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

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raheelsn
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For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Dec 2023, 00:02
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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
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E
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KarishmaB
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Dec 2023, 02:09
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raheelsn wrote:
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


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)
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chetan2u
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Dec 2023, 00:23
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raheelsn wrote:
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



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
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isanyamm
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Dec 2023, 01:26
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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
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Kunal1801
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Dec 2023, 02:28
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raheelsn wrote:
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

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
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   11 Jan 2024, 04:27
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Bunuel, this is focus mock question. Please tag it.
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Bunuel
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   11 Jan 2024, 04:35
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AnkurGMAT20 wrote:
Bunuel, this is focus mock question. Please tag it.

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Added the tag. Thank you!
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   28 Feb 2024, 13:01
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­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*[ 30+ 0.20(x-100)]= 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.
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink] For the rental of a certain type of car, rental agency R charges a fee   03 Apr 2024, 08:25
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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!
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Re: For the rental of a certain type of car, rental agency R charges a fee [#permalink]
03 Apr 2024, 08:25
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