Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x
The OA is C.
Source: GMAT Prep
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Lindsay can paint 1/x of a certain room in 20 minutes. What
This topic has expert replies
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let the room = 20 units.Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x
Let x = 4.
Since Lindsay paints 1/x of the room in 20 minutes -- the equivalent of 1/3 hour -- Lindsay's rate = (1/4) * 20 = 5 units per 1/3 hour = 15 units per hour.
Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour.
Thus, Joseph's rate = (combined rate) - (Lindsay's rate) = 20-15 = 5 units per hour.
In 20 minutes -- the equivalent of 1/3 hour -- the amount of work produced by Joseph = r*t = 5 * (1/3) = 5/3 units.
Thus, the fraction painted by Joseph = (5/3)/20 = 1/12. This is the target.
Now plug x=4 into the answers to see which yields the target value of 1/12.
Only C works:
(x-3)/3x = (4-3)/(3*4) = 1/12.
The correct answer is C.
Last edited by GMATGuruNY on Sun Sep 30, 2018 9:48 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
$$In\ 20\ \min utes\ lindsay\ can\ paint\ \frac{1}{x}$$
$$In\ 60\ \min utes\ \left(1hr\right)lindsay\ can\ paint\ =\frac{\left(\frac{1}{x}\cdot\ 60\right)}{20}$$
$$=\frac{\left(\frac{60}{x}\right)}{20}$$
$$=\frac{60}{x}\cdot\frac{1}{20\ }=\frac{3}{x}in\ 60\ \min utes\ \left(1hour\right)$$
$$If\ lindsay\ can\ paint\ \frac{3}{x}part\ of\ the\ room\ in\ 1\ hour,\ let\ the\ remaining\ part\ of\ the\ room\ be\ =y.$$
Bearing in mind that Joseph paints the remaining pat of the room .
Therefore, Joseph can paint y in 60 minutes,
$$\frac{3}{x\ }+y=x\ \left(total\ room\right)$$
$$y\ =\ x-\frac{3}{x}$$
$$If\ Joseph\ work\ for\ 60\ \min utes\ =\ x-\frac{\left(3\right)}{x},\ then,$$
$$20\ \min utes\ =\ \frac{\left(\left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{20}{1}\right)}{60}$$
$$=\ \frac{\left(\frac{x}{1}-\frac{3}{x}\right)}{3}\ =\ \left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{1}{3}$$
$$\frac{\left(x-3\right)}{3x}$$
Option C is CORRECT.
$$In\ 60\ \min utes\ \left(1hr\right)lindsay\ can\ paint\ =\frac{\left(\frac{1}{x}\cdot\ 60\right)}{20}$$
$$=\frac{\left(\frac{60}{x}\right)}{20}$$
$$=\frac{60}{x}\cdot\frac{1}{20\ }=\frac{3}{x}in\ 60\ \min utes\ \left(1hour\right)$$
$$If\ lindsay\ can\ paint\ \frac{3}{x}part\ of\ the\ room\ in\ 1\ hour,\ let\ the\ remaining\ part\ of\ the\ room\ be\ =y.$$
Bearing in mind that Joseph paints the remaining pat of the room .
Therefore, Joseph can paint y in 60 minutes,
$$\frac{3}{x\ }+y=x\ \left(total\ room\right)$$
$$y\ =\ x-\frac{3}{x}$$
$$If\ Joseph\ work\ for\ 60\ \min utes\ =\ x-\frac{\left(3\right)}{x},\ then,$$
$$20\ \min utes\ =\ \frac{\left(\left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{20}{1}\right)}{60}$$
$$=\ \frac{\left(\frac{x}{1}-\frac{3}{x}\right)}{3}\ =\ \left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{1}{3}$$
$$\frac{\left(x-3\right)}{3x}$$
Option C is CORRECT.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Given: Lindsay can paint 1/x of a certain room in 20 minutesswerve wrote:Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x
The OA is C.
Source: GMAT Prep
So, in 1 HOUR, Lindsay can paint 3/x of the room
Given: Lindsay and Joseph can paint the room in 1 HOUR.
During that one hour, Lindsay can paint 3/x of the room.
So, during that 1 HOUR, Joseph must paint the rest (whatever Lindsay did not paint)
So, during the 1 HOUR, the fraction of the room that Joseph paints = 1 - 3/x
= x/x - 3/x
= (x-3)/x
So, (x-3)/x = the fraction of the room that Joseph paints in one hour.
Since 20 minutes = 1/3 of an hour, Joseph can paint (1/3)[(x-3)/x] of the room in 20 minutes.
(1/3)[(x-3)/3x]
= (x-3)/3x
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
swerve wrote:Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x
We are given that Lindsay can paint 1/x of a room in 20 minutes; thus, she can paint 3/x of a room in 60 minutes (or in 1 hour). Thus, her hourly rate is 3/x room/hr. We are also given that when she works with Joseph, they can paint the entire 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 room/hr. We can create the following equation and isolate j:
work of Lindsay + work of Joseph = 1
(3/x)(1) + (1/j)(1) = 1
3/x + 1/j = 1
Multiplying the entire equation by xj, we obtain:
3j + x = xj
x = xj - 3j
x = j(x - 3)
x/(x - 3) = j
Since j = x/(x - 3) and 1/j = Joseph's rate, then Joseph's rate, in terms of x, is (x - 3)/x.
Since 20 minutes = 1/3 of an hour, and since work = rate x time, Joseph can complete:
[(x - 3)/x](1/3) = (x - 3)/(3x) of the job in 20 minutes.
Alternate Solution:
Since Lindsay and Joseph, working together, can paint the entire room in 1 hour, then in 20 minutes, they can paint 1/3 of the room. If we let r be the fraction of the room that Joseph can paint in 20 minutes, then it must be true that:
1/x + r = 1/3
r = 1/3 - 1/x
r = x/(3x) - 3/(3x)
r = (x - 3)/(3x)
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
