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

 It is currently 20 Sep 2018, 17:20

### 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

# Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 May 2010
Posts: 77
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

Updated on: 18 Dec 2017, 23:39
4
23
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:23) correct 20% (01:40) wrong based on 977 sessions

### HideShow timer Statistics

Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. $$\frac{1}{3x}$$

B. $$\frac{x}{(x-3)}$$

C. $$\frac{(x-1)}{3x}$$

D. $$\frac{x}{(x-1)}$$

E. $$\frac{(x-1)}{x}$$

Originally posted by Jinglander on 08 Aug 2010, 13:46.
Last edited by Bunuel on 18 Dec 2017, 23:39, edited 4 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

09 Aug 2010, 03:12
15
11
Jinglander wrote:
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. $$\frac{1}{3x}$$

B. $$\frac{x}{(x-3)}$$

C. $$\frac{(x-1)}{3x}$$

D. $$\frac{x}{(x-1)}$$

E. $$\frac{(x-1)}{x}$$

If Lindsay can paint $$\frac{1}{x}$$ of a room in 1 hour and together they pain the whole room in 1 hour then Joe can pain1 $$1-\frac{1}{x}=\frac{x-1}{x}$$ of a room in 1 hour --> in 20 minute or in $$\frac{1}{3}$$ of an hour Joe can paint $$\frac{x-1}{3x}$$ of a room.

_________________
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 367
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

08 Aug 2010, 21:14
4
1
Answer is C -- $$(x-1/3x)$$

Given details:

Rate at which L work --1/x
Rate at which L&J work -- x

Rate at which J alone works -- $$(x-1/x)$$

Rate at which J alone works in 20 min. -- $$(x-1/x) * (20/60) => (x-1/x)*(1/3)$$

On a side note, maybe this post needs to be moved to the Problem solving section.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

##### General Discussion
Manager
Joined: 09 Jan 2010
Posts: 84
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

09 Aug 2010, 09:54
bunuel u always hit the nail to the point.......very easy explanation....thanks
Manager
Status: livin on a prayer!!
Joined: 12 May 2011
Posts: 111
Location: Australia
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

28 Oct 2011, 16:31
Just wondering,

if the job took say, 2.5 hours to complete, how would the answer change?

I understand your working though Bunuel, it's very clear.
_________________

Aim for the sky! (800 in this case)
If you like my post, please give me Kudos

Intern
Joined: 02 May 2013
Posts: 4
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

02 May 2013, 12:00
Mindreko wrote:
Just wondering,

if the job took say, 2.5 hours to complete, how would the answer change?

I understand your working though Bunuel, it's very clear.

If the job takes Joseph and Lindsay 2.5 hours together to complete.

and Lindsay take as regular 1/x hours to complete.

Then the rate at which Jospeh works would be = 1/2.5 - 1/x
= (x - 2.5) / (2.5x)

Hence, in 20 minutes

2.5 hours = 150 mins, so in 20 mins he would complete : 2 / 15 * (x - 2.5 ) / (2.5 x )
Intern
Joined: 08 Nov 2012
Posts: 21
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

08 May 2013, 17:17
if you use a smart number 2 for x, then A would be correct. I got this problem wrong two times so far in my studies and make the same mistake. Can someone explain why they would not think to use the number 2 as a smart number going into this problem?
MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5583
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

08 May 2013, 21:51
Richard0715 wrote:
if you use a smart number 2 for x, then A would be correct. I got this problem wrong two times so far in my studies and make the same mistake. Can someone explain why they would not think to use the number 2 as a smart number going into this problem?

Have you checked Option C using x=2 ?

$$\frac{(x-1)}{3x}$$ ----------> $$\frac{(2-1)}{3X2}$$ ----------> $$\frac{1}{6}$$ ------> Same as Option A
_________________
MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5583
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

05 Aug 2013, 01:29
4
1
Well, I am not a fond of trying values or of backsolving methods.

So I will present different method to solve this one - Percent Method.

First some theory.
When we say a person can finish the given task in X hours, we can also say that he can finish $$\frac{100}{X}%$$ task in one hour (Whole task always equals to 100%)
When we say another person can finish the same task in Y hours, we can also say that he can finish $$\frac{100}{Y}%$$ task in one hour.
Finally we can say that they can finish $$(\frac{100}{X} + \frac{100}{Y})%$$ task in one hour.

We will try this method in a simple question
Q :- A can finish certain work in 10 days. B can finish the same work in 20 days. In how many days can they finish the work working together?
A can finish certain work in 10 days ------> He can complete 10% of the work in a day
B can finish the same work in 20 days. -------> He can complete 5% of the work in a day
Working together they can complete (10+5)% work in a day.
Now that we know Total work always equals 100% and that they are finishing 15% work in a day working together, So we can say that they can complete the total work in $$\frac{100}{15}$$ (i.e. 6.66) days.

