A certain NYC taxi driver has decided to start charging a

Question

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

LiveStronger · Accepted Answer

D Almost stepped into the trap

3xr/2 is in cents - 3xr/200 dollars

alpha_plus_gamma · Answer

r/100 dollars per person per mile

one person going x miles will be charged rx/100
50% discount = rx/200

3such people = 3rx/200

spiridon · Answer

rate*miles*passangers/discount

discount has to be in dollars so 1/2/100/1=200

rx3/200

D

GMATinsight · Answer

Charge for One person and One mile = r cents
i.e. Charge for 3 persons and One mile = 3*r cents
i.e. Charge for 3 persons and 'x' miles = 3*r*x cents

After Discount, Charge = 50% of (3*r*x) cents
i.e. Charged Amount = (1/2)*(3*r*x) cents

But 1 Dollar = 100 Cents

i.e. Charged Amount   in Dollar   = (1/2)*(3*r*x)/100 Dollars
i.e. Charged Amount   in Dollar   = (3*r*x)/200  Dollars

Answer: Option  D

GMATinsight · Answer

Hi zahraf You seem to have missed converting Cents in to Dollars I hope it helps!

BrentGMATPrepNow · Answer

Here's an algebraic approach:

A certain taxi driver charges a rate of r CENTS  per person  per mile  
r CENTS = r/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.

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

Abhishek009 · Answer

So, Charges for 3 people to travel x miles will be :  3*x*r % =>  \frac{3rx}{100}

Charges for 3 people to travel x miles will be :  \frac{3rx}{100} * 50 % =>  \frac{3rx}{100}*\frac{50}{100}  =  \frac{3xr}{200}

So, Answer will be (D)  \frac{3xr}{200}

sukeshap · Answer

Answer asked for how many dollars not cents
100 cent equal to 1 dollar. Need to convert it to Dollar means divided by 100

AK92 · Answer

Test values:
let r be 100, so r equals 100 cents or $1. Now the driver charges for one person $1 per mile, that means he will charge for 3 people $3 per mile.
Now let x equals 2. For 2 miles the driver will charge now for the 3 people $6. Now consider the 50% discount, which leads to the final charge of $3 for the 3 people.
If you plug in now the values x=2, r=100 you will get for A 300, which is the amount in cents but the question clearly states that we want the amount in dollars. 
Only option D yields 3 and thus is a match.
D is the answer!

dabhishek87 · Answer

3xr/2 in cents
3xr/200 in dollar

GMATGuruNY · Answer

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 D works:
 \frac{(3xr)}{200} = \frac{(3*2*100)}{200} = 3

D

fskilnik · Answer

Let´s avoid exploring particular cases (undoubtedly very useful) to embrace  UNITS CONTROL , one of the most powerful tools of our method!

\frac{{r\,\,{	ext{cents}}}}{{1\,\,{	ext{person}}\,\, \cdot \,\,1\,\,{	ext{mile}}}}\,\,\,\,\,\mathop 	o \limits^{{	ext{discount}}} \,\,\,\,\,\,\,\frac{{\frac{r}{2}\,\,{	ext{cents}}}}{{1\,\,{	ext{person}}\,\, \cdot \,\,1\,\,{	ext{mile}}}}\,\,\,\, = \,\,\,\,\,\frac{1}{2}\,\,\frac{{r\,\,{	ext{cents}}}}{{\,\,1\,\,{	ext{person}}\,\, \cdot \,\,1\,\,{	ext{mile}}}}

?\,\,\,:\,\,\$ \,\,{	ext{for}}\,\,3\,\,{	ext{people}}\,\,{	ext{for}}\,\,x\,\,{	ext{miles}}\,\,\,\left( {{	ext{with}}\,\,{	ext{discount}}} ight)

?\,\,\, = \,\,\,3\,\,{	ext{person}}\,\,\, \cdot \,\,\,x\,\,{	ext{miles}}\,\,\,\left( {\,\frac{1}{2}\,\,\frac{{r\,\,{	ext{cents}}}}{{\,\,1\,\,{	ext{person}}\,\, \cdot \,\,1\,\,{	ext{mile}}}}\,} ight)\,\,\,\left( {\frac{{1\,\,\$ }}{{100\,\,{	ext{cents}}}}} ight)\,\,\,\,\, = \,\,\,\,\,\,\$ \,\,\,\frac{{3xr}}{{200}}\,

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

Regards, 
Fabio.

GMATWhizTeam · Answer

A great candidate for plugging in values.

Let r = 50 and x = 10.

This means, the NYC taxi driver charges 50 cents per person per mile.

Therefore, cost of travelling 10 miles for ONE person = 50 * 10 = 500 cents
Hence, cost of travelling 10 miles for THREE people = 500 * 3 = 1500 cents.

However, he does give them a 50% discount, therefore, 
Effective cost of travelling 10 miles for THREE people =  \frac{1500 }{ 2}  = 750 cents.

Here’s when we have to be extremely careful about the conversion, the answer is expected in terms of dollars and not cents, therefore, 
Effective cost of travelling 10 miles for THREE people =  \frac{750 }{ 100}  = 7.5 dollars, since 100 cents equals 1 dollar.

Substituting the value of x and r in the options, the expression shown in answer option D gives 7.5

Note that the expression shown in answer option A gives 750. This is a trap, because the cost is 750 cents and not 750 dollars.

The correct answer option is D.

ManishaPrepMinds · Answer

1. Without discount: 
o Rate = r cents/person/mile
o 3 people × x miles × r cents = 3xr cents
2. With 50% discount: 
o 3xr × (1/2) = 3xr/2 cents
o Convert to dollars: 3xr/2 ÷ 100 = 3xr/200 dollars
Answer: D

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A certain NYC taxi driver has decided to start charging a

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