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A certain NYC taxi driver has decided to start charging a

by BTGmoderatorLU » Mon Oct 15, 2018 2:42 pm

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Source: 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. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600

The OA is D.
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by Brent@GMATPrepNow » Tue Oct 16, 2018 4:55 am
BTGmoderatorLU wrote:Source: 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. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600

The OA is D.
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)
= 3rx/200 dollars

Answer: D

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Brent
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by GMATGuruNY » Tue Oct 16, 2018 5:01 am
BTGmoderatorLU wrote:Source: 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. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. 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 the target.

Plug x=2 and r=100 into the answers to see which yields the target value of 3.
Only D works:
3xr/200 = (3*2*100)/200 = 3.

The correct answer is D.
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by fskilnik@GMATH » Tue Oct 16, 2018 10:32 am
BTGmoderatorLU wrote:Source: 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. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600
Let´s avoid exploring particular cases (undoubtedly very useful) to embrace UNITS CONTROL, one of the most powerful tools of our method!
\[\frac{{r\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\,\,\mathop \to \limits^{{\text{discount}}} \,\,\,\,\,\,\,\frac{{\frac{r}{2}\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\, = \,\,\,\,\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\]
\[?\,\,\,:\,\,\$ \,\,{\text{for}}\,\,3\,\,{\text{people}}\,\,{\text{for}}\,\,x\,\,{\text{miles}}\,\,\,\left( {{\text{with}}\,\,{\text{discount}}} \right)\]
\[?\,\,\, = \,\,\,3\,\,{\text{person}}\,\,\, \cdot \,\,\,x\,\,{\text{miles}}\,\,\,\left( {\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,} \right)\,\,\,\left( {\frac{{1\,\,\$ }}{{100\,\,{\text{cents}}}}} \right)\,\,\,\,\, = \,\,\,\,\,\,\$ \,\,\,\frac{{3xr}}{{200}}\,\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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by Scott@TargetTestPrep » Tue Oct 16, 2018 5:14 pm
BTGmoderatorLU wrote:Source: 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. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600
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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