Lindsay can paint $$\frac{1}{X}$$ of a certain room in one hour. --------> This simply states that Lindsay can paint the room in X hours -----------> Lindsay can paint $$(\frac{100}{X})%$$ of the room in one hour

Lindsay and Joseph, working together at their respective rates, can paint the room in one hour --------> Working together they can paint the 100% of the room in one hour

Equation is ( Rate of Lindsay of one hour + Joseph Rate of of one hour) = Rate of Lindsay+Joseph of one hour

$$\frac{100}{X}$$ + Joseph Rate of of one hour = 100 -------> Joseph's Rate of one hour = $$100 - \frac{100}{X}$$ --------->

Joseph's Rate of one hour = $$\frac{100(X - 1)}{X}$$ --------> We can rephrase this as Joseph is completing $$\frac{(100(X-1))}{X}%$$ of 100% room in one hour ----------> In Fraction He is completing $$\frac{(100(X-1))}{100X}$$ in one hour ------> $$\frac{(X-1)}{X}$$

what fraction of the room can Joseph paint in 20 minutes? ------------> what fraction of the room can Joseph paint in $$\frac{1}{3}$$ hour? -------> $$\frac{1}{3} \frac{(x-1)}{x}$$ -----> $$\frac{(x-1)}{3x}$$

Option C

Hope that Helps.
_________________
Director
Joined: 14 Dec 2012
Posts: 790
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

05 Aug 2013, 01:50
3
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A)1/3x

B)x/(x-3)

C)(x – 1)/3x

D)x/(x-1)

E)(x – 1)/x

I used substitution of values for the variable x, when x=2 i get an answer and when x=3 i get another answer! Please highlight my mistake.

LINDSAY ==> 1/X of room in 1 hr
LINDSAY + JOSEPH ==> FULL ROOM i.e 1 ROOM IN 1 HR
JOSEPH 1 HR WORK + LINDSAY 1 HR WORK = FULL ROOM PAINTING = 1
JOSEPH 1 HR WORK + 1/X = 1
JOSEPH 1 HR WORK = 1- 1/X = (X-1)X
THEREFORE JOSEPH WORK IN 20 MINUTES(1/3 OF HOUR) =$$(1/3)*((X-1)/X)$$ = $$(X-1)/3X$$

Hope this helps
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Intern
Joined: 17 May 2013
Posts: 41
GMAT Date: 10-23-2013
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

05 Aug 2013, 18:12
Let Joseph rate of work in 1 hr be y
Given : Lindsay rate of work in 1 hr as 1/x

Together,

1/x + y = 1

So Joseph rate of work would be

y = 1 - 1/x ==> x-1/x

In 20 min(1/3 of an hour), it would be 1/3(x-1/x) ==> x-1/3x
Option C
Manager
Joined: 07 May 2013
Posts: 98
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

30 Aug 2013, 16:58
1/x th of work-----1 hr
1 full work----------? hr --------x hrs by L to complete full work

Now xy/x+y=1
we have to find y i.e., hrs taken by J to complete full work

divide numerator and denominator of L.H.S with y
we get x divided by (x+y)*1/y=1
----x=(x+y)*1/y
----x=x/y+1
----x-1=x/y
----x-1/x=1/y
reciprocal both sides
----x/x-1=y

Now it takes x/x-1 hrs to complete 1 full work by J

then in 1/3 hrs i.e., 20 min----- ? work J completes

=1/3*1 whole divided by (x/x-1)
=1/3*(x-1/x)
=x-1/3x
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

Updated on: 10 Dec 2014, 02:48
1
Rate of Lindsay $$= \frac{1}{60x}$$

Rate of Joseph $$= \frac{1}{60} - \frac{1}{60x} = \frac{x-1}{60x}$$

Work done by Joseph in 20 Minutes $$= \frac{x-1}{60x} * 20 = \frac{x-1}{3x}$$
_________________

Kindly press "+1 Kudos" to appreciate

Originally posted by PareshGmat on 10 Dec 2014, 02:37.
Last edited by PareshGmat on 10 Dec 2014, 02:48, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

10 Dec 2014, 04:06
Similar question to practice: http://gmatclub.com/forum/lindsay-can-p ... 56880.html
_________________
Intern
Joined: 07 Jan 2015
Posts: 1
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

10 Jan 2015, 18:17
Best approach for me is to plug in #s.

Say x=2, so Lindsay paints 1/2 of the room in one hour. Use D=RT for each Lindsay, Joseph and for both. (D:Work, R:Rate, T:Time) Say D=6

Consider Lindsay only: Lindsay paints 1/2 of D=6, meaning 3. Her rate is then R(Lindsay)=3 if T=1.

