A certain NYC taxi driver has decided to start charging a

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

A certain NYC taxi driver has decided to start charging a

by AAPL » Mon Mar 25, 2019 3:20 am

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A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. \(\frac{3xr}{2}\)

B. \(\frac{3x}{200r}\)

C. \(\frac{3r}{200x}\)

D. \(\frac{3xr}{200}\)

E. \(\frac{xr}{600}\)

OA D

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Source: Beat The GMAT — Problem Solving | Mon Mar 25, 2019 3:20 am

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by GMATGuruNY » Mon Mar 25, 2019 3:49 am

AAPL wrote:Manhattan Prep

A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. \(\frac{3xr}{2}\)

B. \(\frac{3x}{200r}\)

C. \(\frac{3r}{200x}\)

D. \(\frac{3xr}{200}\)

E. \(\frac{xr}{600}\)

Let r=100 cents.
For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars.
Let x = 2 miles.
Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars.
With a 50% discount, the cost in dollars = 3. This is our target.

Now we plug x=2 and r=100 into the answers to see which yields our target of 3.
Only answer choice D works:
3xr/200 = (3*2*100)/200 = 3.

The correct answer is D.

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by Scott@TargetTestPrep » Wed Mar 27, 2019 5:55 pm

AAPL wrote:Manhattan Prep

A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. \(\frac{3xr}{2}\)

B. \(\frac{3x}{200r}\)

C. \(\frac{3r}{200x}\)

D. \(\frac{3xr}{200}\)

E. \(\frac{xr}{600}\)

OA D

The cost for 3 people for x miles for a 50% discount, in cents, is:

3 * x * r * 1/2 = 3xr/2

Since 1 dollar = 100 cents, the cost, in dollars, is 3xr/2 * 1/100 = 3xr/200.

Answer: D

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