Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Apr 2015
Posts: 64

The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
02 Jun 2015, 02:40
2
This post received KUDOS
4
This post was BOOKMARKED
Question Stats:
37% (01:56) correct 63% (01:51) wrong based on 81 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.
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by PrepTap on 05 Jun 2015, 03:45, edited 1 time in total.



SVP
Joined: 08 Jul 2010
Posts: 1956
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
02 Jun 2015, 05:47
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 personsLet's take a Second case
Level 1: 2 person Level 2: 4 persons Level 3: 8 persons Level 4: 16 persons Level 5: 32 personsThe 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 SUFFICIENTStatement 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 personsLet'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 personsThe 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 SUFFICIENTCombining 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 personsHence, 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 email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne 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
Joined: 19 Mar 2015
Posts: 20
Location: United States
Concentration: Sustainability, Sustainability

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
24 Jun 2015, 22:55
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 personsLet's take a Second case
Level 1: 2 person Level 2: 4 persons Level 3: 8 persons Level 4: 16 persons Level 5: 32 personsThe 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 SUFFICIENTStatement 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 personsLet'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 personsThe 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 SUFFICIENTCombining 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 personsHence, 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 questionbut 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?



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
25 Jun 2015, 00:26
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 3storey 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



SVP
Joined: 08 Jul 2010
Posts: 1956
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
25 Jun 2015, 00:56
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 personsHence, 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 level5 is 16 which is twice the number of members in level4 i.e. 8 members and level4 is right one level above level5. So I don't see the ambiguity that you are reflecting in your comment.
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne 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
Joined: 19 Mar 2015
Posts: 20
Location: United States
Concentration: Sustainability, Sustainability

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
25 Jun 2015, 07:58
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 personsHence, 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 level5 is 16 which is twice the number of members in level4 i.e. 8 members and level4 is right one level above level5. So I don't see the ambiguity that you are reflecting in your comment. Thanks for the explanation. I got the point.



NonHuman User
Joined: 09 Sep 2013
Posts: 13786

Re: The number of people present at each level, except the topmost, of a [#permalink]
Show Tags
08 Feb 2018, 20:51
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The number of people present at each level, except the topmost, of a
[#permalink]
08 Feb 2018, 20:51






