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Difficulty:
95%
(hard)
Question Stats:
33% (02:22) correct
67%
(02:26)
wrong
based on 105
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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.
(1) The pyramid has 5 levels.
(2) There are fewer than 50 people on the pyramid.
Kudos for correct solutions.
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02 Jun 2015, 06:47
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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
24 Jun 2015, 23:55
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GMATinsight
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?
