Percent - 700 to 800 level Question Types - The Beat The GMAT Forum

Percent - 700 to 800 level Question Types

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GMAT-Zenith: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu May 27, 2010 2:04 am; Thanked: 1 times

by GMAT-Zenith » Wed Jul 04, 2012 5:54 am

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?
3xr / 2 3x / 200r 3r / 200x 3xr / 200 xr / 600

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Source: Beat The GMAT — Problem Solving | Wed Jul 04, 2012 5:54 am

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Wed Jul 04, 2012 6:20 am

charge = r cents per person per mile
there are 3 persons involved
new charge = 3r cents per group of 3 per mile

in 1 mile driver charges 3r cents
in x miles driver charges (3r)(x) cents
he charges 50% of total = (3r)(x)(1/2) cents = 3xr/2 cents
3xr/2 cents = (3xr/2)/ 100 dollars = 3xr / 200 dollars

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 04, 2012 6:21 am

GMAT-Zenith wrote: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?
3xr / 2 3x / 200r 3r / 200x 3xr / 200 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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