# GMAT OFFICIAL GUIDE DS – A taxi company charges f cents…

## Solution:

We are given that a taxi company charges f cents for the first mile of the taxi ride and m cents for each additional mile. We must determine how much the company charges for a 10-mile taxi ride. We can now set up the following equation:

Total Cost = f + m(total miles – 1)

Total Cost = f + m(10 – 1)

Total Cost = f + m(9)

Total Cost = f + 9m

Thus, if we determine the value of f and m, we can determine the total cost of a 10-mile taxi ride.

Statement One Alone:

The company charges \$0.90 for a 2-mile ride.

We are given that the company charges 0.90 dollars for a 2-mile ride. Because we are already using cents in our equation we can convert 0.90 dollars to 90 cents.

90 = f + m(2 –1)

90 = f + m

Since we cannot determine the value of f and m, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The company charges \$1.20 for a 4-mile ride.

We are given that the company charges 1.20 dollars for a 4-mile ride. Because we are already using cents in our equation we can convert 1.20 dollars to 120 cents.

120 = f + m(4-1)

120 = f + 3m

Since we cannot determine the value of f and m, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we have the following two equations:

1) 90 = f + m

2) 120 = f + 3m

Since we have two independent equations with the same two variables, we have enough information to determine values for f and m, and thus we can determine how much a 10-mile taxi ride would cost.