Development planners

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success1111: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Apr 19, 2009 11:07 pm

by success1111 » Tue May 05, 2009 1:22 am

Development planners determined the number of new housing units needed in a certain area by using the formula H = kJ, where H is the number of new housing units needed in the area, J is the number of new jobs to be created in the area, and k is a constant. How many new housing units did the planners determine were needed?

(1) The number of new jobs to be created was 60,000.

(2) According to the formula used by the planners, if 37,500 jobs were to be created, then 7,500 new housing units would be needed

Trust but verify.

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Source: Beat The GMAT — Data Sufficiency | Tue May 05, 2009 1:22 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Tue May 05, 2009 3:13 am

Statement 1:

J = 60,000. However, we don't know the value of k. Insufficient.

Statement 2:

if J = 37,500, then H = 7500. We can calculate the value of k. However, we still lack the actual number of new jobs that were created. Insufficient.

Both statements together:

we know k from statement 2 and we know J from statement 1. Hence, we can use H=kJ to solve for H. Sufficient.

Choose C.

___________________

A different way to think about this is to picture the relationship between H and J on the xy-plane. Let's say H is the y-axis and J is the x-axis. With this, you will see that H=kJ forms a straight line starting from the origin (if J=0, then H must equal 0, regardless of k) and that k is essentially the slope of this line.

In statement 1, with the value of J known, you cannot determine H unless you know the slope. In statement 2, you can construct the H=kJ line since you know a second point (37500, 7500). However, you don't know the actual number of jobs (J) that was created. From this you can conclude that both statements are required to answer the question.

-BM-

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success1111: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Apr 19, 2009 11:07 pm

by success1111 » Tue May 05, 2009 7:29 pm

bluementor wrote:Statement 1:

J = 60,000. However, we don't know the value of k. Insufficient.

Statement 2:

if J = 37,500, then H = 7500. We can calculate the value of k. However, we still lack the actual number of new jobs that were created. Insufficient.

Both statements together:

we know k from statement 2 and we know J from statement 1. Hence, we can use H=kJ to solve for H. Sufficient.

Choose C.

___________________

A different way to think about this is to picture the relationship between H and J on the xy-plane. Let's say H is the y-axis and J is the x-axis. With this, you will see that H=kJ forms a straight line starting from the origin (if J=0, then H must equal 0, regardless of k) and that k is essentially the slope of this line.

In statement 1, with the value of J known, you cannot determine H unless you know the slope. In statement 2, you can construct the H=kJ line since you know a second point (37500, 7500). However, you don't know the actual number of jobs (J) that was created. From this you can conclude that both statements are required to answer the question.

-BM-

OA is C. This is the another approach i was looking for.Thanks a lot

Trust but verify.

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