GMAT Changed on April 16th - Read about the latest changes here

It is currently 23 May 2018, 15:33

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

Events & Promotions in June
Open Detailed Calendar

The number of people present at each level, except the topmost, of a

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

Hide Tags

2 KUDOS received
Manager
Manager
User avatar
Joined: 22 Apr 2015
Posts: 64
The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post Updated on: 05 Jun 2015, 04:45
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (01:58) correct 66% (01:54) wrong based on 122 sessions

HideShow timer Statistics

The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above. What’s the probability that Mr. X and Mr. Y, standing somewhere on the pyramid, are fewer than three levels apart?

(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.

Kudos for correct solutions.

Originally posted by PrepTap on 02 Jun 2015, 03:40.
Last edited by PrepTap on 05 Jun 2015, 04:45, edited 1 time in total.
Expert Post
2 KUDOS received
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2099
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 02 Jun 2015, 06:47
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
PrepTap wrote:
The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above. What’s the probability that Mr. X and Mr. Y, standing somewhere on the pyramid, are fewer than three levels apart?

(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.

The OA will be revealed on Friday, 5th Jun. Kudos for correct solutions.


Statement 1: The pyramid has 5 levels.

Let's take a case

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Let's take a Second case

Level 1: 2 person
Level 2: 4 persons
Level 3: 8 persons
Level 4: 16 persons
Level 5: 32 persons


The probability in the two cases will be different because
in Case 1 x and y can NOT be at the same level at Level 1 whereas
in Case 2 x and y can be at the same level at Level 1

Hence NOT SUFFICIENT

Statement 2: There are fewer than 50 people on the pyramid.
Let's take a case with 3 LEVELS

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons


Let's take a Second case with 5 LEVELS

Level 1: 2 person
Level 2: 4 persons
Level 3: 8 persons
Level 4: 16 persons
Level 5: 32 persons


The probability in the two cases will be different because
in Case 1 x and y can NOT be separated by more than 2 levels hence required probability=1
in Case 2 x and y can be separated by more than 3 levels hence required probability is not equal to 1
Hence NOT SUFFICIENT

Combining the two Statements:

We get only one Case Possible with 5 LEVELS and fewer than 50 people

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Hence, SUFFICIENT to calculate the required probability

Answer: Option

Please Note: We don't have to solve the question till end in Data sufficient because the value of probability doesn't matter the UNIQUENESS and CONSISTENCY of SOlution matter hence we conclude that the two statements together are sufficient to solve the question
_________________

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

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

Intern
Intern
avatar
Joined: 19 Mar 2015
Posts: 19
Location: United States
Concentration: Sustainability, Sustainability
Re: The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 24 Jun 2015, 23:55
GMATinsight wrote:
PrepTap wrote:
The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above. What’s the probability that Mr. X and Mr. Y, standing somewhere on the pyramid, are fewer than three levels apart?

(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.

The OA will be revealed on Friday, 5th Jun. Kudos for correct solutions.


Statement 1: The pyramid has 5 levels.

Let's take a case

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Let's take a Second case

Level 1: 2 person
Level 2: 4 persons
Level 3: 8 persons
Level 4: 16 persons
Level 5: 32 persons


The probability in the two cases will be different because
in Case 1 x and y can NOT be at the same level at Level 1 whereas
in Case 2 x and y can be at the same level at Level 1

Hence NOT SUFFICIENT

Statement 2: There are fewer than 50 people on the pyramid.
Let's take a case with 3 LEVELS

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons


Let's take a Second case with 5 LEVELS

Level 1: 2 person
Level 2: 4 persons
Level 3: 8 persons
Level 4: 16 persons
Level 5: 32 persons


The probability in the two cases will be different because
in Case 1 x and y can NOT be separated by more than 2 levels hence required probability=1
in Case 2 x and y can be separated by more than 3 levels hence required probability is not equal to 1
Hence NOT SUFFICIENT

Combining the two Statements:

We get only one Case Possible with 5 LEVELS and fewer than 50 people

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Hence, SUFFICIENT to calculate the required probability

Answer: Option

Please Note: We don't have to solve the question till end in Data sufficient because the value of probability doesn't matter the UNIQUENESS and CONSISTENCY of SOlution matter hence we conclude that the two statements together are sufficient to solve the question


but the condition of number of members at one level to be twice the number in the next level doesn't hold for the last level. Why have you applied the same condition in the 5th level in your example?
Expert Post
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1345
Re: The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 25 Jun 2015, 01:26
The question doesn't make sense, for two reasons. First, if X and Y are in the pyramid already, they're either less than 3 floors apart or they're not. A priori, the answer has to be either 0 or 1. To ask a probability question here is like asking "What is the probability that New York and Chicago are more than 600 miles apart?"

