Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:24) correct
32%
(02:43)
wrong
based on 8835
sessions
History
Date
Time
Result
Not Attempted Yet
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
If this question felt shaky,
try an adaptive mini quiz of similar problems in
GMAT Club Forum Quiz →. Free plan gives 5 questions per day.
ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Sep 2026
Posts: 22,738
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,738
ganand
We can create the following equation:
Total houses = number with air conditioning + number with sunporch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things
150 = 0.6(150) + 0.5(150) + 0.3(150) - D - 2(5) + 5
150 = 90 + 75 + 45 - D - 10 + 5
150 = 205 - D
D = 55
Answer: D
_________________
Scott Woodbury-Stewart | Founder and
CEO |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
ganand
This can be solved using Venn Diagram (refer the attachment)
AC = 60% of 150 = 90
Sunporch = 50% of 150 = 75
SP = 30% of 150 = 45
Using the venn diagram we can form the following equations
a+b+c+d+e+f+g+h = 150
a+b+c+d+f+g = 140 ----- (1) (as e = h = 5)
Taking 1 circle at a time
AC = a+b+d = 85 ---- (2) .. (as e = 5)
SunPorch = c+b+f = 70 ---- (3) .. (as e = 5)
SP = g+d+f = 40 ---- (4) .. (as e = 5)
equation (2) + (3) + (4)
a+c+g+ 2(d+b+f) = 195
subtracting this with equation (1)
d+b+f = 195 - 140 = 55
Answer option D
Attachments
Ven.png [ 6.81 KiB | Viewed 164207 times ]
General Discussion
Similar problem: of-the-300-subjects-who-participated-in-an-experiment-using
ganand
all three = neither =5 = 10/3 % of 150
working formula :-
Total = AC + sunporch + swimming pool - Exactly two - 2*all three + neither
100 = 60 + 50 + 30- Exactly two - 2*10/3 + 10/3
100 =140 - Exactly two - 10/3
Exactly two = 40 - 10/3 = (120-10)/3 = 110/3 %
110/3 % of 150 = 110*150/300 =55
Ans D
BillyZ
Current Student
Joined: 14 Nov 2016
Last visit: 06 Jun 2026
Posts: 1,134
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,134
ganand
Hi Bunuel,
Why formula (1) is incorrect? https://gmatclub.com/forum/advanced-overlapping-sets-problems-144260.html
(i) In term of percentage
Total = A + B + C − (sum of 2−group overlaps) + (all three) + Neither
100 = 60 + 50 + 30 - (x) + (5/150)(100) + (5/150)(100)
100 = 140 + (20/3) - x
x = 40 + (20/3)
x = 140/3%
(x/150)(100) = (140/3)
x = (140/300)(150)
x = 70
(ii) In term of number
Total = A + B + C − (sum of 2−group overlaps) + (all three) + Neither
150 = 90 + 75 + 45 - x + 5 + 5
x = 70
warriorguy
Retired Moderator
Joined: 04 Aug 2016
Last visit: 08 Feb 2023
Posts: 375
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE:Engineering (Telecommunications)
Posts: 375
hazelnut
We need to find exact two. The formula you have listed is for general sum of 2 group overlap. The total you have listed is 100 while in the question it is 150.
Formula for exact two is: Total = A + B + C + Neither - (exact 2) - 2 * (all three)
150=90+75+45+5-10-sum of exact 2.
205-150= sum of exact 2
sum of exact 2=55
D
somtsat99
Current Student
Joined: 10 Jan 2016
Last visit: 30 Jan 2021
Posts: 97
Status:MBA Candidate Class of 2020
Location: India
Concentration: Operations, Strategy
Schools: Rotman '20 (D) Sauder '20 (D) Ivey '19 (D) Schulich Sept 18 Intake (A$) ISB '19 (D) Alberta"20 (WD)
GMAT 1: 620 Q47 V29
GMAT 2: 670 Q50 V31
GPA: 4
WE:Business Development (Consulting)
Schools: Rotman '20 (D) Sauder '20 (D) Ivey '19 (D) Schulich Sept 18 Intake (A$) ISB '19 (D) Alberta"20 (WD)
GMAT 2: 670 Q50 V31
Posts: 97
Total = A + B +C - (exactly two) - 2(all three) + none
Refer to GMAT Club math book for more details.
Refer to GMAT Club math book for more details.
If anyone is looking for 3-set Venn Diagram questions to practice on from the Official Guide, I have compiled a list at the following link:
Three-set Venn Diagrams
On this question, while I would still draw the Venn Diagram myself, the key is to know the formula for three-set Venn Diagrams that has been mentioned in this thread:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + None
Then, all we need to do is plug in the numbers we are given (converting percents to numbers) and solve for the sum of 2-group overlaps, because that is what the question is asking us for.
Please let me know if you have any questions, or if you want me to post a video solution!
Three-set Venn Diagrams
On this question, while I would still draw the Venn Diagram myself, the key is to know the formula for three-set Venn Diagrams that has been mentioned in this thread:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + None
Then, all we need to do is plug in the numbers we are given (converting percents to numbers) and solve for the sum of 2-group overlaps, because that is what the question is asking us for.
Please let me know if you have any questions, or if you want me to post a video solution!
Posts: 1
Please kindly post a video solution. I cannot seem to understand where 2(5) came from. I seem to get the other workings but not sure about the 2(5).
JeffYin
deethompson
Sure, deethompson, I would be happy to post a video solution! I should be able to get to that later this week. In the meantime, I think that the key thing is to understand why we are subtracting some numbers in the first place. We subtract the overlaps because we are double- or triple-counting some houses if we add up all of the houses that have each of the 3 features. We are double-counting those that have exactly 2 of the features, so we need to subtract those once to account for that. We are triple-counting those that have all 3 of the features, so we need to subtract 2X that number of houses to account for that. Because we are told that 5 houses have all 3 features, we need to subtract 2 times that number, or 2*5, to account for this triple-counting.
