Question

A taxi company charges f cents for the first mile of the taxi ride and m cents for each additional mile. How much does the company charge for a 10-mile taxi ride?
(1) The company charges $0.90 for a 2-mile ride.
(2) The company charges $1.20 for a 4-mile ride.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is C Both statements together are sufficient, but neither statement alone is sufficient.

If a taxi company charges f cents for the first mile and m cents for each additional mile, determine the charge for a 10-mile taxi ride, which can be expressed as F + 9M.

1. Since the charge for a 2-mile ride is $0.90, F + M = 0.90 and so, F + 9M = 0.9 + 8M, but the value of M is unknown. So, statement 1 is insufficient.
2. Since the charge for a 4-mile ride is $1.20, F + 3M = 1.20 and so F + 9M = 1.20 + 6M, but the value of M is unknown. So, statement 2 is insufficient.
3. Taking (1) and (2) together and subtracting the equation in (1) from the equation in (2) gives 2M = 0.30 from which M = 0.15. Then from (1), F + 0.15 = 0.90 and F = 0.75. Therefore, the charge for a 10-mile taxi ride is $0.75+9\ast ($0.15) = $2.10.

• Alternatively, the graphs of f + m = 0.90 and f + 3m = 1.20 in the (f,m) coordinate plane are lines that intersect at exactly one point, and therefore values of f and m can be determined, from which f + 9m can then be determined.
• The correct answer is C; both statements together are sufficient.