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

Let \(n\) be the number of offices in the building. The original question: \(n=?\)

1) We know that the floor space used for offices is \(\frac{3}{4}\cdot 6000=4500 \ m^2\), but no information is given about the average area of the offices. Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know that the number executive offices is 20 and that the average area of the executive offices is \(3A\) if the average area of the non-executive offices is \(A\), but no information is given about the floor space used for offices in the building. Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

1&2) We can set up an equation about the floor space used for offices and can test possible cases.

\(20\cdot 3A+(n-20)\cdot A=4500\)
\(A(40+n)=4500\)

\(n=60\) if \(A=45\). However, \(n=210\) if \(A=18\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

Answer: E

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:

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

Hola amigos

The number of offices = \(x\), so what is \(x\)?

1. Exactly \(1/4\) of the floor space is not used for offices.
Since unused part is \(\frac{6000}{4} = 1500 m^2\), \(4500 m^2\) is available for offices. However we don't know the average area the offices take and thus not able to find \(x\).
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.
Area of ex. offices = \(3y\)
Area of re. offices = \(y\)
So \(20*3y + (x - 20)*y\). Neither \(x\) nor \(y\) is known, thus we can't find \(x\).
Insufficient

1 + 2. \(20*3y + (x - 20)*y = 4500\). Still neither \(x\) nor \(y\) is known, thus we can't find \(x\).
Insufficient

The answer is E

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• A building has 6000 square meters of floor space.

We need to determine

• The number of offices present in the building.

As in the question statement, we have no other pertinent information about the building or the offices, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information present in statement 1, exactly ¼ of the floor space is not used.

• Therefore, used floor space = [6000 – (6000 × ¼)] = 4500 square meters

However, in the used 4500 square meters floor space, how many offices are present is not known.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information present in statement 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.

• However, from this statement, we cannot determine whether these offices occupying the whole 6000 square meters space or not.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Combining both statements, we get

• In a span of 4500 square meters, 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.

Although we can say there are 20 executive offices, we cannot determine the number of non-executive offices present in the floor space.

Hence, the correct answer is option E.

Answer: Option E

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