Bunuel wrote:
In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment on the lower floor. If the total monthly rent is $15,300 when rent is collected on all of the apartments, what is the monthly rent on each apartment on the lower floor?
(1) An apartment on the lower floor rents for $150 more per month than an apartment on the upper floor.
(2) There are 6 more apartments on the upper floor than on the lower floor.
DS20357
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 = 15,300Target 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) = 15,300Expand: 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
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