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

It is currently 10 Dec 2018, 16:15

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

Two number cubes with faces numbered 1 to 6 are rolled. What is the

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

Hide Tags

Intern
Intern
avatar
Joined: 23 Feb 2014
Posts: 33
GMAT 1: 560 Q41 V26
GMAT 2: 610 Q46 V28
Premium Member
Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post Updated on: 09 Jul 2017, 01:36
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:05) correct 26% (01:22) wrong based on 173 sessions

HideShow timer Statistics

Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

A. 1/12
B. 1/11
C. 1/9
D. 5/36
E. 1/6


I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?

Originally posted by vingmat001 on 02 Mar 2014, 19:20.
Last edited by Bunuel on 09 Jul 2017, 01:36, edited 2 times in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 02 Mar 2014, 21:22
3
vingmat001 wrote:
I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?


Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)?
Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one.

In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one.
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
avatar
Joined: 23 Feb 2014
Posts: 33
GMAT 1: 560 Q41 V26
GMAT 2: 610 Q46 V28
Premium Member
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 03 Mar 2014, 15:30
Wow !! Thanks for the explanation Karishma!- Just add color to the dice and it all becomes clear. :-D
Intern
Intern
avatar
Joined: 04 Jan 2014
Posts: 3
Location: Canada
Concentration: Finance, Strategy
GMAT Date: 07-31-2014
GPA: 3.95
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 03 Mar 2014, 21:47
2
vingmat001 wrote:
I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?


Another way to visualize this problem is as shown in the attached diagram. In the test, you do not need to list all possible sums. Just look for the one you are interested in and count them.
Attachments

File comment: Probability of getting a defined sum from the sum of the numbers on two faces of a randomly rolled cube.
2 rolled cubes numbered 1 to 6.docx [58.01 KiB]
Downloaded 154 times

To download please login or register as a user

Intern
Intern
avatar
B
Joined: 24 Feb 2017
Posts: 37
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Basic conceptual question in probability  [#permalink]

Show Tags

New post 08 Jul 2017, 18:01
"Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" (MGMAT example question Guide 5 Chapter 4)

We all know the right way solve this question, which is - Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36.

My question - why is the # of total outcomes not 11? Why are we considering the total outcomes of die-rolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11

Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below.

Sum # outcomes
2 1
3 2
4 3
.
.
....
11 2
12 1

My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"?
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1004
Re: Basic conceptual question in probability  [#permalink]

Show Tags

New post 08 Jul 2017, 19:41
1
rbramkumar wrote:
"Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" (MGMAT example question Guide 5 Chapter 4)

We all know the right way solve this question, which is - Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36.

My question - why is the # of total outcomes not 11? Why are we considering the total outcomes of die-rolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11

Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below.

Sum # outcomes
2 1
3 2
4 3
.
.
....
11 2
12 1

My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"?



number of ways u get 8
2,6
6,2
3,5
5,3
4,4
= 5ways

and total possible outcomes of two dice = 6*6=36

thus probability = 5/36....
Intern
Intern
avatar
B
Joined: 24 Feb 2017
Posts: 37
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Re: Basic conceptual question in probability  [#permalink]

Show Tags

New post 08 Jul 2017, 23:55
Sorry, I don't think you read my question right. Anyway, thanks for your input.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: Basic conceptual question in probability  [#permalink]

Show Tags

New post 09 Jul 2017, 00:22
1
rbramkumar wrote:
"Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" (MGMAT example question Guide 5 Chapter 4)

We all know the right way solve this question, which is - Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36.

My question - why is the # of total outcomes not 11? Why are we considering the total outcomes of die-rolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11

Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below.

Sum # outcomes
2 1
3 2
4 3
.
.
....
11 2
12 1

My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"?


Since there are 1 outcome for getting sum of 2 and this pattern increases till 7(where the number of outcomes is 6)
The maximum outcomes happen, when the sum if 7 {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} and then the outcomes reduce till we reach 12 as sum,
where the number of outcomes is 1(6,6)

The probability of an event happening = \(\frac{P(A)}{P(T)}\)
where P(A) = Possibility_of_an_event_happening
and P(T) = Total_number_of_outcomes

Here the Possibility of getting 8 is 5 {(2,6),(3,5),(4,4),(5,3),(6,2)}
Total possibilities are 1+2+3+4+5+6+5+4+3+2+1 = 36.

Thats why the probability is 5/36 and not 1/11 as your had asked.

Hope that helps!
_________________

You've got what it takes, but it will take everything you've got

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51072
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 09 Jul 2017, 01:46
rbramkumar wrote:
"Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" (MGMAT example question Guide 5 Chapter 4)

We all know the right way solve this question, which is - Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36.

My question - why is the # of total outcomes not 11? Why are we considering the total outcomes of die-rolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11

Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below.

