Data Sufficiency

datonman 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.

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?
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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 = 90
Is 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) = 170
Case b: f = 85 and m = 5, in which case f + 9m = 85 + 9(5) = 130
Since we cannot answer the 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 = 120
Is 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) = 180
Case b: f = 105 and m = 5, in which case f + 9m = 105 + 9(5) = 150
Since 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 = 90
Statement 2 tells us that f + 3m = 120
We COULD solve this system of equation for f and m, which means we COULD determine the value of f + 9m
Since we COULD answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

datonman 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.

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.

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.

Answer: C

Hi All,

We're told that a taxi company charges F cents for the first mile of the taxi ride and M cents for each additional mile. We're asked how much the company charges for a 10 mile taxi ride. This question can be solved with a mix of Algebra and TESTing VALUES.

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

With the information in Fact 1, we can create the following equation for a 2-mile ride:
F + M = 90
With two variables though, there's no way to determine the value of F and M (and the cost of a 10-mile ride would vary). For example,
IF....
F=40, M=50, then a 10-mile ride would cost 40 + 9(50) = 490 cents
F=80, M=10, then a 10-mile ride would cost 80 + 9(10) = 170 cents
Fact 1 is INSUFFICIENT

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

With the information in Fact 2, we can create the following equation for a 2-mile ride:
F + 3M = 120
With two variables though, there's no way to determine the value of F and M (and the cost of a 10-mile ride would vary). For example,
IF....
F=60, M=20, then a 10-mile ride would cost 60 + 9(20) = 240 cents
F=90, M=10, then a 10-mile ride would cost 90 + 9(10) = 180 cents
Fact 2 is INSUFFICIENT

Combined, we know...
F + M = 90
F + 3M = 120

This is a 2-variable 'system', so we can solve it (either with Substitution or Combination). You'll find that M = 15 and F = 75, so we can calculate the value of a 10-mile ride (it would be 75 + 9(15) = 210 cents, but that work would be unnecessary at this point).
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich