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

It is currently 18 Nov 2018, 19:06

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

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

Hide Tags

Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 245
Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 29 May 2017, 02:27
8
44
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

59% (02:00) correct 41% (02:11) wrong based on 1285 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 15 Nov 2017, 16:22
9
3
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


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

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

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 27 Jan 2017
Posts: 23
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 29 May 2017, 05:24
8
5
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



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
Ven.png [ 6.81 KiB | Viewed 14100 times ]

General Discussion
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 245
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 29 May 2017, 02:31
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1000
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 29 May 2017, 07:23
2
1
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



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
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1317
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 28 Jun 2017, 05:54
1
1
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


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
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Retired Moderator
avatar
P
Joined: 04 Aug 2016
Posts: 508
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)
Premium Member
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 28 Jun 2017, 05:58
hazelnut wrote:
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


Hi Bunuel,

Why formula (1) is incorrect? https://gmatclub.com/forum/advanced-overlapping-sets-problems-144260.html

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


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
Manager
Manager
avatar
S
Status: MBA Candidate Class of 2020
Joined: 10 Jan 2016
Posts: 112
Location: India
Concentration: Operations, Strategy
GMAT 1: 620 Q47 V29
GMAT 2: 670 Q50 V31
GPA: 4
WE: Business Development (Consulting)
GMAT ToolKit User Premium Member
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 07 Jul 2017, 06:32
2
1
Total = A + B +C - (exactly two) - 2(all three) + none

Refer to GMAT Club math book for more details.
Intern
Intern
avatar
B
Joined: 21 Aug 2017
Posts: 11
Schools: HBS '20 (A)
GMAT 1: 550 Q34 V31
GMAT 2: 560 Q36 V31
GMAT 3: 660 Q47 V34
GMAT 4: 700 Q45 V41
GPA: 3.7
Reviews Badge
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 07 Oct 2017, 09:29
I can solve this problem with the appropriate formula. Is there a way to solve this problem by backsolving
Intern
Intern
avatar
B
Joined: 05 Sep 2017
Posts: 3
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 15 Nov 2017, 20:28
150= 90+75+45-Both-10+5

Both = 55

This is a 30% level question imo.
VP
VP
User avatar
P
Joined: 09 Mar 2016
Posts: 1091
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 08 May 2018, 11:40
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



pushpitkc generis hello

here is my solution ...I just need to understand what I did wrong here

60 percent have air-conditioning = 90

50 percent have a sunporch = 75

30 percent have a swimming pool = 45

5 houses has all three amenities

5 houses has non of these amenities

we need to find number of houses that have exactly two of the ameneties X = both


so here is my equation

150 = 90+75+45-(5+x)+5 ( let me explain what i did here, i summed up three groups 90+75+45 minus ( 5 houses with all three feature +houses with only both features ) +neither

isnt it correct , i know it is not :) but why :)
Attachments

Overapping sets 2.jpg
Overapping sets 2.jpg [ 67.21 KiB | Viewed 7308 times ]

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 08 May 2018, 12:26
1
Hi dave13

Attachment:
Set(s).png
Set(s).png [ 7.6 KiB | Viewed 7275 times ]


Given: P(Neither) = 5 | P(All 3) = 5

What we need to understand while solving problems like these is that

P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3)
P(Sunporch) = 0.5(150) = 75 = P(Only SunPorch) + A + C + P(All 3)
P(SwimmingPool) = 0.3(150) = 45 = P(Only SwimmingPool) + B + C + P(All 3)

P(Total) = P(Only Airconditioner) + P(Only SunPorch) + P(Only SwimmingPool) + (A + B + C) + P(All 3)
150 = 90 + 75 + 45 - (A + B + C) - 2*P(All 3) + 5

Therefore, the houses which have only two amenities are P(Only 2) = A + B + C = 205 - 150 = 55 (Option D)

Hope this helps you!
_________________

You've got what it takes, but it will take everything you've got

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2111
Premium Member CAT Tests
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 08 May 2018, 12:35
1
dave13 wrote:
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

pushpitkc generis hello

here is my solution ...I just need to understand what I did wrong here

60 percent have air-conditioning = 90

50 percent have a sunporch = 75

30 percent have a swimming pool = 45

5 houses has all three amenities

5 houses has non of these amenities

we need to find number of houses that have exactly two of the ameneties X = both

so here is my equation

150 = 90+75+45-(5+x)+5 ( let me explain what i did here, i summed up three groups 90+75+45 minus ( 5 houses with all three feature +houses with only both features ) +neither

isnt it correct , i know it is not :) but why :)

dave13
EDIT
pushpitkc 's answer should help.

AND

- your issue is addressed in warriorguy 's post HERE
I am a fan of Venn diagrams.
I am not a fan of Venn diagrams for three overlapping set questions,
which typically involve a very specific question.

