DS Permuts/Combins

[CSASHISHPANDAY]

A national park is printing a chart that lists the shortest hiking distance from each of its trailheads to each of its other trailheads. If each pair of trailheads, regardless of order, is represented by exactly one entry in the chart, how many trailheads are in the park?



(1) The number of entries in the chart is greater than the number of trailheads.



(2) There are 10 entries in the chart.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

Answer is B

[Brent@GMATPrepNow]

A national park is printing a chart that lists the shortest hiking distance from each of its trailheads to each of its other trailheads. If each pair of trailheads, regardless of order, is represented by exactly one entry in the chart, how many trailheads are in the park?
(1) The number of entries in the chart is greater than the number of trailheads.
(2) There are 10 entries in the chart.

Answer is B

Let t = the total number of trailheads
Let E = the number of entries in the chart

Rephrased target question: What is the value of t?

Since there is one entry for every pair of trailheads (every 2 trailheads), we can say that e = tC2 (tC2 represents the total number of selections of 2 trailheads from a total of t trailheads)

Statement 1: E > t
In other words, tC2 > t
There are many possible cases to consider. Here are two:
case a: t=4 (since 4C2 > 4)
case b: t=5 (since 5C2 > 5)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: E =10
In other words, tC2 = 10
Since t=5 is the value of t such that tC2=10, so t must equal 5
Since we can answer the target question with certainty, statement 2 IS SUFFICIENT

Answer = B

Cheers,
Brent

[Brent@GMATPrepNow]

If anyone is interested, we have a free video for calculating combinations (like 5C2) in your head. You can find it here: https://www.gmatprepnow.com/module/gmat-counting?id=789

Cheers,
Brent