In a two-story apartment complex, each apartment on the upper floor

Given: Each apartment on the upper floor rents for 75 percent as much as each apartment on the lower floor. The total monthly rent is $15,300 when rent is collected on all of the apartments
Let x = the rent PER UNIT on the lower floor
So, 0.75x = the rent PER UNIT on the upper floor

Let y = the NUMBER of units on the lower floor
Let z = the NUMBER of units on the upper floor

Since the total rent is $15,300, we can write: xy + (0.75x)(z) = 15,300
In other words: xy + 0.75xz = 15,300

Target question: What is the value of x?

Statement 1: An apartment on the lower floor rents for $150 more per month than an apartment on the upper floor.
In other words: (rent PER UNIT on the lower floor) = (rent PER UNIT on the upper floor) + 150
Substitute values to get: x = 0.75x + 150 you may already recognize that we can solve this equation for x. But let's complete our work....
Subtract 0.75x from both sides to get: 0.25x = 150
Solve: x = 150/0.25 = 600 (i.e., the monthly rent on the bottom floor is $600)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are 6 more apartments on the upper floor than on the lower floor.
In other words: (number of apartments on upper floor) = (number of apartments on lower floor) + 6
In other words: z = y + 6
Let's combine this information, with the equation we determined with the given information (xy + 0.75xz = 15,300)

Replace z with y + 6 to get: xy + 0.75x(y+6) = 15,300
Expand: xy + 0.75xy + 4.5x = 15,300
Simplify: 1.75xy + 4.5x = 15,300
Factor to get x(1.75y - 4.5) = 15,300
As you might imagine, there are many possible values of x and y that satisfy this equation, which means we can't determine the value of x
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Bunuel VeritasKarishma
Is it only me or someone who is thinking that Statement 2 is illogical to begin with??

If we are saying that it is a two-story complex, which basically means every building has two floors only, one upper and one lower. Then how is it possible that there will be more UF's than LF's ? If it would have been the other way around , i.e. LF > UP, that would have made some sense.

Or, Am i missing something here ?

How about the possibility that there is a large covered parking space on the lower floor and apartments above it or perhaps the office of apartment complex on the lower floor? There could be many reasons why there may be more apts on the upper floor.

The way I tackled this was, and please correct me if I was wrong in my approach.


This was the question, the each told me that all we needed to find was the cost of one apartment.

Statement 1 - Gives us 25% of the rent. Thus adding 75% + 25% gives us the entire rent and the answer.
Statement 2 - Is irrelevant because we need "Each" apartment's rent cost, not the total or sum.

Felt confused as though I missed something, so maybe someone can let me know here. I think I tackled it logically.

let lower floor rent = \(R\)
upper floor rent = \(0.75R\)
lower floor apartments = \(x\)
upper floor apartment = \(y\)

Therefore \(0.75Ry + Rx = $15,300\)

(1) An apartment on the lower floor rents for $150 more per month than an apartment on the upper floor.

\(0.75R + $150 = R\)

\(R = $600\)

SUFFICIENT.

(2) If there are six more apartments on the upper floor than the lower floor:

\(y = x + 6\)

\(0.75R(x+6) + Rx = $15,300\)

We still have two variables in one equation; INSUFFICIENT.

Answer is A.

KarishmaB Bunuel ScottTargetTestPrep, can we use numbers to solve this such as:

Rent of Upper Floor = 100
Rent of Lower Floor = 75% of 100 = 75
Number of Upper Floor Apartments = x
Number of Lower Floor Apartments = y

 
 No, the question asks, "What is the monthly rent on each apartment on the lower floor?" and you assume from the beginning that it's $100, by doing so you are answering the question with your assumption. Additionally, the ratio you use there is incorrect. "Each apartment on the upper floor rents for 75 percent as much as each apartment on the lower floor" implies that if each apartment on the lower floor rents for $x, then each apartment on the upper floor rents for $0.75x, not vice versa. So, for example, $100 for the first floor and $75 for the second floor.

Am I missing something here? But which part of the question indicated that the rent of each room on either floor is the same?

 
The question says that ­each apartment on the upper floor rents for 75 percent as much as each apartment on the lower floor, implying that rents are the same within each floor level.