# GMAT question - A car hire firm charges \$30 a day plus a x cents for... - Review

Type: Data Sufficiency

Difficulty:

A car hire firm charges \$30 a day plus a x cents for each mile travelled over 30 miles a day. How many cents per mile does the car hire firm charge after the first 30 miles?

1. The cost of hiring the car for one day in which it travelled 100 miles was \$51.
2. The cost of hiring the car to travel 120 miles in one day was \$6 more than hiring the car to travel 100 miles.
1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

### Explanation

#### Simplify the question

The cost of hiring a car for a day has a fixed component, \$30, and a variable component, $\lineskip 1em \textstyle x$ cents for each mile beyond an initial 30.

Assuming that you travel more than 30 miles in a day we can express this as an equation, where $\lineskip 1em \textstyle C$ is the cost of hiring the car for a day and $\lineskip 1em \textstyle m$ is the number of miles travelled.

$\lineskip 1em C = 30 + (m - 30)\frac{x}{100}$

#### Is statement (1) sufficient?

Statement (1) tells us the cost will be \$51 if we travel 100 miles

Substituting this into the equation it should be clear that we have an equation with just one unknown, $\lineskip 1em \textstyle x$, and so it can be solved and statement (1) is sufficient.

$\lineskip 1em 51 = 30 + (100 - 30)\frac{x}{100}$

#### Is statement (2) sufficient?

Statement (2) tells us that to travel an extra 20 miles will cost us an extra \$6

It should be clear that this implies that 20 miles at $\lineskip 1em \textstyle x$ cents a mile costs \$6 which can be solved and statement (2) is sufficient.

$\lineskip 1em 6 = \frac{20x}{100}$