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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Tue Mar 03, 2015 9:33 am

A certain taxi driver charges a rate of r cents per person per mile. How much money, in dollars, would it cost three people to travel x miles if he gives them a 50% discount? (100 cents = 1 dollar)

A)3xr/2

B)3x/200r

C)3r/200x

D)3xr/200

E)xr/600

My method:

Let r= 200 cents which is equal to 2$
For 3 person it will be 6$

Let x = 10 miles

Total dollars will be = 60$

After discount = 30$

Now our target is to find 30$ from the options .

My question is if i put $2 instead of 200 cents will it be wrong?

because i am not getting an answer if i am putting $2.

Please advise and correct me if i am wrong.

Thanks,

Shreyans

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Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2015 9:33 am

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 » Tue Mar 03, 2015 9:42 am

j_shreyans wrote:A certain taxi driver charges a rate of r cents per person per mile. How much money, in dollars, would it cost three people to travel x miles if he gives them a 50% discount? (100 cents = 1 dollar)

A)3xr/2

B)3x/200r

C)3r/200x

D)3xr/200

E)xr/600p

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.

My method:

Let r= 200 cents which is equal to 2$
For 3 person it will be 6$

Let x = 10 miles

Total dollars will be = 60$

After discount = 30$

Now our target is to find 30$ from the options .

My question is if i put $2 instead of 200 cents will it be wrong?

because i am not getting an answer if i am putting $2.

Please advise and correct me if i am wrong.

Thanks,

Shreyans

Since you plugged in r=200, you must plug this value into the answer choices.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Mar 03, 2015 8:43 pm

Hi j_shreyans,

The numbers that you picked work nicely and you've properly deduced what you should be looking for in the correct answers. With these types of "unit conversion" questions, you have to make sure that you enter the proper value and find the answer that answers the question that is ASKED. Since R and X appear in the answer choices, you have to TEST the values that YOU chose for R and X (re: 200 and 10, respectively). In this prompt, we're for an answer in DOLLARS.

When you deal with similar questions in the future, it helps to take a few more notes (label your work) and keep careful track of the UNITS that each variable represents.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Mar 06, 2015 8:16 am

j_shreyans wrote:A certain taxi driver charges a rate of r cents per person per mile. How much money, in dollars, would it cost three people to travel x miles if he gives them a 50% discount? (100 cents = 1 dollar)

A)3xr/2
B)3x/200r
C)3r/200x
D)3xr/200
E)xr/600

Here's an algebraic approach:

A certain taxi driver charges a rate of r CENTS per person per mile
r CENTS = r/100 DOLLARS [e.g., 3 cents = 3/100 dollars]
Since there are 3 people, the rate is (3)(r/100) DOLLARS per mile
In other words, the rate is 3r/100 dollars per mile.
With a 50% discount, the new rate = (1/2)(3r/100)
In other words, the discounted rate = 3r/200 dollars per mile.

[how much] would it cost three people to travel x miles?
TOTAL cost = (rate)(distance)
= (3r/200 dollars per mile)(x miles)
= [spoiler]3rx/200 dollars[/spoiler]
= D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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