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

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Math Expert
Joined: 02 Sep 2009
Posts: 45180
A taxi company charges f cents for the first mile of the [#permalink]

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01 Oct 2012, 05:22
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81% (01:00) correct 19% (01:09) wrong based on 1207 sessions

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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
[Reveal] Spoiler: OA

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Posts: 45180
Re: A taxi company charges f cents for the first mile of the [#permalink]

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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.

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

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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

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

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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

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

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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.

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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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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Posts: 2442
Re: A taxi company charges f cents for the first mile of the [#permalink]

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07 Aug 2017, 10:38
1
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Expert's post
Top Contributor
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

[Reveal] Spoiler:
C

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Re: A taxi company charges f cents for the first mile of the   [#permalink] 07 Aug 2017, 10:38
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