## In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment on

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### In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment on

by BTGmoderatorDC » Mon May 22, 2023 1:17 am

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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

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### Re: In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment o

by GMATJourneyman » Fri May 26, 2023 6:37 am

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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?

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### Re: In a two-story apartment complex, each apartment on the upper floor rents for 75 percent as much as each apartment o

by Brent@GMATPrepNow » Fri May 26, 2023 5:55 pm

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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
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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