NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 17:38 It is currently 25 Apr 2024, 17:38
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Of the 150 houses in a certain development, 60 percent have

SORT BY:
Date
Kudos
   1   2 
Tags:
Difficulty: 655-705 Levelx   Overlapping Setsx                     
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
s1804singh
Intern
Intern
Joined: 25 Jun 2020
Posts: 21
Own Kudos [?]: 10 [0]
Given Kudos: 25
Location: India
Schools:
GMAT 1: 660 Q48 V33
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   05 Oct 2021, 08:55
ganand wrote:
Of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses have exactly two of these amenities?

(A) 10
(B) 45
(C) 50
(D) 55
(E) 65



OG 2019 PS07712


So while solving this question, I followed the below approach:

AC= 60-(5+x+y)=55-(x+y)
Sunporch= 50-(5+x+z)= 45-(x+z)
Swimming Pool= 30-(5+y+z)=25-(y+z)

55-(x+y)+45-(x+z)+25-(y+z)+5+x+y+z = 100........(Since total % is equal to 100)

30-(x+y+z)=0

x+y+z= 30% of the total 150 houses have exactly 2 amenities. This equals 45 houses. I am not able to figure out why this leads me to a wrong answer. Can someone please guide? Bunuel
Attachments

Untitled.png
Untitled.png [ 6.47 KiB | Viewed 2421 times ]

User avatar
S
debupal
Intern
Intern
Joined: 18 Mar 2021
Posts: 6
Own Kudos [?]: 26 [0]
Given Kudos: 59
Location: India
Concentration: Operations, Finance
GPA: 3.7
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   29 Nov 2021, 07:45
x, y, z are overlap of 2 sets only
85-(x+z) + 70- (y+z) + 40-(z+y) + (x+y+z) + 5 + 5 = 150
x+y+z= 205-150= 55
User avatar
B
sushmita2294
Current Student
Joined: 22 Jul 2021
Posts: 29
Own Kudos [?]: 12 [0]
Given Kudos: 18
Location: India
Concentration: Technology, General Management
Schools: Great Lakes (A) (A) XLRI (I) Stern Tech MBA '23 (S)
GPA: 3.33
WE:Account Management (Retail)
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   22 Jan 2022, 20:50
Hi Scott,
Though I get the logic behind your explanation of this question, what I am confused about is, there are many other questions of overlapping sets which has been solved here using the below formula. Is their a reason for both of the formula's existing for different questions? Is that possible?
Total = (Set1) + (Set2) + (Set3) - (Set12 + Set23 + Set 13) + (All 3) + (Neither)
Would love to understand this from you and clear this doubt.
Refards,
Sushmita
User avatar
B
Alvaro20172027
Intern
Intern
Joined: 12 Oct 2020
Posts: 5
Own Kudos [?]: 0 [0]
Given Kudos: 41
Send PM
Of the 150 houses in a certain development, 60 percent have [#permalink] New post   28 Jul 2022, 04:27
An alternative approach not involving using so many variables (from a to f) could be like this:

a= number of houses with one amenitie
b= " " " 2 amenities
c= " " " 3 amenities
d= " " " no amenities at all

knowing beforehand that c and d are 5 and 5, respectively,

a + b + c + d= 150 , c + d = 10
a + b = 140

Then also by the percentages given,
90 + 75 + 45 = 210
knowing that the ones have 2 amenities are counted twice, and those having 3, three times, it goes like this:
a + 2b + 3c = 210
knowing that 3c=3 * 5 = 15
a + 2b = 195

we substract them both:
a + 2b = 195 -
a + b = 140
----------------
b = 55
User avatar
S
GmatPoint
Senior Manager
Senior Manager
Joined: 02 Jan 2022
Posts: 266
Own Kudos [?]: 94 [0]
Given Kudos: 3
GMAT 1: 760 Q50 V42
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   28 Jul 2022, 04:59
Total houses with air-conditioning = 150*60/100 = 90

Total houses with sunporch = 150*50/100 = 75

Total houses with swimming pool = 150*30/100 = 45

Now, let the houses with exactly one development be a, with 2 developments be b, with 3 developments be c and with no developments be d.

