single-family homes

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

single-family homes

by sanju09 » Fri Aug 27, 2010 5:31 am

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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.

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 27, 2010 5:31 am

niksworth: Legendary Member; Posts: 520; Joined: Mon Jun 14, 2010 10:44 am; Thanked: 70 times; Followed by:6 members

by niksworth » Fri Aug 27, 2010 7:06 am

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IMO E.

Statement 1 alone is insufficient to answer, we do not know how many single family homes are there in total in city X

Statement 2 gives the total occupancy of all single family homes, but it does not tell how many of them were built last year.

Combining the two together,
7200 single family homes were occupied last year which was 90% of the total single family homes. So total single family homes existing in City X = 7200/0.9 = 8000.

We still do not know that of the 230 of these 8000 homes built last year, how many were occupied. In fact there is no way to know this data from the given information. Hence the answer must be E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: single-family homes

by Scott@TargetTestPrep » Wed Jun 16, 2021 6:55 am

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sanju09 wrote: ↑
Fri Aug 27, 2010 5:31 am
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.

Solution:

Question Stem Analysis:

We need to determine the number of the 230 single-family homes built in City X last year that were occupied at the end of the year.

Statement One Alone:

Even though we know 90% of all single-family homes were occupied at the end of last year, we don’t know the number of the 230 newly-built single-family homes that were occupied at the end of the year. It’s possible that all 230 were occupied, none of them were occupied, or some of them were occupied. Statement one alone is not sufficient.

Statement Two Alone:

Even though we know 7,200 single-family homes were occupied at the end of last year, we don’t know the number of the 230 newly-built single-family homes that were occupied at the end of the year. It’s possible that all 230 were occupied, none of them were occupied, or some of them were occupied. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we can determine there were a total of 7,200/0.9 = 8,000 single-family homes in City X last year. However, we still can’t determine the number of the 230 newly-built single-family homes that were occupied at the end of the year. It’s possible that all 230 were occupied, none of them were occupied, or some of them were occupied. Both statements are not sufficient.

Answer: E

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