ardz24 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.

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

If we know the structure of the pyramid we can determine the probability. The structure is determined by the number of the people on the top level and the number of levels. If we know that we can tell how many people are on each level and how many people there are total.

(1) is not sufficient because it only tells us that there are 5 levels. Different structures with 5 levels:

Structure 1 (Top level to bottom level): 1, 2, 4, 8, 16
Structure 2 (Top level to bottom level): 2, 4, 8, 16, 32
Structure 3 (Top level to bottom level): 3, 6, 12, 24, 48
Structure 4 (Top level to bottom level): 4, 8, 16, 32, 64
Structure 5 (Top level to bottom level): 5, 10, 20, 40, 80

(2) is not sufficient because it only tells us how many people are in the structure. Different structures with less than 50 people:

Structure 1 (Top level to bottom level): 1, 2, 4, 8, 16
Structure 2 (Top level to bottom level): 2, 4, 8, 16
Structure 3 (Top level to bottom level): 3, 6, 12, 24
Structure 4 (Top level to bottom level): 4, 8, 16
Structure 5 (Top level to bottom level): 5, 10, 20

(1) and (2) together: sufficient as structure 1 (1, 2, 4, 8, 16) is the only structure that has five levels and less than 50 people.