GMAT OFFICIAL GUIDE PS

Solution:

This problem can best be solved using combinations. It is similar to a problem in which 30 sports teams are playing in a tournament where every team plays every other team. No team plays itself, obviously, and the order of each pairing doesn’t matter. [For example, if Team A plays Team B, the pairing of (Team A vs Team B) is identical to (Team B vs. Team A)]. We would calculate 30C2, or the number of combinations of 30 items taken 2 at a time.

The table of distances presented in this problem is similar to the sports team example. We don’t pair up a city with itself, and the pairing of City A to City B is identical to pairing City B to City A. With 30 cities in the table, we can solve the problem by calculating 30C2.

30C2 = 30! / [2! x (30 – 2)!] 30! / [2! x (28)!] (30 x 29)/2!
(30 x 29) / 2
15 x 29 = 435

Answer: B

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.