BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

GMAT OG Of the 150 houses in a certain development

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 394
Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members
Thanked: 1 times
by AbeNeedsAnswers » Sat Aug 19, 2017 3:10 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

GMAT Official Guide

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

D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members
Location: Boston, MA
Thanked: 1153 times
GMAT Score:770

by DavidG@VeritasPrep » Mon Aug 21, 2017 10:37 am
AbeNeedsAnswers 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

D
We can break out our trusty formula for dealing with three-set overlaps:

Total = Group 1 + Group 2 + Group 3 - [# in exactly 2 groups] - 2[# in all 3 groups] + # in none of the 3 groups

Total = 150
Group 1 = 60% of 150 = 90
Group 2 = 50% of 150 = 75
Group 3 = 30% of 150 = 45
# with all three = 5
# with one of the three = 5

Plug and chug: 150 = 90 + 75 + 45 - x - 2[5] + 5
150 = -x + 205
-55 = -x
55 = x; The answer is D
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8137
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Thu Nov 16, 2017 7:16 am
AbeNeedsAnswers 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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Fri Mar 16, 2018 10:52 am
Hi All,

We're told that of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, 30 percent have a swimming pool, 5 of the houses have ALL three of these amenities and 5 have NONE of them. We're asked for the number of houses that have EXACTLY TWO of these amenities. This question is a 3-group Overlapping Sets question and can be solved with either a 3-circle Venn Diagram or the 3-group Overlapping Sets Formula:

Total = (None) + (Group 1) + (Group 2) +(Group 3) - (Gp 1 & Gp 2) - (Gp 1 & Gp 3) - (Gp 2 & Gp 3) - 2(All 3)

Based on the percentages in the prompt, we can fill in most of the formula:

150 = (5) + (90) + (75) + (45) - (Gp 1 & Gp 2) - (Gp 1 & Gp 3) - (Gp 2 & Gp 3) - 2(5)
150 = 205 - (Gp 1 & Gp 2) - (Gp 1 & Gp 3) - (Gp 2 & Gp 3)
(Gp 1 & Gp 2) + (Gp 1 & Gp 3) + (Gp 2 & Gp 3) = 55

Thus, the sum of the three "groups of 2" is 55.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1