Try this formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + None

Bunuel explains in this post, with a diagram

Also see Bunuel and VeritasPrepKarishma , here, Overlapping Sets Made Easy

The pictorial representation I can find most quickly, albeit with a different fact pattern, is here
VP
VP
User avatar
P
Joined: 09 Mar 2016
Posts: 1091
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 09 May 2018, 02:22
1
pushpitkc wrote:
Hi dave13

Attachment:
Set(s).png


Given: P(Neither) = 5 | P(All 3) = 5

What we need to understand while solving problems like these is that

P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3)
P(Sunporch) = 0.5(150) = 75 = P(Only SunPorch) + B + C + P(All 3)
P(SwimmingPool) = 0.3(150) = 45 = P(Only SwimmingPool) + B + C + P(All 3)

P(Total) = P(Only Airconditioner) + P(Only SunPorch) + P(Only SwimmingPool) + (A + B + C) + P(All 3)
150 = 90 + 75 + 45 - (A + B + C) - 2*P(All 3) + 5

Therefore, the houses which have only two amenities are P(Only 2) = A + B + C = 205 - 150 = 55 (Option D)

Hope this helps you!


pushpitkc , generis many thanks for explanation, almost got it :) appreciate!

pushpitkc , just one question. Didnt you make a typo here (see highlighted part of your solution above or below :) )

P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3)
P(Sunporch) = 0.5(150) = 75 = P(Only SunPorch) + B + C + P(All 3)
P(SwimmingPool) = 0.3(150) = 45 = P(Only SwimmingPool) + B + C + P(All 3)


Lets start from case #1: this one one P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3) I interpert it as follows: So there are 90 houses with air conditioning among which are houses featuring only Airconditioner, OR both amenties Airconditioner+Porch and Airconditioner + Swimming pool OR three amenites. Am i understanding it correctly ? :?

If the above mentioned information i understand correctly, then why here P(Sunporch) = 0.5(150) = 75 = P(Only SunPorch) + B + C + P(All 3) are you adding up
+ B + C + P(All 3) and not +A+C+(All 3) ? As per your diagram Sunporch has intersection with air conditioning and swimming pool. I am just following the pattern as in case #1.

Case # 1 has intersection with A, B and P so you added A + B + P(All 3)

But case # 2 has this intersection +A+C+P but you sum up B + C + P

i would appreaciate if you could expain this :)

Further to the above questions can you please confirm if the detaled solution based on suggested formula is correct :) pls see below :)

\(150 = 90+75+45 -(A+B+C)-2(5) +5\)

\(150= 210-(A+B+C)-10+5\)

\(150= 210 -A-B-C-5\)

many thanks and have a great day :)

\(A+B+C = 55\)
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 09 May 2018, 02:44
1
Hi dave13

You have the eyes of a hawk. You spotted the typo, which I've now edited in my solution for this problem.

dave13 wrote:
Lets start from case #1: this one one P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3) I interpert it as follows: So there are 90 houses with air conditioning among which are houses featuring only Airconditioner, OR both amenties Airconditioner+Porch and Airconditioner + Swimming pool OR three amenites. Am i understanding it correctly ? :?


Your understanding is spot on, here! The same line of reasoning for the other 2 aspects of the house - P(Sunporch)
and P(SwimmingPool). It was the typo which caused the confusion :( Sorry about that!

Also, the understanding of the final solution is perfect :)

Hope this helps you
_________________

You've got what it takes, but it will take everything you've got

Intern
Intern
avatar
B
Joined: 07 May 2018
Posts: 3
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 10 May 2018, 00:59
Let
a = # of houses with only one
b = # of houses with two *We're solving for b.
c = # of houses with all three (given: 5)
d = # of houses with none (given: 5)

There are 150 houses total:
a + b + c + d = 150
substitute c=5 & d=5
==> a + b = 140.
So 140 houses have either one or two amenities.

They gave us 60% + 50% + 30% = 140% so there is some overlap - some houses have multiple amenities.

Because b's are double counted and c's are triple counted,
a + 2b + 3c = 150(140%) = 210
Substitute 3c = 3*5 = 15
a + 2b + 15 = 210
From above, a + b = 140. Therefore,
(140) + b + 15 = 210
b = 210 - 155 = 55

Answer: D.
Intern
Intern
User avatar
B
Joined: 28 Apr 2016
Posts: 30
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 11 Aug 2018, 17:04
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!
_________________

Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Please read and share my free GMAT Timing Strategy Guide!

Intern
Intern
avatar
Joined: 02 Aug 2018
Posts: 1
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 12 Sep 2018, 04:37
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 wrote:
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:


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!
Intern
Intern
User avatar
B
Joined: 28 Apr 2016
Posts: 30
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 12 Sep 2018, 11:59
deethompson wrote:
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).


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!
_________________

Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Please read and share my free GMAT Timing Strategy Guide!

Intern
Intern
User avatar
B
Joined: 28 Apr 2016
Posts: 30
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

Show Tags

New post 14 Sep 2018, 08:04
1
Hi deethompson, I have now posted my video solution to YouTube (see below).

You can also see more information about the question and links to similar questions on this page of my website, YinTutoring.com:

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

Please let me know if you have any more questions!


_________________

Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Please read and share my free GMAT Timing Strategy Guide!

GMAT Club Bot
Re: Of the 150 houses in a certain development, 60 percent have &nbs [#permalink] 14 Sep 2018, 08:04

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.