• 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
  • 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
  • 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
  • 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
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Raffle tickets numbered consecutively from 101 through 350

This topic has 5 expert replies and 2 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
Joined
25 Apr 2016
Posted:
93 messages
Upvotes:
1

Raffle tickets numbered consecutively from 101 through 350

Post Mon Apr 25, 2016 2:39 pm
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?

A) 2/5

B) 2/7

C) 33/83

D) 99/250

E) 100/249

Answer: A

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Apr 25, 2016 3:49 pm
Hi boomgoesthegmat,

This is an example of a 'fence post' problem (meaning that you have to remember to count the tickets at the 'beginning' and 'end' of each sub-list.

We're asked for the probability of selecting a ticket with a "2" in the hundreds digit from a group of tickets numbered 101 through 350, inclusive.

The number of tickets is 350 - 101 + 1 = 250 total tickets
The number that have a 2 in the hundreds spot = 100 (200 through 299, inclusive).

So the probability is 100/250 = 2/5

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
OptimusPrep Master | Next Rank: 500 Posts
Joined
13 Mar 2015
Posted:
410 messages
Followed by:
7 members
Upvotes:
120
GMAT Score:
770
Post Mon Apr 25, 2016 8:26 pm
boomgoesthegmat wrote:
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?

A) 2/5

B) 2/7

C) 33/83

D) 99/250

E) 100/249

Answer: A
This is a straight forward probability question.

Always remember, the total numbers between a and b = b - a + 1

Total number of tickets = 350 - 101 + 1 = 250
Tickets with 2 in the hundreds digit = 299 - 200 + 1 = 100

Probability of picking a ticket with 2 in the hundredth digit = 100/250 = 2/5

Correct Option: A

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Apr 26, 2016 9:35 am
Quote:
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?

A) 2/5

B) 2/7

C) 33/83

D) 99/250

E) 100/249
Rich and Ankur have provided nice solutions, so I won't solve the question again.
However, I do want to add a pro tip to remember when answering questions using calculating probabilities using the formula:

P(event A occurs) = (# of outcomes where event A occurs)/(total # of outcomes)

In these cases, calculate the denominator first
There are two reasons for this:
1) The denominator is usually the easier value to calculate
2) If you can't calculate the numerator, you can probably use the denominator to eliminate answer choices.

Here's what I mean:

In this question, P(number has a hundreds digit of 2) = (# of integers with hundreds digit of 2)/(# of integers to choose from)

# of integers to choose from = 350 - 101 + 1 = 250

So, P(number has a hundreds digit of 2) = ??)/(250)

This tells us that the correct answer EITHER has 250 in its denominator OR, when the probability is simplified, the new denominator is a factor of 250

At this point, if we can't calculate the numerator, we eliminate some answer choices
A) 2/5 [5 is a factor of 250, so this answer COULD be correct]

B) 2/7 [7 is NOT a factor of 250. ELIMINATE B]

C) 33/83 [83 is NOT a factor of 250. ELIMINATE C]

D) 99/250 [250 is a factor of 250, so this answer COULD be correct]

E) 100/249 [249 is NOT a factor of 250. ELIMINATE E]

So, we were able to deduce that the correct answer is either A or D.

For more on this concept, see the following videos:
- Introduction to Probability: https://www.gmatprepnow.com/module/gmat-probability/video/742
- General Probability Strategies: https://www.gmatprepnow.com/module/gmat-probability/video/757

Cheers,
Brent

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

Check out the online reviews of our course
Come see all of our 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!
OptinumGmat Newbie | Next Rank: 10 Posts Default Avatar
Joined
06 Oct 2015
Posted:
7 messages
Upvotes:
1
Post Tue Apr 26, 2016 12:44 pm
OptimusPrep wrote:
boomgoesthegmat wrote:
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?

A) 2/5

B) 2/7

C) 33/83

D) 99/250

E) 100/249

Answer: A
This is a straight forward probability question.

Always remember, the total numbers between a and b = b - a + 1

Total number of tickets = 350 - 101 + 1 = 250
Tickets with 2 in the hundreds digit = 299 - 200 + 1 = 100

Probability of picking a ticket with 2 in the hundredth digit = 100/250 = 2/5

Correct Option: A
How do you simply 100/250 to 2/5?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Apr 26, 2016 6:33 pm
Hi boomgoesthegmat,

When simplifying a fraction, you can do the math in 'stages' or you can do it all at once (depending on your comfort level with the work involved). When dealing with a fraction, you can multiply BOTH the numerator and the denominator by the same number or you can divide BOTH the numerator and the denominator by the same number.

With 100/250, if you recognize that both numbers are multiples of 50, then you can divide 100 by 50 and 250 by 50... you end up with 2/5.

You could also divide in 'stages' though. Notice how both 100 and 250 both end in a 0... That means that you can divide both by 10:

100/250 = 10/25

Now you can divide both by 5... and you'll still end up with 2/5.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Apr 27, 2016 2:39 pm
In this problem,

Probability = # of target events / # of possible events

The target is "hundreds digit of 2". We have 200 -> 299, or 00 -> 99. That's 00 + (01 -> 99), for a total of 100 numbers.

The total is "anything from 101 to 350". We want everything from 1 to 350 MINUS everything from 1 to 100, or 350 - 100, or 250 numbers.

That gives us

100 / 250 => 2/5

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Post Thu Mar 15, 2018 9:26 am
boomgoesthegmat wrote:
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?

A) 2/5

B) 2/7

C) 33/83

D) 99/250

E) 100/249
There are a total of 350 - 101 + 1 = 250 raffle tickets in the box, and there are 299 - 200 + 1 = 100 raffle tickets with a hundreds digit of 2; thus, the probability is

100/250 = 2/5

Answer: A

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 71 first replies
2 Rich.C@EMPOWERgma... 48 first replies
3 Brent@GMATPrepNow 37 first replies
4 Jay@ManhattanReview 26 first replies
5 ErikaPrepScholar 10 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 GMATGuruNY

The Princeton Review Teacher

129 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

106 posts
4 image description Max@Math Revolution

Math Revolution

92 posts
5 image description Scott@TargetTestPrep

Target Test Prep

92 posts
See More Top Beat The GMAT Experts