Workbook Wednesdays: Boats on the Lake Answer

As promised, here is the answer to yesterday’s Manhattan GMAT Challenge Question!

The key to this problem is to make the common term in both ratios equal. We should set up a table to display both ratios:

Now, we can double any of the ratios. In fact, we can multiply any row by any positive-integer factor (x2, x3, x10, etc.). We are constrained to positive-integer factors, though, because the actual number of any boat must be a positive integer.

The number of canoes in each row should be the same, so that we can merge the ratios. The least common multiple of 7 and 5 is 35, so we multiply the top row by 5 and the bottom row by 7:

This means that the “3-way” ratio of catamarans, canoes, and kayaks is 20:35:63. That is, for every 20 catamarans on the lake, there are 35 canoes and 63 kayaks. This ratio is already reduced to lowest integers, because there are no prime factors in common among all 3 integers.

The smallest number of boats that can be on the lake is 20 + 35 + 63 = 118. Since the total number of boats must be an integer, any possible number of boats must be a multiple of 118. To check which number is a multiple of 118, we factor 118 into its primes: 2 and 59. This allows us to spot 590, which is 59 x 10 and therefore 118 x 5.

The answer is D.