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

It is currently 06 Jul 2020, 12:24

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

A painting crew painted 80 houses. They painted the first y houses at

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65012
A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 09 Jun 2015, 01:56
2
15
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:48) correct 30% (02:58) wrong based on 297 sessions

HideShow timer Statistics

A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.

_________________
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8753
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 09 Jun 2015, 02:20
4
2
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.


total weeks= \(\frac{y}{x}\) +\(\frac{(80-y)}{1.25x}\) ...
=\(\frac{(y +320)}{(5x)}\)
ans B
_________________
General Discussion
Manager
Manager
avatar
S
Joined: 12 Mar 2015
Posts: 75
Concentration: Leadership, Finance
GPA: 3.9
WE: Information Technology (Computer Software)
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 09 Jun 2015, 12:16
1
Let w1 and w2 be number of weeks.
So
First Week= x * w1 =y

Second Week = 5/4x * w2 = 80-y (Remaining houses)

Question is to find w1 + w2

i.e y/x + 80-y / 5/4x

= y+320/5x
= B
Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 44
Location: United States
GMAT ToolKit User Reviews Badge
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 10 Jun 2015, 00:32
4
Another way to do this quickly is to plug in sets of easy numbers, such as \(Y=20, x=4\) -> the first 20 take 5 weeks, and the second 60 at 5 houses per week take 12 so it totally takes 17 weeks.
In the answer choices, the denominator is either \(5x=20\) or \(4x=16\) so we want the numerator to be either 340 or 272
A: \(\frac{320-20}{20}=\frac{300}{20}\) not 17.
B: \(\frac{20+320}{20}=\frac{340}{20}\) is 17.
C: \(\frac{5*(80-20)}{16}=\frac{200}{16}\) not 17.
D: \(\frac{400+20}{16}=\frac{420}{16}\) not 17.
E: \(\frac{80-320}{20}=\frac{400}{20}\) not 17.

So the answer is B.
Manager
Manager
avatar
B
Joined: 27 Jul 2014
Posts: 223
Schools: ISB '15
GMAT 1: 660 Q49 V30
GPA: 3.76
GMAT ToolKit User Reviews Badge
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 10 Jun 2015, 09:45
1
IMO answer is B
Total weeks= y/x +(80−y)/1.25x ...
=(y+320)/(5x)
Manager
Manager
avatar
Joined: 02 Jun 2015
Posts: 71
Location: Brazil
Concentration: Entrepreneurship, General Management
GPA: 3.3
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 10 Jun 2015, 18:23
2
first part:
y houses at a x houses per week = y/x

second part:
rest of the houses at a 1.25x houses per week = 80-y / 1.25x

calculation:
y/x + 80-y/1.25x (multiple by 4 to make it easy)
4y/4x + 320 - 4y/5x
20y + 1280 - 16y / 20x
4y + 1280 / 20x (divide by 4 again)
y + 320 / 5x

Kudos if you like it
Intern
Intern
avatar
Joined: 07 May 2015
Posts: 13
Location: India
Concentration: International Business, Finance
GPA: 3.5
WE: Information Technology (Computer Software)
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 12 Jun 2015, 18:03
1
y/x + (80-y)/1.25 --> Work together

Solve above equation gives

(y/4 + 80)/(5/4)x=y+320/5x. Ans is B
Director
Director
avatar
P
Joined: 21 May 2013
Posts: 603
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 13 Jun 2015, 09:20
1
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.


Painted first y houses @x houses per week
To paint 1 house, time taken=1/x weeks
Therefore, to paint y houses, time taken=y/x weeks
Similarly, time taken to paint 80-y houses=80-y/1.25x
Total time taken=y/x+80-y/1.2x=4(0.25y+80)/5x=y+320/5x
Answer B
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65012
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 15 Jun 2015, 02:12
1
Bunuel wrote:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 1.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?

A. (320 - y)/(5x)
B. (y +320)/(5x)
C. 5(80 - y)/(4x)
D. (y + 400)/(4x)
E. (4y + 320)/(5x)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

This is a combined work problem, so we will use the work formula: rate × time = work. The work and rates are given, but we need to calculate time, so we manipulate the formula: time = work/rate. This is also a Variable In the answer Choices (VIC) problem, so it is efficient to pick numbers and test the answer choices.

We are told that there are 80 houses, that y houses are painted at a rate of x houses per week, and that the rate increases to 1.25x houses per week for the remaining 80 – y houses. We will pick values such that x and 1.25x are integers (i.e., x is a multiple of 4) and y and 80 – y are divisible by x and 1.25x, respectively.
Attachment:
2015-06-15_1409.png
2015-06-15_1409.png [ 52.77 KiB | Viewed 5581 times ]


The total painting time is:
20 houses painted at a rate of houses/week = 5 weeks
60 houses painted at a rate of 5 houses/week = 12 weeks
Total time for 80 houses = 5 + 12 = 17 weeks
Attachment:
2015-06-15_1412.png
2015-06-15_1412.png [ 45.33 KiB | Viewed 5577 times ]

The correct answer is B.
_________________
Intern
Intern
avatar
Joined: 14 Jul 2014
Posts: 11
Concentration: Operations, Marketing
WE: Consulting (Computer Software)
A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 10 Aug 2016, 04:34
Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 1.25 x => 1.25 * 20 = 25 houses per week

total time they took = (40/20) + (40/25) = 3.6 weeks

Putting the values of x and y in equation B

(y +320)/(5x) = (40+320)/5*20 = 360/100 = 3.6
Manager
Manager
User avatar
S
Joined: 06 Oct 2015
Posts: 86
Location: Bangladesh
Concentration: Accounting, Leadership
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 10 Aug 2016, 06:23
Plug x=4 and y=40. Then It took 10 weeks to paint the first 40 houses.
Now the new working rate is 1.5*4=5 houes per week. So it takes 8 weeks to paint the remaining 40 houses.
Total 10+8=18 weeks.

Now plug the values in the answer choices and see only B gives 18.
Intern
Intern
avatar
B
Joined: 26 Mar 2020
Posts: 10
Re: A painting crew painted 80 houses. They painted the first y houses at  [#permalink]

Show Tags

New post 29 May 2020, 00:49
Let Y=60 houses at X=4 houses per week. So it takes 15 weeks
Now balance 20 house at 1.25X is 5 house per week. So it takes 4 weeks.
On putting Y= 60 and X=4
Total weeks= 15+4= 19 weeks.
Option B satisfies.

Posted from my mobile device
GMAT Club Bot
Re: A painting crew painted 80 houses. They painted the first y houses at   [#permalink] 29 May 2020, 00:49

A painting crew painted 80 houses. They painted the first y houses at

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





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