1 and 0, then which of the following is true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.