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

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Manager
Joined: 22 Apr 2015
Posts: 63
The number of people present at each level, except the topmost, of a  [#permalink]

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Updated on: 05 Jun 2015, 04:45
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Difficulty:

95% (hard)

Question Stats:

35% (02:21) correct 65% (02:26) wrong based on 128 sessions

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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.
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Re: The number of people present at each level, except the topmost, of a  [#permalink]

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02 Jun 2015, 06:47
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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

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
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Re: The number of people present at each level, except the topmost, of a  [#permalink]

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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

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?
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Re: The number of people present at each level, except the topmost, of a  [#permalink]

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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

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Re: The number of people present at each level, except the topmost, of a  [#permalink]

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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

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.
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Re: The number of people present at each level, except the topmost, of a  [#permalink]

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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

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.
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The number of people present at each level, except the topmost, of a  [#permalink]

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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

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The number of people present at each level, except the topmost, of a   [#permalink] 24 Feb 2018, 05:10
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