• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

Raffle tickets numbered consecutively from 101 through 350

tagged by: Brent@GMATPrepNow

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

Raffle tickets numbered consecutively from 101 through 350

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

GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9425 messages
Followed by:
480 members
2867
GMAT Score:
800
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

OptimusPrep Master | Next Rank: 500 Posts
Joined
13 Mar 2015
Posted:
410 messages
Followed by:
7 members
120
GMAT Score:
770
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

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

GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11487 messages
Followed by:
1229 members
5254
GMAT Score:
770
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 â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!
OptinumGmat Newbie | Next Rank: 10 Posts
Joined
06 Oct 2015
Posted:
7 messages
1
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

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?

GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9425 messages
Followed by:
480 members
2867
GMAT Score:
800
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

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
625
Target GMAT Score:
V51
GMAT Score:
780
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

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!

GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
983 messages
Followed by:
6 members
43
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

_________________
Scott Woodbury-Stewart Founder and CEO

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 GMATGuruNY

The Princeton Review Teacher

129 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
3 Jeff@TargetTestPrep

Target Test Prep

106 posts
4 Max@Math Revolution

Math Revolution

92 posts
5 Scott@TargetTestPrep

Target Test Prep

92 posts
See More Top Beat The GMAT Experts