GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close

It is currently 24 Jan 2021, 01:32
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If a^6 + b^6 = 144 then the greatest possible value for b is between
9 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags :
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 70582
CAT Tests Top Member of the Month
If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  10 Sep 2017, 04:30
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:32) correct 38% (01:51) wrong based on 177 sessions

Hide Show timer Statistics

If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
avatar
B
Ejiroghene
Intern
Intern
Joined: 27 Feb 2015
Posts: 7
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  Updated on: 10 Sep 2017, 07:20
1
Kudos
greatest possible value of b is when a is zero.

so b^6 = 144
b^3 = 12 b = 2.xxx
b is between 3 and 4 so

Ans D

Sent from my SM-G935F using GMAT Club Forum mobile app

Originally posted by Ejiroghene on 10 Sep 2017, 05:58.
Last edited by Ejiroghene on 10 Sep 2017, 07:20, edited 1 time in total.
avatar
B
kumarparitosh123
Manager
Manager
Joined: 02 Nov 2015
Posts: 160
GMAT 1: 640 Q49 V29
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  10 Sep 2017, 06:14
1
Kudos
2
Bookmarks
It's a D. Between 2 and 4.

B is maximum when value of A is zero.

And since no condition has been given for A and B to be integers, so B can take decimal values also.

Again b^6=144
b^3=12.
So B can also be 2.1 or 2.2.
But it cannot be 3 or greater than 3.
So it has to be somewhere between 2 and 3.
So option D holds good in this case.



Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
avatar
D
niks18
Retired Moderator
Joined: 25 Feb 2013
Posts: 1115
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  10 Sep 2017, 06:20
1
Bookmarks
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0


The question states that \(b^6 = 144-a^6\). Hence for \(b\) to be maximum \(a=0\)
so \(b^6=144\) taking square root of both the sides, we get
\(b^3 = 12\). Now,
\(8<12<27\) or \(8<b^3<27\). Taking cube root of the inequality we get
\(2<b<3\). Hence \(b\) is definitely greater than \(2\) but less than \(3\) (to be precise; \(b^3 = 12\), or \(b= 2.289428\))

Ideally the greatest possible value of \(b\) is between \(2\) & \(3\), but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors
User avatar
G
testcracker
Senior Manager
Senior Manager
Joined: 24 Mar 2015
Status:love the club...
Posts: 255
If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  Updated on: 16 Oct 2017, 23:56
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0


The question states that \(b^6 = 144-a^6\). Hence for \(b\) to be maximum \(a=0\)
so \(b^6=144\) taking square root of both the sides, we get
\(b^3 = 12\). Now,
\(8<12<27\) or \(8<b^3<27\). Taking cube root of the inequality we get
\(2<b<3\). Hence \(b\) is definitely greater than \(2\) but less than \(3\) (to be precise; \(b^3 = 12\), or \(b= 2.289428\))

Ideally the greatest possible value of \(b\) is between \(2\) & \(3\), but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors


niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..

Originally posted by testcracker on 16 Oct 2017, 21:47.
Last edited by testcracker on 16 Oct 2017, 23:56, edited 2 times in total.
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 70582
CAT Tests Top Member of the Month
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  16 Oct 2017, 22:22
Expert Reply
gmatcracker2017 wrote:
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0


The question states that \(b^6 = 144-a^6\). Hence for \(b\) to be maximum \(a=0\)
so \(b^6=144\) taking square root of both the sides, we get
\(b^3 = 12\). Now,
\(8<12<27\) or \(8<b^3<27\). Taking cube root of the inequality we get
\(2<b<3\). Hence \(b\) is definitely greater than \(2\) but less than \(3\) (to be precise; \(b^3 = 12\), or \(b= 2.289428\))

Ideally the greatest possible value of \(b\) is between \(2\) & \(3\), but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors


niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..


The greatest possible value of b turns out to be ~2.3, which is indeed between 2 and 3, but it will also be true to say that it's between -1,000 and 10,000 isn't it? Between x and y, here means in the range from x to y. So, we can say that 2.3 is between 2 and 4.
_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
G
testcracker
Senior Manager
Senior Manager
Joined: 24 Mar 2015
Status:love the club...
Posts: 255
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  16 Oct 2017, 23:57
gmatcracker2017 wrote:
niks18 wrote:
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0


The question states that \(b^6 = 144-a^6\). Hence for \(b\) to be maximum \(a=0\)
so \(b^6=144\) taking square root of both the sides, we get
\(b^3 = 12\). Now,
\(8<12<27\) or \(8<b^3<27\). Taking cube root of the inequality we get
\(2<b<3\). Hence \(b\) is definitely greater than \(2\) but less than \(3\) (to be precise; \(b^3 = 12\), or \(b= 2.289428\))

Ideally the greatest possible value of \(b\) is between \(2\) & \(3\), but we don't have any option stating that.
Hi Bunuel can you confirm whether Option D is correct and there are no typo errors


niks18
hi

I agree with you completely
though I approached the problem similar way, I don't understand how everybody is claiming "b" to be between 2 and 4

certainly, we need some Bunuel here ..


thanks a lot to you Bunuel

you are super helpful
thanks 8-)
User avatar
V
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 13211
Location: United States (CA)
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  19 Oct 2017, 09:21
Expert Reply
Bunuel wrote:
If a^6 + b^6 = 144 then the greatest possible value for b is between

A. 8 and 10
B. 6 and 8
C. 4 and 6
D. 2 and 4
E. 2 and 0


Since we want to maximize the value of b, we want to minimize the value of a^6. Since a has an even power, the minimum value of a^6 is 0, which occurs when a = 0 (note: if a ≠ 0, then a^6 > 0). Thus, when a^6 = 0, we have:

b^6 = 144

Since 2^6 = 64 and 3^6 = 729, b is greater than 2 but less than 3.

Answer: D
_________________

★ ★ ★ ★ ★   250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 17553
Re: If a^6 + b^6 = 144 then the greatest possible value for b is between [#permalink] New post  23 Mar 2019, 10:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
[#permalink]
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9312 posts
Bunuel
Math Expert
70582 posts
VeritasKarishma
Veritas Prep GMAT Instructor
11375 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2364 posts
generis
Senior SC Moderator
4462 posts
Feedback

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions