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

It is currently 14 Nov 2018, 12:02

Stanford R1 Interview Decisions:

Join Chat Room for Live Updates


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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Working alone at a constant rate, Alan can paint a house in a hours.

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

Hide Tags

Manager
Manager
avatar
Joined: 18 Aug 2011
Posts: 51
Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 26 Aug 2011, 01:10
7
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (02:34) correct 22% (02:55) wrong based on 337 sessions

HideShow timer Statistics

Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?

a) (3ac)/(a+c)
b) (4a-12c)/(3ac)
c) (3ac)/(4a-12c)
d) (ac)/(a+2c)
e) (ac)/(a+c)
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 664
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 26 Aug 2011, 16:38
1
work time

A 1 a
B 1/4 b

A+B 1/3 c


A's rate = 1/a

B's rate = 1/4b

when they are working together , their combined rate is 1/a + 1/(4b) = (1/3)/c

1/(4b) = 1/(3c) - 1/a

=> b = 3ac /(4a-12c)

Answer is C.
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1829
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 27 Aug 2011, 06:42
2
Berbatov wrote:
Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?

a) (3ac)/(a+c)
b) (4a-12c)/(3ac)
c) (3ac)/(4a-12c)
d) (ac)/(a+2c)
e) (ac)/(a+c)


Alan's rate= 1/a
Bob's rate= 1/(4b)
Combined rate= 1/(3c)

\(\frac{1}{a}+\frac{1}{4b}=\frac{1}{3c}\)

Upon solving:
\(b=\frac{3ac}{4a-12c}\)

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 25 May 2011
Posts: 121
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 30 Oct 2011, 09:19
Alan's time to complete the task: a
Bob's time to complete the task: 4b
Together: 3c

\(\frac{1}{a}+\frac{1}{4b}=\frac{1}{3c}\)


\(b=\frac{3ac}{4a-12c}\)

Answer C
Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 97
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 08 Dec 2015, 07:57
1
shahideh wrote:
Alan's time to complete the task: a
Bob's time to complete the task: 4b
Together: 3c

\(\frac{1}{a}+\frac{1}{4b}=\frac{1}{3c}\)


\(b=\frac{3ac}{4a-12c}\)

Answer C


how do you isolate B on its own to figure out the other side of the equation?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12853
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 08 Dec 2015, 23:11
Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

We're told that:
1) Alan can paint a house in A hours
2) Bob can paint the same house in 4B hours
3) Together, Alan and Bob can paint the house in 3C hours

Using the Work Formula, we would have....

(A)(4B) / (A + 4B) = 3C

We're asked to solve for B in terms of A and C....

(A)(4B) = (3C)(A + 4B)
4AB = 3AC + 12BC
4AB - 12BC = 3AC
B(4A - 12C) = 3AC
B = (3AC)/(4A - 12C)

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 97
Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 10 Dec 2015, 11:24
EMPOWERgmatRichC wrote:
Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

We're told that:
1) Alan can paint a house in A hours
2) Bob can paint the same house in 4B hours
3) Together, Alan and Bob can paint the house in 3C hours

Using the Work Formula, we would have....

(A)(4B) / (A + 4B) = 3C

We're asked to solve for B in terms of A and C....

(A)(4B) = (3C)(A + 4B)
4AB = 3AC + 12BC
4AB - 12BC = 3AC
B(4A - 12C) = 3AC
B = (3AC)/(4A - 12C)

Final Answer:

GMAT assassins aren't born, they're made,
Rich


But isn't the equation:

\(\frac{1}{A} + \frac{1}{4B} =3C\)
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12853
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 10 Dec 2015, 17:26
Hi nycgirl212,

The approach I used involved the Work Formula. If you want to use the 'unit' approach, then you should review the explanations offered by Spidy001, shahideh and fluke.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 16 Jan 2017, 17:27
Berbatov wrote:
Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?

a) (3ac)/(a+c)
b) (4a-12c)/(3ac)
c) (3ac)/(4a-12c)
d) (ac)/(a+2c)
e) (ac)/(a+c)


We are given that Alan can paint a house in a hours and Bob can paint 1/4 of the same hours in b hours. Thus, we can say the following:

rate of Alan = 1/a

rate of Bob = (1/4)/b = 1/(4b)

Rate together = 1/a + 1/(4b).

However, since we are also given that working together Alan and Bob can paint 1/3 of the house in c hours, we can express their combined rate as (1/3)/c = 1/(3c). Since the combined rate has to be the sum of their individual rates, we can say 1/a + 1/(4b) = 1/(3c), and we can solve for b in terms of a and c.

Multiplying the entire equation by 12abc, we obtain:

12bc + 3ac = 4ab

3ac = 4ab - 12bc

3ac = b(4a - 12c)

3ac/(4a - 12c) = b

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

Manager
Manager
User avatar
B
Joined: 20 Jan 2017
Posts: 60
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Reviews Badge
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 30 Jan 2017, 03:35
1) First of all we need to find the rates of Alan and Bob: A: \(r*a=1; r=\frac{1}{a}, B:r*b=\frac{1}{4}, r=\frac{1}{4}/b=\frac{1}{4b}\)
2) Working together Alan and Bob's rate is \(\frac{1}{a}+\frac{1}{4b}\)
3) Let's set up the equation using the information in the third sentence. \((\frac{1}{a}+\frac{1}{4b})*c=\frac{1}{3}, \frac{c}{a}+\frac{c}{4b}=\frac{1}{3}\).........b=\(\frac{3ac}{4a-12c}\)

The correct answer is C
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8774
Premium Member
Re: Working alone at a constant rate, Alan can paint a house in a hours.  [#permalink]

Show Tags

New post 08 Apr 2018, 06:38
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

GMAT Club Bot
Re: Working alone at a constant rate, Alan can paint a house in a hours. &nbs [#permalink] 08 Apr 2018, 06:38
Display posts from previous: Sort by

Working alone at a constant rate, Alan can paint a house in a hours.

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.