But even if the question tells us they are going to be randomly assigned to floors, it still doesn't make sense to ask a probability question like this as a DS question, because there's no way to know what information should be considered sufficient to answer it. If I invent a simpler question to illustrate:

Employees A and B will be assigned to different random floors in a 3-storey office building. What is the probability they will be on adjacent floors?
1. A will be assigned to the topmost floor
2. B will not be assigned to the bottom floor

This question makes no sense as a DS question. From the stem alone, using no statements at all, we can calculate the probability they will be on adjacent floors (the answer is 2/3, because each of the three floors is equally likely to be the empty floor, and they are only not adjacent if the middle floor is empty). Then using Statement 1 alone, we have more information, so we can make a better calculation of the the probability (the answer is 1/2, because there are two floors left, one of which is adjacent to the top floor). But using Statement 2 alone, we can also calculate the probability (the answer is 3/4, which one can work out by considering the two possible cases). But then if we use both statements, we have even more information and can make an even better calculation of the probability (the answer is 1, because they must be adjacent). So is the answer A, B, C, or D? It's impossible to guess, because there's no way to tell what information we should consider sufficient to answer a question like this. A DS question simply cannot be posed this way.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Expert Post
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2099
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 25 Jun 2015, 01:56
Yogita25 wrote:
GMATinsight wrote:
The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above. What’s the probability that Mr. X and Mr. Y, standing somewhere on the pyramid, are fewer than three levels apart?

(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.

The OA will be revealed on Friday, 5th Jun. Kudos for correct solutions.

Combining the two Statements:

We get only one Case Possible with 5 LEVELS and fewer than 50 people

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Hence, SUFFICIENT to calculate the required probability

Answer: Option


but the condition of number of members at one level to be twice the number in the next level doesn't hold for the last level. Why have you applied the same condition in the 5th level in your example?


Hi Yogita25,

The Question has mentioned that The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above.

So the only level that is exempted from this condition is level 1 because there is no level above it.

Level 5 is following the rule as the Number of members in level-5 is 16 which is twice the number of members in level-4 i.e. 8 members and level-4 is right one level above level-5.

So I don't see the ambiguity that you are reflecting in your comment.
_________________

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

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

Intern
Intern
avatar
Joined: 19 Mar 2015
Posts: 19
Location: United States
Concentration: Sustainability, Sustainability
Re: The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 25 Jun 2015, 08:58
GMATinsight wrote:
Yogita25 wrote:
GMATinsight wrote:
The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above. What’s the probability that Mr. X and Mr. Y, standing somewhere on the pyramid, are fewer than three levels apart?

(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.

The OA will be revealed on Friday, 5th Jun. Kudos for correct solutions.

Combining the two Statements:

We get only one Case Possible with 5 LEVELS and fewer than 50 people

Level 1: 1 person
Level 2: 2 persons
Level 3: 4 persons
Level 4: 8 persons
Level 5: 16 persons


Hence, SUFFICIENT to calculate the required probability

Answer: Option


but the condition of number of members at one level to be twice the number in the next level doesn't hold for the last level. Why have you applied the same condition in the 5th level in your example?


Hi Yogita25,

The Question has mentioned that The number of people present at each level, except the topmost, of a pyramid is twice the number present just one level above.

So the only level that is exempted from this condition is level 1 because there is no level above it.

Level 5 is following the rule as the Number of members in level-5 is 16 which is twice the number of members in level-4 i.e. 8 members and level-4 is right one level above level-5.

So I don't see the ambiguity that you are reflecting in your comment.


Thanks for the explanation. I got the point.
Manager
Manager
avatar
B
Joined: 29 Nov 2016
Posts: 52
The number of people present at each level, except the topmost, of a [#permalink]

Show Tags

New post 24 Feb 2018, 05:10
I don't understand this. Even if you get this unique set
1
2
4
8
16

How is it that the probability of X at level 1 and Y at level 2 equal to probability of X at level 1 and Y at level 3. Since there are more than 1 solution possible for this question the answer should be E. Even after combining two you don't have a unique solution

Posted from my mobile device
The number of people present at each level, except the topmost, of a   [#permalink] 24 Feb 2018, 05:10
Display posts from previous: Sort by

The number of people present at each level, except the topmost, of a

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


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®.