Now, total number of houses = a + b + c + d = 150

Since c = d = 5, a + b = 140......(i)

Also,

a + 2b + 3c + d = 90 + 75 + 45 + 5

a + 2b + 3*5 + 5 = 215

a + 2b = 195.....(ii)

(i)- (ii),

b = 55

Thus, the correct option is D.
avatar
B
Varane
Manager
Manager
Joined: 24 Mar 2022
Posts: 71
Own Kudos [?]: 5 [0]
Given Kudos: 482
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   01 Aug 2022, 03:55
Why do we add all three in this https://gmatclub.com/forum/in-a-class-o ... l#p1080954

But subtract it 2x over here.

Can any expert please clear this doubt.

Posted from my mobile device
User avatar
B
TheGMATStrategy
Tutor
Joined: 14 Jan 2020
Posts: 13
Own Kudos [?]: 3 [0]
Given Kudos: 1
GMAT 1: 760 Q49 V44
Send PM
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   06 Feb 2023, 10:47
Expert Reply


Want more help? http://linktr.ee/thegmatstrategy :cool:
User avatar
B
Gmatguy007
Manager
Manager
Joined: 07 Feb 2024
Posts: 76
Own Kudos [?]: 5 [0]
Given Kudos: 94
Send PM
Of the 150 houses in a certain development, 60 percent have [#permalink] New post   12 Mar 2024, 11:41
 
somtsat99 wrote:
Total = A + B +C - (exactly two) - 2(all three) + none

Refer to GMAT Club math book for more details.

­Hello,

Overlapping sets are a daunting task and this formula is very helpful. I want to make sure that I translated correctly for n sets with n≥3.

So, the formula is Total = a+b+..+n + none - (n-1)*n - nk where nk is the number of sets in which I want to find how many objects there are in EXACTLY nk sets ?

For instance, if I have a total of 260 objects with 4 sets (a,b,c,d) and each one has 25% of the total and 8 there aren't in none sets and I want to find how many there are in EXACTLY 3 sets then I'll do: 260 = 4*0.25*260 + 8 - (4-1)*3 - 3 = 256?

Thank you in advance!­
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619030 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: Of the 150 houses in a certain development, 60 percent have [#permalink] New post   12 Mar 2024, 11:44
1
Kudos
Expert Reply
Gmatguy007 wrote:
somtsat99 wrote:
Total = A + B +C - (exactly two) - 2(all three) + none

Refer to GMAT Club math book for more details.

­Hello,

Overlapping sets are a daunting task and this formula is very helpful. I want to make sure that I translated correctly for n sets with n≥3.

So, the formula is Total = a+b+..+n + none - (n-1)*n - nk where nk is the number of sets in which I want to find how many objects there are in EXACTLY nk sets ?

For instance, if I have a total of 260 objects with 4 sets (a,b,c,d) and each one has 25% of the total and 8 there aren't in none sets and I want to find how many there are in EXACTLY 3 sets then I'll do: 260 = 4*0.25*260 + 8 - (4-1)*3 - 3 = 256?

Thank you in advance!­

­That formula is explained in details here: ADVANCED OVERLAPPING SETS PROBLEMS.

Hope it helps.­
User avatar
B
demawtf
Intern
Intern
Joined: 18 Mar 2024
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 144
Send PM
Of the 150 houses in a certain development, 60 percent have [#permalink] New post   20 Mar 2024, 06:23
cat        # houses          #countings
1       *     140-x             140-x
2       *      x                    2x
3       *      5                   15
0       *      5                     0

tot           150              210 = (90+75+45)

140-x+2x+15=210
x=55­
GMAT Club Bot
gmatclubot
Of the 150 houses in a certain development, 60 percent have [#permalink]
20 Mar 2024, 06:23
   1   2 
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions