Data Sufficiency

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.


OA A

Source: GMAT Prep

BTGmoderatorDC wrote: ↑

Mon May 22, 2023 1:17 am

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.


OA A

Source: GMAT Prep

Let's denote:

L = rent for an apartment on the lower floor
U = rent for an apartment on the upper floor

We're told that each upper floor apartment rents for 75% as much as each lower floor apartment. That means U = 0.75L.

The total monthly rent collected is $15,300, so let's represent the total number of lower floor apartments as 'a' and the total number of upper floor apartments as 'b'.

Then we can write the equation: aL + bU = $15,300.

Now let's look at each statement individually:

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

This tells us that L = U + $150. We already know that U = 0.75L. So substituting U in the equation, we get L = 0.75L + $150. Solving for L, we find that L = $600. So we have the monthly rent for each lower floor apartment, making Statement 1 sufficient.

(2) There are 6 more apartments on the upper floor than on the lower floor.

This tells us that b = a + 6. But we still don't know how much each individual apartment rents for, making this information insufficient.

So, the answer is (A), Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Any experts have a faster approach?