Consider Lindsay and Joseph: D=RT, D=6 and T=1, R becomes 6. R here is combined i.e., R= R(Lindsay)+R(Joseph)
R(Joseph) = 3 since R(Lindsay)=3.

Consider Joseph only: D=RT, R=3 and T= 20 min or 1/3 hr
D becomes 1. In other words, Joseph has painted 1/6 of the room in 20 min or 1/3 hr. 1/6 is target value. Plugin x=2 in Answer choices to match the target, C works.
Manager
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
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

30 Jan 2017, 05:00
1) First, let's find Lindsay's rate: $$r*1=\frac{1}{x}, r=\frac{1}{x}$$
2) Now let's find Lindsay and Joseph's rate when working together: R*1=1; R=1
3) Joseph's rate is equal to Lindsay and Joseph's rate together - Lindsay's rate: $$R-r=1-\frac{1}{x}$$
4) Joseph's work in 20 minutes is equal to his rate (per hour) divided by 3. $$(1-\frac{1}{x})/3=\frac{x-1}{x}*\frac{1}{3}=\frac{x-1}{3x}$$
VP
Joined: 07 Dec 2014
Posts: 1087
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

30 Jan 2017, 13:34
Jinglander wrote:
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. 1/3x
B. x/(x-3)
C. (x-1)/3x
D. x/(x-1)
E. (x-1)/x

let 1/j=J's rate
1/j=1-(1/x)
1/j*1/3=1/3-1/3x=(x-1)/3x
C
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3516
Location: United States (CA)
Re: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

01 Feb 2017, 09:16
1
Jinglander wrote:
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. 1/3x
B. x/(x-3)
C. (x-1)/3x
D. x/(x-1)
E. (x-1)/x

We are given that Lindsay's rate to paint a room is 1/x. We are also given that when she works with Joseph, they can paint the room in 1 hour. If we let total work = 1 and j = the number of hours it takes Joseph to paint the room by himself, then Joseph’s rate = 1/j. We can create the following equation and isolate j.

work of Lindsay + work of Joseph = 1

(1/x)(1) + (1/j)(1) = 1

1/x + 1/j = 1

Multiplying the entire equation by xj, we obtain:

j + x = xj

x = xj - j

x = j(x - 1)

x/(x-1) = j

Since j = x/(x-1) and 1/j = Joseph’s rate, Joseph’s rate in terms of x is (x - 1)/x.

Since 20 minutes = 1/3 of an hour, and since work = rate x time, Joseph can complete:

[(x - 1)/x](1/3) = (x - 1)/(3x) of the job in 20 minutes.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Senior SC Moderator
Joined: 22 May 2016
Posts: 1977
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

12 Apr 2018, 16:57
1
Jinglander wrote:
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. $$\frac{1}{3x}$$

B. $$\frac{x}{(x-3)}$$

C. $$\frac{(x-1)}{3x}$$

D. $$\frac{x}{(x-1)}$$

E. $$\frac{(x-1)}{x}$$

If the algebraic equation eludes you, pick an unusual number for $$x$$. Rates are in $$\frac{rooms}{hr}$$

Let $$x = 6$$
L's rate = $$\frac{1}{x}=\frac{1}{6}$$

L and J's combined rate =
$$(\frac{1}{6}+\frac{1}{J})=\frac{1}{1}$$

J's rate: $$\frac{1}{J}=(\frac{1}{1} - \frac{1}{6}) = \frac{5}{6}$$

Work competed in 20 minutes = $$\frac{1}{3}$$ hour?
$$RT= W$$
In 20 minutes, J completes
$$(\frac{5}{6}*\frac{1}{3}) =\frac{5}{18}$$ of a room

Using x = 5, find the answer* that yields $$\frac{5}{18}$$

A. $$\frac{1}{3x}=\frac{1}{(3*6)}=\frac{1}{18}$$ - NO

B. $$\frac{x}{(x-3)}=\frac{6}{(6-3}=\frac{6}{3}=2$$ - NO

C. $$\frac{(x-1)}{3x}=\frac{(6-1)}{18}=\frac{5}{18}$$ - MATCH

D. $$\frac{x}{(x-1)}=\frac{6}{(6-1)}=\frac{6}{5}$$- NO

E. $$\frac{(x-1)}{x}=\frac{(6-1)}{6}=\frac{5}{6}$$ - NO

*1) if your answer is a fraction, do not reduce it (your answer is based on an assigned value for x - don't depart from that value); and 2) with this method you have to check all the answer choices
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Intern
Joined: 06 Nov 2017
Posts: 5
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo  [#permalink]

### Show Tags

26 Jul 2018, 11:30
I don't think this is a good question since you can plug the number 2 in and you would get A or C as the answer.

Can someone comment their opinion on the question quality?
Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Jo &nbs [#permalink] 26 Jul 2018, 11:30

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

# 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®.