2017 AMC 10B Problem 12

Question

Elmer’s new car gets

50\%

better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is

20\%

more expensive per liter than the gasoline his old car uses. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

20\%

26\tfrac23\%

27\tfrac79\%

33\tfrac13\%

41\tfrac23\%

Answer: A

Concepts:rate percentage

Difficulty rating: 1280

Small hint:

Compare cost per kilometer, not cost per liter

Big hint:

New fuel uses fewer liters but each liter costs more

Solution:

Let the old car’s fuel efficiency be

M

kilometers per liter and let gasoline cost

C

dollars per liter. The old car therefore costs

\dfrac CM

dollars per kilometer to fuel.

The new car gets

1.5M

kilometers per liter and its fuel costs

1.2C

dollars per liter, so its fuel cost per kilometer is

\dfrac{1.2C}{1.5M}=0.8\dfrac CM.

The new fuel cost is

80\%

of the old one, so Elmer saves

20\%.

Thus, the correct answer is A .