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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

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?

We need to find the value of \(f+9m\) (f cents for the first mile and m cents 9 miles).

(1) The company charges $0.90 for a 2-mile ride --> \(f+m=0.9\). Not sufficient. (2) The company charges $1.20 for a 4-mile ride --> \(f+3m=1.2\). Not sufficient.

(1)+(2) We have 2 distinct linear equations with 2 unknowns, hence we can solve for them and get the value of \(f+9m\). Sufficient.

Re: A taxi company charges f cents for the first mile of the [#permalink]

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01 Oct 2012, 08:22

2

This post received KUDOS

\(\)

carcass wrote:

X is the first mile and y are the additional miles

So, \(1*x + y * 9\) (9 because we have the additional miles less the first mile X \(10 - 1 = 9\) )

1)\(x + 9y = 0.90 + 8y\) ( we can't solve) INSUFF

2) \(x + 9y = 1.20 + 6y\) INSUFF

1) + 2) we can subsistute and solve

C should be the answer

The answer is correct, it is C. Just something to consider: when you are already given the variables - \(f\) and \(m\) the prices in cents for the first mile and the additional miles, respectively, no need to define new variables, just to have the prices in dollars. And I wouldn't suggest just picking automatically the \(x\) and \(y\) variables when dealing with some quantities with some specific meaning. \(f\) from first and \(m\) from miles are suggestive. With \(f\) and \(m\) your two equations would be: \(f+9m=90+8m\) \(f+9m=120+6m\)
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A taxi company charges f cents for the first mile of the [#permalink]

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04 Oct 2012, 14:04

Bunuel wrote:

SOLUTION

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?

We need to find the value of \(f+9m\) (f cents for the first mile and m cents 9 miles).

(1) The company charges $0.90 for a 2-mile ride --> \(f+m=0.9\). Not sufficient. (2) The company charges $1.20 for a 4-mile ride --> \(f+3m=1.2\). Not sufficient.

(1)+(2) We have 2 distinct linear equations with 2 unknowns, hence we can solve for them and get the value of \(f+9m\). Sufficient.

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

\(f\) and \(m\) are prices in cents, so the equations should be \(f+m=90\) and \(f+3m=120\).
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A taxi company charges f cents for the first mile of the [#permalink]

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10 Jan 2014, 07:22

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

We are given: f + 9*m = Total Cost, by the stem.

1) Tells us that f + m = 0.9, given that we have three unknowns but two equations, this is not enough. 2) This gives us f + 3m = 1.2, (which btw clearly is NOT the same info as in 1), so we have 3 unknowns and 2 equations, insufficient.

1 + 2. 3 equations and 3 unknowns, sufficient. We can add 1 and 2 together to solve for total cost, and we can add the info from the stem with one of the statements in 1 or 2 to solve for the third. C is our answer.

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 = 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 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 = 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