Sum # outcomes
2 1
3 2
4 3
.
.
....
11 2
12 1

My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"?


Merging topics.

I think pushpitkc answers your question but just to make sure you understand. Not all sums out of 11 have the same number of occurrences. The sum of 2 can occur in 1 way - (1, 1) but the sum of two can occur in 2 way - (1, 2) and (2, 1).

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 24 Feb 2017
Posts: 37
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 09 Jul 2017, 04:19
Thank you, pushpitkc and bunuel.

I understand the concept of "# on dice 1, # on dice 2" as an outcome, but was merely speculating how the answer looked like when we look at "SUM" as an outcome.

Let me elaborate my thoughts:

Former: Outcome (# on dice1, # on dice 2)
Total outcomes 36

Latter: Outcome is defined as the "Sum" of the #s in 2 dices
Total outcomes 11

I was getting derailed by the fact that the # Total outcomes needed to be 11, but I think the latter definition of "outcome" changes the basic assumption in Probability questions, i.e., equally likely outcomes (no bias). I missed the fact that this is a probability distribution where we (sum the area of desired/sum the total area under histogram) to get to the required probability. This seems to result in the original answer of 5/36.

There's really no need to think in the latter manner, just trying out different ways. Thanks and all the best!
Intern
Intern
avatar
B
Joined: 10 Sep 2012
Posts: 4
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 17 Oct 2017, 04:20
VeritasPrepKarishma wrote:
vingmat001 wrote:
I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?


Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)?
Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one.

In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one.


Hi, I can understand why in the "total number of desired outcome" we count only 1 combination {4;4}

However, in the "total number of possible outcome" we put 36 = 6*6. This number include all the duplicated {1;1}, {2,2}.... {6,6}; Otherwise we don't have 36, we only have 30 = 6*5 possible outcome.

May someone please help?

Thank you!
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 17 Oct 2017, 20:39
1
phanthibaovien wrote:
VeritasPrepKarishma wrote:
vingmat001 wrote:
I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?


Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)?
Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one.

In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one.


Hi, I can understand why in the "total number of desired outcome" we count only 1 combination {4;4}

However, in the "total number of possible outcome" we put 36 = 6*6. This number include all the duplicated {1;1}, {2,2}.... {6,6}; Otherwise we don't have 36, we only have 30 = 6*5 possible outcome.

May someone please help?

Thank you!


These are the 36 cases:

{1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}
{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}
{3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}
{4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6}
{5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6}
{6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Senior Manager
Senior Manager
avatar
P
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Reviews Badge
Two number cubes with faces numbered 1 to 6 are rolled. What is the  [#permalink]

Show Tags

New post 27 Jan 2018, 16:30
1
vingmat001 wrote:
Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

A. 1/12
B. 1/11
C. 1/9
D. 5/36
E. 1/6


I am struggling to understand a concept - This seems like an error in MGMAT book - But i want to get it clarified and get a better understanding.

The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

The Concern/Error: The successful outcomes is being counted as 2-6, 3-5,4-4, 5-3, 6-2.
I think there needs to be another 4-4 that should be counted.

Because 4 in Dice 1 is different from 4 in dice 2.

Can someone please explain? Anyone facing same issue?


Here is an alternate approach.

We choose 1 dice and individually calculate the possibility that it will make a sum of 8 when combined with a number in the 2nd dice.

If the first dice rolls a...

1: \(\frac{0}{6}\) possibility of it making a sum of 8 when combined with a number in the second dice.

2: \(\frac{1}{6}\) chance (need 6 on the second dice) it will make a sum of 8.

3: \(\frac{1}{6}\) chance (need 5 on the second dice) it will make a sum of 8.

4: \(\frac{1}{6}\) chance (need 4 on the second dice) it will make a sum of 8.

5: \(\frac{1}{6}\) chance (need 3 on the second dice) it will make a sum of 8.

6: \(\frac{1}{6}\) chance (need 2 on the second dice) it will make a sum of 8.

Each digit in the first dice makes 6 combinations (one with each digit in second dice) and added up, they all make 36 combinations. So each digit's weight or contribution in total probability is 1/6. Adding probability sums.

\(\frac{0}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6}\)

\(= 0 + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{5}{36}\)


It is important to understand that of the 6 digits on a dice, only 5 make a combination that sums up to 8. The digit 1 cannot possibly add up to make 8 as the maximum digit in the second dice is 6 which would make the sum 7.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

GMAT Club Bot
Two number cubes with faces numbered 1 to 6 are rolled. What is the &nbs [#permalink] 27 Jan 2018, 16:30
Display posts from previous: Sort by

Two number cubes with faces numbered 1 to 6 are rolled. What is the

  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®.