Bunuel wrote:
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.
Practice Questions
Question: 54
Page: 279
Difficulty: 600
Target question: How much does the company charge for a 10 mile taxi ride? Given: A taxi company charges 'f' cents for the first mile of the taxi ride and 'm' cents for each additional mile. 1 mile at f cents/mile will cost f cents
9 miles at m cents/mile will cost 9m cents
So, the TOTAL cost of a 10-mile trip costs f + 9m cents
REPHRASED target question: What is the value of f + 9m? Statement 1: The company charges $0.90 for a 2-mile ride 1 mile at f cents/mile will cost f cents
1 mile at m cents/mile will cost m cents
So, the total cost of this 2-mile ride = f + m cents
Since the cost is 90 cents, we can conclude that
f + m = 90Is this enough information to find the value of
f + 9m? No!
Here's why. There are several values of f and m that satisfy the equation
f + m = 90. Here are two:
Case a: f = 80 and m = 10, in which case
f + 9m = 80 + 9(10) = 170Case b: f = 85 and m = 5, in which case
f + 9m = 85 + 9(5) = 130Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The company charges $1.20 for a 4-mile ride 1 mile at f cents/mile will cost f cents
3 miles at m cents/mile will cost 3m cents
So, the total cost of this 4-mile ride = f + 3m cents
Since the cost is 120 cents, we can conclude that
f + 3m = 120Is this enough information to find the value of
f + 9m? No!
Here's why. There are several values of f and m that satisfy the equation
f + 3m = 120. Here are two:
Case a: f = 90 and m = 10, in which case
f + 9m = 90 + 9(10) = 180Case b: f = 105 and m = 5, in which case
f + 9m = 105 + 9(5) = 150Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that
f + m = 90Statement 2 tells us that
f + 3m = 120We COULD solve this system of equation for f and m, which means we COULD determine the value of
f + 9mSince we COULD answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
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