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

\(\)

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:
\(f+9m=90+8m\)
\(f+9m=120+6m\)

f+ 9m=?
1) f + m = 90 ---->Insufficient
2) f+ 3m = 120--->Insufficient
1+2) Two equations & 2 variables - Sufficient.
Answer C

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

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.

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: C

RELATED VIDEO

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:

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

According to EmpowerGmat, the answer is B since you can determine for a fact that M = 0.

What is the correct answer?

f + 9m

1. f + m = 0.9

we cannnot determine the value of 2 variables from 1 equation. hence insuff.

2. f+3m = 1.2

Again we cannot determine the value

Hi gladkian,

In my explanation (which is directly above your post), I explain how the correct answer is . Are you looking at a different practice question?

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

Hello Bunuel
Which one could be the perfect equation. Could you clarify, please?
(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.

or,

(1) The company charges $0.90 for a 2-mile ride --> \(f+m=90\). Not sufficient.
(2) The company charges $1.20 for a 4-mile ride --> \(f+3m=120\). Not sufficient.
The question is in cents (¢), but the statements are in dollars ($) value.

Thanks__

Hi Asad,

Sometimes GMAT questions purposely put different 'units' into the prompt to 'test' your ability to perform a proper unit conversion. For example, you might be given information in 'dollars', but asked for an answer in 'cents.' or given information in 'minutes' and asked for an answer in 'hours.' In these situations, you MUST do a proper conversion, otherwise you might select an incorrect answer. However, in this DS question, using either 'cents' or 'dollars' would be fine - you just have to make sure that you are clear on which units you are using so that you can create the proper equations and correctly work through the logic.

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

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

(DS) This is a 2 variables question with Condition(1) with 1 equation and Condition (2) with 1 equation

We are aware that each condition would usually give us an equation, resulting in a total of 2 equations, one each from condition (1), and condition (2). Since we need 2 equations to match the number of variables and equations in the original condition, an equal number of equations and variables should logically give us an answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

=> We have to find how much does the company charges for a 10-mile taxi ride.

=> Company charges: First mile(f cents) and Each additional mile(m cents).

=> For 10 miles: 1 mile (f cents) + 9 miles(m cents)

=> We have to find the value of f + 9m.

Second and the third step of Variable Approach: From the original condition, we have 2 variables (f and m). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

The answer is C because the number of variables and equations is 2. You should never get this question wrong as it is a basic, 30-39 level question.

Let’s take a look at both conditions together

Condition 1: The company charges $0.90 for a 2-mile ride => f + m = 0.90 [first mile(f cents) + second mile is additional(m cents)]

Condition 2: The company charges $1.20 for a 4-mile ride => f + 3m = 0.90[first mile(f cents) + three miles are additional(m cents)]

Solving both the equations:

=> f + m = 0.90 and f + 3m = 1.20

=> f + m + 2m = 1.20

=> 0.90 + 2m = 1.20

=> 2m = 0.30

=> m = 0.15

Therefore, f + m = 0.90 => f + 0.15 = 0.90 => f = 0.75

For 10 miles: f + 9m => 0.75 + 9(0.15) = $2.1


NOTE: We ideally don't have to get the value of 'f + 9m'. We just want to check whether data is sufficient enough to give the individual and unique value for 'f' and 'm', after we combine both the conditions together

The answer is unique according to CMT(2), so the conditions combined are sufficient.

Both conditions (1) and (2) together are sufficient.

So, C is the correct answer.

Answer: C

the difference in price between first two and next two miles is 0.3 cents. Since after the first mile the price per mile is constant, just divide 0.3 cents by two, hence 0.15 cents is the cost of the additional mile and 0.65 cents is first mile

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