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OG DS

This topic has 1 expert reply and 1 member reply

OG DS

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Of the 230 single-family homes built in City X last year. how many were occupied at the end of the year?

(1) Of all single-family homes in City X, 90 percent were occupied at the end of last year.
(2) A total of 7,200 single-family homes in City X were occupied at the end of last year.
E

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Hi,

Of the 230 single-family homes built in city X last year how many were occupied at the end of the year?

Looking at both the statement, we may think that they are sufficient, see right away but the statements only give us information about the occupancy of single-family homes in city X. None of the
statements talks about the occupancy of the newly built homes.

Therefore, even by combining both options we cannot reach the answer.

So, the answer is E.

Just to add more clarity. Let’s look this by forming equations.

From the question we get:

Total Homes in City X = [Homes built before last year] + 230(home built last year)

We are asked how many of the 230 homes were occupied.

So we also have equation:

230 = [Occupied Homes Built last year] + [Unoccupied Homes Built last year]

Question: Occupied Homes built last year?

Statement I is insufficient:

Of all single-family homes in City X, 90 percent were occupied at the end of last year.

It talks about the entire single family homes, we want something very specific which is built last year.

Total Homes in City X = Total Occupied (90%) + Total Unoccupied (10%)

No information about the newly built homes last year.

So Insufficient.

Statement II is insufficient:

A total of 7,200 single-family homes in City X were occupied at the end of last year.

Similar to statement I, it talks about the entire single family homes.

Total Homes In City X = 7200 + Total Unoccupied

Insufficient.

Even combining these two statements it is impossible to get any information on the homes built last year to answer the question.

So the answer is E.

Hope this helps.

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GMAT/MBA Expert

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Hi rashedhbs,

To start, you would like receive more of a response if you make sure to post your questions in the proper forums. For example, the DS forum can be found here:

https://www.beatthegmat.com/data-sufficiency-f7.html

We're told that 230 single-family homes that were BUILT in City X last year. We're asked for the number (of those 230) that were occupied at the end of the year. This question can be approached in a number of different ways. It's more of a 'logic problem' though, so you can beat it with some basic notes and TESTing VALUES (as needed).

1) Of all single-family homes in City X, 90 percent were occupied at the end of last year.

From the prompt, we don't know how many single-family homes existed BEFORE the 230 additional single-family homes were built. Thus, we have no way to determine what the TOTAL number of single-family homes was - nor what 90% of that number would be - nor how many of the 230 new single-family homes were occupied.
Fact 1 is INSUFFICIENT

2) A total of 7,200 single-family homes in City X were occupied at the end of last year.

Fact 2 gives us an 'absolute' number of single-family homes that were occupied, but we have no way of knowing how many of the 230 single-family homes that were built last year are included in that 7200.
Fact 2 is INSUFFICIENT

Combined, we know...
-Of all single-family homes in City X, 90 percent were occupied at the end of last year.
-A total of 7,200 single-family homes in City X were occupied at the end of last year.

With these two pieces of information, we can determine the TOTAL number of single-family homes in the city. (.9)(X) = 7200 --> X = 8000. This total includes the 230 additional homes that were built. However, we still have no idea how many of THOSE homes were occupied, so the answer to the question could be anything from 0 to 230.
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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