It is currently 20 Feb 2018, 19:16

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Albert and Bob are painting rooms at constant, but different

Author Message
TAGS:

### Hide Tags

Intern
Joined: 04 Aug 2011
Posts: 41
Location: United States
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)
Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

05 Feb 2012, 18:24
1
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

65% (03:37) correct 35% (04:38) wrong based on 270 sessions

### HideShow timer Statistics

Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15
[Reveal] Spoiler: OA
Manager
Joined: 31 Jan 2012
Posts: 73
Re: Work and Rate tough question !!! [#permalink]

### Show Tags

05 Feb 2012, 21:51
2
KUDOS
1
This post was
BOOKMARKED
rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time

Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
5*3 = 3n
15 = 3n.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India
Re: Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

06 Feb 2012, 01:31
9
KUDOS
Expert's post
8
This post was
BOOKMARKED
sourabhsoni wrote:
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

a) 7
b) 9
c) 11
d)13
e) 15

First of all, I don't like unnecessary variables. The data given is in terms of n rooms but the answer is independent of n. This means, no matter what value I put for n, the answer would be the same. So I will just put n = 1 and proceed.

Albert takes an hour longer than Bob to paint one room.
Time taken by Albert to paint 1 room = A hrs, Time taken by Bob = A-1 hrs

"they can paint a total of 3/5 rooms in 4/3 hours"
W = R*T
3/5 = R*(4/3)
R = 9/20 which is the combined rate of the two.

We obtained this by adding their rates together: 9/20 = 1/A + 1/(A-1)
Over here, please remember that numbers fall in place in GMAT questions. You should be able to figure that since the denominator is 20, A = 5 gives 5*4 in the denominator so it should work. Check before proceeding though.

So Albert paints a room in 5 hrs. For 3 rooms, he takes 3*5 = 15 hrs.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 27 Dec 2011 Posts: 66 Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 14 Sep 2012, 16:07 3 This post received KUDOS 1 This post was BOOKMARKED Hi, This question can be done very quickly if you understand what they asking for. I will present a very general way of solving ANY work,rate and time related question: Question will always ask for something out of rate or time or work. (obviously coz its a work time rate related question ) ex. in this question they want "time" for "3n" work done by Albert, right?? This means ------> rate * TIME = 3n =====> All you have to do it find out the RATE for albert and then put it here to find the TIME!!!!! (easy right??) Let see what is given here: some relation between Albert and bob's individual time and their combined time. In combined time: some work and time is given, we don't care what it is, all we will do is find their rate by writing WORK/TIME i.e. (3n/5) / 4/3 = 9n/20 = 9/20 From individual relationships just find Albert and Bob's respective rates: A: takes 'a' time to complete n rooms===> rate becomes : n/a = 1/a B: takes 1 hr less than A to complete n rooms =====> rate becomes : n/(a-1) = 1/a-1 now add individual rates and equate 'em to the combined rate: 1/a + 1/(a-1) = 9/20 From my experience I feel that from thus point its faster and much easier to put values than solve the quadratic: if u see that answer I feel 9 and 15 stand out as they are multiples of 3 and they represent 3n work, we can do 3n=15 => n = 5 and put "5" in place of "a" in the equation. it will be equal to 9/20 thats ur answer. BOTTOM LINE: first thing always look for what is need to in final answer and how can I get their, if yo start by what's given then u will start doing actions not even necessary to reach the solutions. I hope this helps, thanks, -Kartik Non-Human User Joined: 09 Sep 2013 Posts: 13817 Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 20 Sep 2013, 19:57 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. _________________ Current Student Joined: 06 Sep 2013 Posts: 1954 Concentration: Finance Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 14 Jan 2014, 10:29 Sourabh2012 wrote: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself? a) 7 b) 9 c) 11 d)13 e) 15 Please help, totally stumped. Looking for some simpler and quick approach. Did a similar approach but somewhat shorter A = B+1 Then 4/3 (1/B+1/(B+1)) = 3/5 Hence 1/B + 1/(B+1) = 9/20 So B = 4 Therefore A = 5 And so we will take 5*3 = 15 to paint three rooms Answer is E Just my 2c Hope it helps Cheers! J Director Joined: 03 Aug 2012 Posts: 896 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 28 Mar 2014, 23:57 Rate * Time = Work Let B be the hours that Albert takes to paint 'n' rooms then For (Albert) => n/B * B = n For (BOB) => n/(B-1) ( (B-1) = n Combined rate = n/B + n/(B-1) Again Rate * Time = Work Then {n/B + n/(B-1)} * 4/3 = 3n/5 2B-1/{B(B-1)}=9/20 Substituting values B=5 then answer takes 3B since 3n rooms then (E) _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Current Student Joined: 06 Sep 2013 Posts: 1954 Concentration: Finance Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 08 May 2014, 14:25 Here's another way. May be shorter A = B+1 B = A-1 Now then we have 1/A + 1/ (A-1) = (3/5) / (3/4) = 9n/20 We need to find 3n Let's see To get 9/20, we need something like 1/4 + 1/5 = 9/20 So A must be 5 If A takes 5 to paint 'n', it takes 15 to paint '3n' Answer: E Senior Manager Joined: 07 Apr 2012 Posts: 441 Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 11 May 2014, 02:05 VeritasPrepKarishma wrote: Over here, please remember that numbers fall in place in GMAT questions. You should be able to figure that since the denominator is 20, A = 5 gives 5*4 in the denominator so it should work. Check before proceeding though. So Albert paints a room in 5 hrs. For 3 rooms, he takes 3*5 = 15 hrs. Hi Karishma, What do you mean "numbers fall in place in GMAT"? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7942 Location: Pune, India Re: Albert and Bob are painting rooms at constant, but different [#permalink] ### Show Tags 12 May 2014, 19:14 ronr34 wrote: VeritasPrepKarishma wrote: Over here, please remember that numbers fall in place in GMAT questions. You should be able to figure that since the denominator is 20, A = 5 gives 5*4 in the denominator so it should work. Check before proceeding though. So Albert paints a room in 5 hrs. For 3 rooms, he takes 3*5 = 15 hrs. Hi Karishma, What do you mean "numbers fall in place in GMAT"? It means that GMAT doesn't expect you to do any funny decimal calculations. You won't find yourself multiplying 2.3 by 6.7. If the rate of work comes out to be 1/11, I would expect that the time for which you would have to work to complete it would be 22 hrs/33 hrs... etc Since GMAT doesn't give you a calculator, it doesn't expect you to waste time doing these calculations in the test when you can easily use a calculator in real life. You don't need to have the skill to perform arduous calculations in a short span of time. You need to understand concepts and that's what they test. The numbers they use to test those concepts will be clean and easy to work with. Recognizing the concept will be the tough part. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Non-Human User
Joined: 09 Sep 2013
Posts: 13817
Re: Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

