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 →

If three different integers are selected at random from the integers 1 through 8, what is the probability...

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2558
Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members
by BTGmoderatorLU » Mon Apr 20, 2020 5:06 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

Source: Manhattan Prep

If three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle?

A. 11/28
B. 27/56
C. 1/2
D. 4/7
E. 5/8

The OA is A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

Re: If three different integers are selected at random from the integers 1 through 8, what is the probability...

by Jay@ManhattanReview » Tue Apr 21, 2020 12:55 am
BTGmoderatorLU wrote: ↑
Mon Apr 20, 2020 5:06 am
 Source: Manhattan Prep

If three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle?

A. 11/28
B. 27/56
C. 1/2
D. 4/7
E. 5/8

The OA is A
Note that one of the important properties of a triangle is that the sum of any two sides must be greater than the third side.

Keeping that in mind, let's pick and choose the integers that follow the above rule. The eligible values are

• (2, 3, 4) (3, 4, 5) (4, 5, 6) (5, 6, 7) (6, 7, 8): No. of ways = 5
• (2, 4, 5) (3, 4, 6) (4, 5, 7) (5, 6, 8): No. of ways = 4
• (2, 5, 6) (3, 5, 6) (4, 5, 8) (5, 7, 8): No. of ways = 4
• (2, 6, 7) (3, 5, 7) (4, 6, 7): No. of ways = 3
• (2, 7, 8) (3, 6, 7) (4, 6, 8): No. of ways = 3
• (3, 6, 8) (4, 7, 8): No. of ways = 2
• (3, 7, 8): No. of ways = 1

Total no. of ways = 22

Required probability = 22/56 = 11/28

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review Test Prep

Locations: Manhattan Review Bangalore | Free GRE Practice Test | GRE Prep Hyderabad | Kukatpally GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8156
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: If three different integers are selected at random from the integers 1 through 8, what is the probability...

by Scott@TargetTestPrep » Tue Apr 21, 2020 2:22 pm
BTGmoderatorLU wrote: ↑
Mon Apr 20, 2020 5:06 am
 Source: Manhattan Prep

If three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle?

A. 11/28
B. 27/56
C. 1/2
D. 4/7
E. 5/8

The OA is A
The total number of ways to randomly pick 3 integers from 8 (without any restrictions) is:

8C3 = (8 x 7 x 6)/(3 x 2) = 8 x 7 = 56

To ensure the 3 integers picked can be the side lengths of a triangle, the sum of the two smaller integers must be greater than the largest integer. Let’s list all the triples that have this property (notice that the smallest integer that can be in a triple is 2):

(2, 3, 4), (2, 4, 5), (2, 5, 6), (2, 6, 7), (2, 7, 8)

(3, 4, 5), (3, 4, 6), (3, 5, 6), (3, 5, 7), (3, 6, 7), (3, 6, 8), (3, 7, 8)

(4, 5, 6), (4, 5, 7), (4, 5, 8), (4, 6, 7), (4, 6, 8), (4, 7, 8)

(5, 6, 7), (5, 6, 8), (5, 7, 8)

(6, 7, 8)

We see that there are 5 + 7 + 6 + 3 + 1 = 22 such triples. Therefore, the probability is 22/56 = 11/28,

Answer: A

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
Post new topic Post Reply
• Page 1 of 1