• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If 3 different integers are randomly selected from the integ

This topic has 1 expert reply and 0 member replies

GMAT/MBA Expert

If 3 different integers are randomly selected from the integ

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



If 3 different integers are randomly selected from the integers from 1 to 12 inclusive, what is the probability that a triangle can be constructed so that its 3 sides are the lengths of the 3 selected numbers?

A) 3/8
B) 7/18
C) 19/44
D) 39/88
E) 11/24

Answer: C
Source: www.gmatprepnow.com
Difficulty level: 700+

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post
Brent@GMATPrepNow wrote:
If 3 different integers are randomly selected from the integers from 1 to 12 inclusive, what is the probability that a triangle can be constructed so that its 3 sides are the lengths of the 3 selected numbers?

A) 3/8
B) 7/18
C) 19/44
D) 39/88
E) 11/24

Answer: C
Source: www.gmatprepnow.com
Difficulty level: 700+

Cheers,
Brent
I specifically created this question to illustrate the importance of calculating the denominator first (when using counting techniques to solve a probability question)
There are two reasons why you should calculate the denominator first:

1) The denominator is almost always easier to calculate than the numerator, and while calculating the denominator, you may gain some insight into how to calculate the numerator.
2) Once you know the denominator, you can use this to eliminate answer choices. So, even if you don't know the correct answer, you can still eliminate some answers and increase your chances of guessing correctly.

If you're lucky, you can eliminate 4 of the 5 answer choices, as you have done above!!

For this question, P(a triangle can be constructed with the 3 selected lengths) = (number of triangles with 3 lengths from 1 to 12 inclusive)/(TOTAL number of ways to select 3 numbers)

Let's calculate the denominator.

TOTAL number of ways to select 3 numbers
Since the order in which we select the 3 numbers doesn't matter, we can use COMBINATIONS.
We can select 3 numbers from 12 numbers in 12C3 ways.
12C3 = (12)(11)(10)/(3)(2)(1) = 220 ways

So, the correct answer will either be in the form k/220, OR some equivalent fraction in which the denominator is a FACTOR of 220.
For example, IF we calculate the numerator and get 110, then the answer = 110/220 = 1/2 (notice that 2 is a FACTOR of 220)
IF we calculate the numerator and get 15, then the answer = 15/220 = 3/44 (notice that 44 is a FACTOR of 220) And so on.

When we check the answer choices, we see that only one answer choice (C) has a denominator that's a FACTOR of 440.
So, C must be the correct answer.

We can answer the question without having to calculate the numerator (which is a time-consuming task)

On test day, it's unlikely that this technique will allow you to eliminate 4 answer choices. HOWEVER, if you're pressed for time, or you can't calculate the numerator, this technique may allow you to eliminate some of the answer choices and increase your likelihood of a correct guess.

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review

Top First Responders*

1 Ian Stewart 44 first replies
2 Jay@ManhattanReview 35 first replies
3 Brent@GMATPrepNow 34 first replies
4 Scott@TargetTestPrep 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

129 posts
2 image description Max@Math Revolution

Math Revolution

89 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

50 posts
5 image description Jay@ManhattanReview

Manhattan Review

35 posts
See More Top Beat The GMAT Experts