Let me know if you have any other questions that you want me to address in my video solution!
proabhinav
Joined: 02 Aug 2018
Last visit: 20 Jan 2026
Posts: 55
Location: India
Concentration: Strategy, Operations
GMAT 1: 590 Q45 V26
GPA: 3.5
GMAT 1: 590 Q45 V26
Posts: 55
ScottTargetTestPrep
Dear Scott
Thanks for a detailed response, I always like your responses.
I need your help though, if you could please advice, why are we using 2(5) in the equation. I understand 5 is for people who are doing all three activities but multiplication by 2?
Frankly, I have made similar error in other question as well, not having understood the secret of multiplication by 2?
Thank You
Abhinav
ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Sep 2026
Posts: 22,738
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,738
proabhinav
Notice that in a 3-circle Venn diagram, when we add each individual circle, we include the “triple overlap” three times since each circle has the “triple overlap.” However, we only can count it once, so we have to subtract 2 times whatever number in the “triple overlap.”
_________________
Scott Woodbury-Stewart | Founder and
CEO |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
ScottTargetTestPrep
Hi Scott,
I follow your solutions very closely. And this is an optimum way to work out the problem. I only have a question that why have you taken all three houses i.e 5 multiplied by 2?
Is there something that I missed in the question?
Posted from my mobile device
ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Sep 2026
Posts: 22,738
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,738
Shef08
I am guessing it is clear that there are 90 houses with AC, 75 houses with sunporch and 45 houses with swimming pool. Some houses have two of the above amenities, some have all three while some have none. Let's see what happens when we add all three: The houses that have exactly two of the above amenities will be counted twice; for instance, when you add 90 houses with AC and 75 houses with sunporch and find 90 + 75 = 165, any house with both AC and sunporch has been double counted. The same is true for all other choices of two amenities. Since every house with exactly two of the amenities has been double counted, we subtract the sum of the houses with exactly two of the amenities so that the sum includes each house only once. The reason we multiply the number of houses with all three amenities by 2 before subtracting is very similar: Every house that has all three amenities has been represented three times in the sum; for instance, if house H has all three of the amenities, when you add 90 + 75 + 45, house H is one of the 90 houses with AC, one of the 75 houses with sunporch and one of the 45 houses with swimming pool. As you can see, house H is counted exactly three times, but we would like the summation to contain only one count of house H. That's why we subtract 2 times the number of houses with all three amenities from the sum 90 + 75 + 45.
_________________
Scott Woodbury-Stewart | Founder and
CEO |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Posts: 7
Hi! Can please someone explain why we multiply by 5 (all three options) by 2?
aaliyahkhalifa
That formula is explained in details here: ADVANCED OVERLAPPING SETS PROBLEMS.
Hope it helps.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
GMAT 1: 760 Q51 V42
Posts: 10,057
Total of 150
=> 60 percent have Air-conditioning: \(\frac{60}{100}\) * 150 = 90
=> 50 percent have a Sunporch: \(\frac{50}{100}\) * 150 = 75
=> 30 percent have a Swimming pool: \(\frac{30}{100}\)* 150 = 45
Total - Neither = Air-conditioning + Sunporch + Swimming pool - Exactly two - 2*(Air-conditioning + Sunporch + Swimming pool - all together)
=> 150 - 5 = 90 + 75 + 45 - Exactly two - 2(5)
=> 145 = 210 - 10 - Exactly two
=> Exactly two = 200 - 145 = 55
Answer D
=> 60 percent have Air-conditioning: \(\frac{60}{100}\) * 150 = 90
=> 50 percent have a Sunporch: \(\frac{50}{100}\) * 150 = 75
=> 30 percent have a Swimming pool: \(\frac{30}{100}\)* 150 = 45
Total - Neither = Air-conditioning + Sunporch + Swimming pool - Exactly two - 2*(Air-conditioning + Sunporch + Swimming pool - all together)
=> 150 - 5 = 90 + 75 + 45 - Exactly two - 2(5)
=> 145 = 210 - 10 - Exactly two
=> Exactly two = 200 - 145 = 55
Answer D
Posts: 4,849
Solution:
Given total number of houses =150
Number of houses that have air-conditioning =60% of 150 = 90
Number of houses that have a sun-porch = 50% of 150 =75
Number of houses that have a swimming pool =30% of 150 = 45
Number of houses that have all three of these amenities =5
Number of houses that have none of them = 5
We are asked houses have exactly two of these amenities.
Its a straight question of using the formulae on overlapping sets
Total = A + B+ C -(Exactly two) - 2(all) + None
Total houses = number with air conditioning + number with sun-porch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things
=>150 = 90 + 75 + 45 - (Exactly two) - 10 + 5
=> Exactly two = 55 (option d)
Devmitra Sen
GMAT SME
Given total number of houses =150
Number of houses that have air-conditioning =60% of 150 = 90
Number of houses that have a sun-porch = 50% of 150 =75
Number of houses that have a swimming pool =30% of 150 = 45
Number of houses that have all three of these amenities =5
Number of houses that have none of them = 5
We are asked houses have exactly two of these amenities.
Its a straight question of using the formulae on overlapping sets
Total = A + B+ C -(Exactly two) - 2(all) + None
Total houses = number with air conditioning + number with sun-porch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things
=>150 = 90 + 75 + 45 - (Exactly two) - 10 + 5
=> Exactly two = 55 (option d)
Devmitra Sen
GMAT SME
ganand
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 [ 6.47 KiB | Viewed 28275 times ]
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.