GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Jan 2019, 20:23

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Three dice (each having six faces with each face having one number

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Current Student
avatar
V
Joined: 27 May 2014
Posts: 525
GMAT 1: 730 Q49 V41
GMAT ToolKit User Premium Member
Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 05 Feb 2017, 23:06
1
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:29) correct 37% (01:24) wrong based on 103 sessions

HideShow timer Statistics

Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116

_________________

440 to 730: If I Can, You Can Too

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 06 Feb 2017, 00:56
1
1
saswata4s wrote:
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116


Hi

#1 Direct counting:

one 2 + two 2's + three 2's = 1*5*5*3!/2! + 1*1*5*3!/2! + 1*1*1 = 75 + 15 + 1 = 91

# Indirect counting:

Total # of outcomes - # of outcomes without 2's = \(6^3 - 5^3 = 91\)

Answer C.
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2723
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 06 Feb 2017, 07:54
2
2
saswata4s wrote:
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116


Number of possible outcomes such that at least one dice shows the number 2 = Total Outcomes - All outcomes without any 2

Total Outcomes on three dice = 6*6*6 = 216

Total Outcomes Without any 2 = 5*5*5 (as all 5 outcomes except "2" on each die is acceptable) = 125

Required Outcomes = 216 - 125 = 91

Answer: Option C
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4548
Location: United States (CA)
Re: Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 08 Feb 2017, 18:48
saswata4s wrote:
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116


We need to determine, when rolling three dice, the number of outcomes in which at least one die shows a 2.

We should first recall the following formula:

Total number of ways to roll 3 dice = number of ways with at least one 2 + number of ways with no 2s.

Since there are 6 x 6 x 6 = 216 possible outcomes when rolling 3 dice, we have:

216 = number of ways with at least one 2 + number of ways with no 2s

number of ways with at least one 2 = 216 - number of ways with no 2s

There are 5 x 5 x 5 = 125 outcomes in which no 2 is shown.

Thus, there are 216 - 125 = 91 outcomes in which at least one 2 is shown.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Senior Manager
avatar
G
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 289
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge
Re: Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 05 May 2017, 08:14
For 1 time 2 -

1*5*5*3 = 75

For 2 times = 1*1*5*3 = 15

For 3 times = 1 = 75+15+1 = 91.
Intern
Intern
avatar
Joined: 20 Oct 2018
Posts: 1
Three dice (each having six faces with each face having one number  [#permalink]

Show Tags

New post 30 Dec 2018, 10:58
vitaliyGMAT wrote:
saswata4s wrote:
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116


Hi

#1 Direct counting:

one 2 + two 2's + three 2's = 1*5*5*3!/2! + 1*1*5*3!/2! + 1*1*1 = 75 + 15 + 1 = 91

# Indirect counting:

Total # of outcomes - # of outcomes without 2's = \(6^3 - 5^3 = 91\)

Answer C.


Posted from my mobile device

Why do we divide by 2! In the direct counting method?
GMAT Club Bot
Three dice (each having six faces with each face having one number &nbs [#permalink] 30 Dec 2018, 10:58
Display posts from previous: Sort by

Three dice (each having six faces with each face having one number

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.