A certain car rental agency rented 25 vehicles yesterday, each of whic

Yes, the answer is E.

My analysis is as follows (C be the number of Compact cars and L be the number of compact cars)

C+L=25

Option A:

Let the daily rental of compact car= X, then Luxy car= X+15 (Not suff)

Option B:

Not sufficient.

Together

C+L=25

CX- (25-C) (X+15)=105

from the above equation, we get two variable and ehnce cannot be solved.

Let C be the number of Compact Cars and L be the number of Luxury cars

Given that,

C + L =25

1) Let c be the daily rental rate of compact cars and l be the rental rate for luxury cars

l-c=15

Not sufficient

2)

lL- cC = 150

Not sufficient

Combining 1) & 2) we have
C + L =25
l-c=15


lL- cC = 150
=>( c+15 ) x (25 - C) - cC = 150
=> 25c + cC +375 - 15C = 150
=>15C - 25c = 225

Still we have two unknowns

Not Sufficient

E should be the answer

Given total cars rented \(\,=\,25\)

Statement (i):
\(Luxury's\,rent \,=\,Compact's\,+$15\); no info about how much was paid in total and Compact's rent
Not Sufficient

Statement (ii):
\(Luxury's\,rates \,=\,Compact's\,+$105\); no info about how much was paid in total and each car's rent
Not Sufficient

From (i) + (ii)
we can find \(\frac{105}{15}\,=\,7\) Luxury cars' worth of rent was paid in EXCESS
so, it will hold good for \(14\) cars, \(7\) cars each, but here the total is \(25\)

e.g. if Luxury's rent \(\,=\,$15\) and Compact's rent \(\,=\,$0\)
then, \(7\,*\,$15\,-\,18\,*$0\,=\,105\); Compact cars rented are \(18\)

if Luxury's rent \(\,=\,$24\) and Compact's rent \(\,=\,$9\)
then, \(10\,*\,$24\,-\,15\,*9\,=\,105\); Compact cars rented are \(15\)
Both together Not Sufficient

Answer E

VERITAS PREP OFFICIAL SOLUTION

Looking at what’s provided in the question stem, there are two types of cars being rented. The total number of cars rented is 25, and every car is either compact or luxury. We only have to determine how many compact cars were rented, so something as small as the number of luxury cars rented would solve our problem very quickly. Looking at the statements, we only have information about prices. The daily rate for the compact car is 15$ less than the luxury vehicle. That’s great (and a little unrealistic), but it doesn’t help us answer the question about the number of vehicles. Statement 2 also talks about money, this time talking about the total revenue instead of a per-car basis. This doesn’t help either, so answer choices A, B and D are all out.

This type of question visibly needs you to combine statements in order to get anywhere. There is a danger in combining statements without thinking, because there is often a relationship that’s just hard enough to detect linking the two statements that gets test-takers thinking they’re on the right track. In this question, the fact that 105$ is 7 times the luxury car premium of 15$ makes it feel like 7 more luxury cars were rented than compact cars. This type of connector is hard enough to see that people feel encouraged that they’ve stumbled upon something useful. Unfortunately, when you’re feeling clever is when you’re most vulnerable to fall into a GMAT trap (Something about pride going before a fall).

Let’s delve into these numbers a little. If 7 more luxury cars got rented than compact cars, and the numbers add up to 25, then that means the company rented 16 luxury cars and 9 compacts. If we stop here, we might think that the answer is C. However, applying arbitrary numbers might make us realize the error of our ways. Let’s say a compact car is 100$ an hour (easy number to work with). This makes the luxury cars 115$. We can quickly calculate that the compact cars will bring in exactly (9×100) 900$. The luxury cars will bring in well over 1600$. These two numbers don’t respect the 105$ difference mentioned in statement 2. Why is that? Maybe I picked the wrong prices? Let’s go smaller: 20$ compacts and 35$ luxury cars. That’s 180$ for the compacts and 525$ for the luxury cars. We’re getting closer, but this still doesn’t work. What’s happening?

The number of cars we chose (16 luxury cars and 9 compacts) has a solution, but it’s not one that makes any real world sense. Solving for the two equations and two unknowns with our chosen number of cars:

L+C = 25

L(x+15) = C*x+105

Replacing L by 16 and C by 9

16(x+15) = 9*x+105

16x+240 = 9x+105

7x = -135

x = -19.286

That’s right, this solution works if we give people 19$ to rent compact cars and only 4$ to rent out luxury cars. Clearly this solution does not work in the real world because it does not mean what we expected. On test day, you don’t have to go through the actual math to solve for x, but being able to recognize that renting out 16 cars at a 15$ premium will yield at least (16*15) = 240$ more dollars for the luxury line than the compact line. The relationship of 7 additional cars only works if we rent a total of 7 cars, all luxury liners. Any other rental will throw off this delicate balance, highlighting that it was nothing but a mathematical mirage.

So what’s the answer to this question? As many of you probably figured out, it’s just going to be answer choice E. There are multiple values that will work (and even be positive) for the two constraints given. Many test takers can solve these questions without having to write a single digit down. However, if you’re ever unsure, write down a few numbers and see what they tell you. The reason some people dislike math is the same reason some people love math: it tells the truth. If your understanding of the question is shoddy, a couple of concrete numbers will tell you more than all the x’s and y’s in an alphabet soup (or a Jerry Springer show).

Statement 1
We do not know any detail about the number of cars. (There are 4 unknowns and only 1 equation)
Not sufficient.

Statement 2
This statement only tells that overall rent was greater by $105. (There are 4 unknowns and only 1 equation)
Not sufficient.

Combining Statements 1 and 2
Even when we combine, we have 2 unknowns and only one equation.
Not sufficient.

(E) is the answer.

C+L=25

(1) The daily rental rate for a luxury car was $15 higher than the rate for a compact car.
Let the rental/compact car= x and total rental = Cx
Then the rental/luxury car= x+15 and total rental = L(x+15)

We don't know the value of x, C or L. Insufficient.

(2) The total rental rates for luxury cars was $105 higher than the total rental rates for compact cars yesterday

Let the rental of compact car is x and total rental is Cx
Let the rental of Luxury car is y and total rental is Ly

statement tells us Ly= Cx+105

Combining both statements:-

L(x+15) = Cx +105
But we do not have any value- x, C or L

E is the answer

Responding to a pm:

Obviously, either statement alone does not give the answer.

Consider them together:

Daily rate for luxury cars is 15 higher.
Total rates for luxury cars is 105 higher. What constitutes this $105? It is the higher rent of each luxury car and could also be the extra number of luxury cars hired. So we should not be able to find the number of compact cars hired.

Let's find 2 cases to ensure that answer should be (E).
105/15 = 7
Say, out of 25 cars, 7 are luxury and 18 are compact. So if the rent of compact cars is $0 (theoretically), the rent of luxury cars is $15 and the extra rent charged is $105 - Valid

Say out of 25 cars, 10 are luxury and 15 are compact (split 25 into easy numbers). So the total rent is $10*15 = $150 extra but 5 extra compact cars were hired and their combined rent would be 45/5 = $9 - Valid
etc

Answer (E)

My solution:
In exam i would NEVER try to solve such an equation....

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