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A taxi company charges f cents for the first mile of the

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

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New post 01 Oct 2012, 05:22
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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.

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Difficulty: 600

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

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New post 01 Oct 2012, 05:22
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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.
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 01 Oct 2012, 06:14
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
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 01 Oct 2012, 09:22
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\(\)
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:
\(f+9m=90+8m\)
\(f+9m=120+6m\)
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 01 Oct 2012, 20:12
1
f+ 9m=?
1) f + m = 90 ---->Insufficient
2) f+ 3m = 120--->Insufficient
1+2) Two equations & 2 variables - Sufficient.
Answer C
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 04 Oct 2012, 15:04
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 \(f+3m=120\).
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 10 Jan 2014, 08:22
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.
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Re: A taxi company charges f cents for the first mile of the  [#permalink]

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New post 07 Aug 2017, 10:38
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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 = 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

Answer:

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

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New post 23 Sep 2018, 11:35
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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

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Re: A taxi company charges f cents for the first mile of the &nbs [#permalink] 23 Sep 2018, 11:35
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