21 Mar 2016, 15:35
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.
_________________
Director
Joined: 07 Dec 2014
Posts: 906
Re: Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

23 Mar 2016, 13:10
let t=Albert's time to paint n rooms
Albert's rate=n/t
Bob's rate=n/(t-1)
Albert and Bob's rate=(3n/5)/(4/3)=9n/20
dividing out n, 1/t+1/(t-1)=9/20
t=5 hours
3t=15 hours
Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 74
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

25 Aug 2017, 01:41
Since options are taking about hrs taken by Albert to paint 3n rooms, we can use options which are divisible by 3, thus working on option B and E,
Option B
If for 3n rooms, Albert takes 9 hrs, so for n rooms he takes 3 hrs. Thus Bob will take 2 hrs to paint n rooms
Now if n = 60
Rate of Albert = $$\frac{60}{3}$$ = 20 rooms per hour
Rate of Bob = $$\frac{60}{2}$$ = 30 rooms per hour
So combined rate = 20+30 = 50 rooms per hour
So together they complete 50* $$\frac{4}{3} = \frac{200}{3}$$ rooms which is not equal to $$\frac{3*60}{5}$$

Option E:
If for 3n rooms, Albert takes 15 hrs, so for n rooms he takes 5 hrs. Thus Bob will take 4 hrs to paint n rooms
Now if n = 60
Rate of Albert = $$\frac{60}{5}$$ = 12 rooms per hour
Rate of Bob = $$\frac{60}{4}$$ = 15 rooms per hour
So combined rate = 12+15 = 27 rooms per hour
So together they complete 27* $$\frac{4}{3}$$ = 36 rooms which is equal to $$\frac{3*60}{5}$$
Thus option E
_________________

Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Director
Joined: 07 Dec 2014
Posts: 906
Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

26 Aug 2017, 12:03
Sourabh2012 wrote:
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15

let n=1
A's rate=1/t+1
B's rate=1/t
A+B rate=(3/5)/(4/3)=9/20
because the ratio of A's rate to B's rate=t/t+1,
assume A's rate to B's rate=(4/20)/(5/20)
20/4=5 hours
3*5=15 hours
E
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)
Re: Albert and Bob are painting rooms at constant, but different [#permalink]

### Show Tags

29 Aug 2017, 16:20
Sourabh2012 wrote:
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

A. 7
B. 9
C. 11
D.13
E. 15

We can let b = the number of hours Bob takes to paint n rooms; thus, Bob’s rate = n/b and Albert’s rate = n/(b + 1). Knowing that they complete 3n/5 rooms in 4/3 hours, we can create the following equation:

(n/b)(4/3) + [n/(b + 1)](4/3) = 3n/5

4n/3b + 4n/[3(b + 1)] = 3n/5

Multiplying the entire equation by 3b x 5 x (b + 1) = 15b(b + 1), we have:

4n[5(b + 1)] + 4n(5b) = 3n[3b(b + 1)]

Dividing by n, we have:

20(b + 1) + 20b = 9b(b + 1)

20b + 20 + 20b = 9b^2 + 9b

9b^2 - 31b - 20 = 0

(9b + 5)(b - 4) = 0

b = -5/9 or b = 4

Since b can’t be negative, b = 4. Thus, it takes Albert 4 + 1 = 5 hours to paint n rooms and 5 x 3 = 15 hours to paint 3n rooms.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: Albert and Bob are painting rooms at constant, but different   [#permalink] 29 Aug 2017, 16:20
Display posts from previous: Sort by