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If a building has 6,000 square meters of floor space

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If a building has 6,000 square meters of floor space

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If a building has 6,000 square meters of floor space, how many offices are in the building?

(1) Exactly 1/4 of the floor space is not used for offices.
(2) There are exactly 20 executive offices and each of these occupies 3 times as much floor space as the average for all of the remaining offices.

E

Source: Official Guide 2020

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Let the number of offices in the building be x
How many offices are in the building I.e What is the value of x

Statement 1
Exactly 1/4 of the floor space is not used for Offices.
This means that 3/4 of the floor space is used as offices.
$$\frac{3}{4}\cdot6000=4500 m^2$$
But there is no information regarding the average area of the offices. Hence statement 1 is INSUFFICIENT.

Statement 2
There are exactly 20 executive offices and each of these occupies 3 times as much as floor space as the average for all the remaining offices.
Let the average area for all the non executive offices = y
Average area of the executive offices = 3y
There is no information about the floor space used for offices in the question, hence statement 2 is NOT SUFFICIENT.

Combining statements 1 and 2 together.
$$20\cdot3y+\left(x-20\right)\cdot y=4500$$
$$y\left(40+x\right)=4500$$

If y=45, then x=60
If y=18, then x=210
Information given is not enough to arrive at a definite value, both statements combined together are NOT SUFFICIENT.

$$Answer\ is\ Option\ E$$

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Hi All,

We're told that a building has 6,000 square meters of floor space. We're asked for the number offices in the building. Since we're given the total floor space, to answer this question, we'll need to have some really specific data about the respective size(s) of the offices. This question can be solved with a bit of logic and TESTing VALUES.

(1) Exactly 1/4 of the floor space is NOT used for offices.

With the information in Fact 1, we know that 3/4 of the office space (re: 3/4 x 6000 = 4500 square meters) is used for office space, but we don't know the size(s) of the offices, so we don't know how many there are.
Fact 1 is INSUFFICIENT

(2) There are exactly 20 executive offices and each of these occupies 3 times as much floor space as the AVERAGE for all of the remaining offices.

Fact two gives us a ratio between 1 executive office and the AVERAGE of the remaining offices, but we don't know how many "other" offices there actually are - and no actual areas to work with.
Fact 2 is INSUFFICIENT

Combined, we know...
-Exactly 1/4 of the floor space is not used for offices (re: 4500 square meters of space).
-There are exactly 20 executive offices and each of these occupies 3 times as much floor space as the AVERAGE for all of the remaining offices.

Combined, we still don't have much information to work with.
IF....
-Each executive office is 150 square meters, then the average of the remaining office is 50 square meters - and we have 20 executive offices and 30 other offices (since 20x150 + 50x30 = 4500) and the answer to the question is 20+30=50.
-Each executive office is 180 square meters, then the average of the remaining office is 60 square meters - and we have 20 executive offices and 15 other offices (since 20x180 + 15x60 = 4500) and the answer to the question is 20+15=35.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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