For the rental of a certain type of car, rental agency R charges a fee

Question

For the rental of a certain type of car, rental agency R charges a fee of $30 per day plus a fee of $0.20 for each mile traveled in excess of 100 miles per day. For the rental of the same type of car, rental agency S charges a fee of $65 per day with free unlimited mileage. If a car of this type is to be rented for 3 days and will be driven the same number of miles each day, for what total number of miles will the cost of renting the car from rental agency R be the same as the cost of renting the car from rental agency S ?

A) 352
B) 405
C) 525
D) 750
E) 825

A) 352
B) 405
C) 525
D) 750
E) 825

KarishmaB · Accepted Answer

Agency S charges $35 more than agency R per day. 
The number of miles that make up $35 at the rate of $0.20 per mile will be 35/0.2 = 175 miles

So cost of 100 + 175 = 275 miles from agency R is $30 + $35 = $65 which is also the cost of renting from agency S. Hence in 3 days, a distance of 275 * 3 = 825 miles

Answer (E)

chetan2u · Answer

Let us work out the rent by each agency by taking y as the number of miles per day.

1) Rental Agency R: 30+0.20(y-100) per day
2) Rental Agency S: 65 per day.

If both are equal =  30+0.20(y-100) = 65.......\frac{1}{5}(y-100)=35.......y-100=175.......y=275 
Since we are looking for miles in 3 days => 3*275 = $825

E

isanyamm · Answer

Given values
daily_fee_R = 30
mileage_fee_R = 0.20
daily_fee_S = 65
days = 3

Equation to find the total cost equality
3 * (30 + 0.20 * (m - 100)) = 3 * 65

Simplify the equation 
90 + 0.60 * (m - 100) = 195

Solve for m
0.60 * (m - 100) = 105
m - 100 = 175
m = 275

Total number of miles for 3 days
total_miles = days * (275 + 100) 
The total number of miles is: 825

Kunal1801 · Answer

Given for company R: $30 per day for 100 miles, $0.2 for every mile after 100 miles
Given for S: 65$ per day with unlimited miles
 My Approach 
S=65+65+65=$195 (as mentioned unlimited)
S=30+30+30= l90-195l = (105)/0.2 = 525miles + 300 Miles as mentioned in terms and conditions of S

Approach 2 
The difference between per day price is $35
therefore 35(0.2)(3) for three days = 525 miles + 300 Miles as mentioned in terms and conditions of S

AnkurGMAT20 · Answer

Bunuel , this is focus mock question. Please tag it.

Bunuel · Answer

_____________________
Added the tag. Thank you!

preetisehrawat · Answer

Let in one day a car travelled x miles.

Now, Equation of Rental Agency R :
 30+ 0.20(x-100)

Equation for Rental Agency S:
65 * NUMBER OF DAYS

Since,it is for three days.And we have to find out the number of miles by which both the car agency will cost same.

So,

3* = 65*3
90+ 0.60(x-100)= 195
 0.60(x-100)= 195-90
x-100= 105/0.60
x= 175+100
x=275

Therefore,distance travelled by car in 1 day is 275 and for three days it will be 275*3 which is 825.

ADHDDyslexic · Answer

The approach I used here was all about spotting a shortcut knowing that the GMAT likes to set traps with their answer choices.

With the need to add 300 miles at some point, I looked for a jump in the answer options that matched.

825 stood out as being 300 more than 525.

I plugged in 525 to the equation of 3*30 + 525/5 = 3*65 and it worked. Done in 40 sec!

shrayshray14 · Answer

For this one.. why would we do 3*(30 +0.20 * (m-100)) = 3*65?

Why could we not do 30d + 0.20*(m-100) = 65d and plug in 3 for d?

Apk641 · Answer

First we need to find the break even point in mileage cost

Let Y represent mileage 
And lets make R=S to find the break even point 
Rental R=Rental S
30+.2(y-100)=65
30+.2y-20=65
.2y=55
y=275

Since there are 3 days 
275*3= 825 miles

Dbrunik · Answer

there are two methods to solving. either one day at a time, or by distributing the 3 days.

Dbrunik · Answer

constructive feedback:

the "dot dot dot" here is really pretty confusing and messy. doesnt really show the algebraic steps being taken here.

consider revising this line: " If both are equal =  
  30+0.20(y−100)=65.......15(y−100)=35.......y−100=175.......y=275"

Juangui17 · Answer

I am confused aren't we already solving for the amount of miles in three days if we are multiplying by 3 each price? What am I not getting?

GMATGuruNY · Answer

R --> 3 days at $30 per day = $90
S --> 3 days at $65 per day = $195
Difference = 195-90 = $105 = 10,500 cents

Which answer choice will increase R's total cost by 10,500 cents so that the cost at R is the same as the cost at S? 
   A car will be driven the same number of miles each day.   
   R charges a fee of $0.20 for each mile traveled in excess of 100 miles per day .

D: 750 miles --> 250 miles per day --> 150 miles each day beyond the 100-mile threshold
Mileage cost at R = (150 miles each day)(3 days)(20 cents per mile) = 9000 cents
Since the cost increase is too small, a greater answer choice is needed.

E

E: 825 miles --> 275 miles per day --> 175 miles each day beyond the 100-mile threshold
Mileage cost at R = (175 miles each day)(3 days)(20 cents per mile) = 10,500 cents
Success!

Krunaal · Answer

Let total no. of miles driven over 3 days be m, then total cost for  R for 3 days   =   90 + 0.2*(m-300)  and total cost for  S for 3 days = 3*65

90 + 0.2*(m-300) = 3*65
90 + 0.2*(m-300) = 195
0.2*(m-300) = 105
(m-300) = 525

m = 825 
 
Answer E.

yazlal25 · Answer

We want to find the no. of miles for which the rental would be same for both agency R and agency S.

Lets equate the rent for both agencies for travelling a total of x miles in 3 days.

Rent for agency R = Rent for agency S
30*3 + 0.2 (x-300) = 65*3
90 + 0.2x - 60 = 195
0.2x = 165
x = 165 / 0.2
x = 825 miles

Answer is E.

For the rental of a certain type of car, rental agency R charges a fee

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

For the rental of a certain type of car, rental agency R charges a fee

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards