Each of 15 branches of a regional department store chain are plotted

Question

8.jpg Each of 15 branches of a regional department store chain are plotted on the graph shown. The x-axis shows the change in variable cost for each branch during the first half of the year, and the y-axis shows the change in variable cost for that same branch during the second half of the year. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. Of the branches that saw an increase in variable costs during the period 7/2/2011 to 12/31/2011, the branch with the median change in cost during the period 1/1/2011 to 7/1/2011 had an approximate change in variable cost of GRAPH_1_PLACEHOLDER during the first half of the year. Approximately GRAPH_2_PLACEHOLDER of the branches showed a net decrease in costs for the entire period 1/1/2011 to 12/31/2011. -

rocky620 · Accepted Answer

Of the branches that saw an increase in variable costs during the period 7/2/2011 to 12/31/2011, the branch with the median change in cost during the period 1/1/2011 to 7/1/2011 had an approximate change in variable cost of___________during the first half of the year.

There are 9 branches, which saw and increase in variable cost in 2nd half (+ve Y-axis). Of those branches, the branch with the median change in cost during the 1st half will be the 5th one either form left or from right. We can visually see that its the top most data point in the figure. The Value (change in 1st half) is between 0 & -5. So, option B

A. -$10,000
  B. -$3,500  
C. $2,000
D. $7,500

Approximately___________of the branches showed a net decrease in costs for the entire period 1/1/2011 to 12/31/2011.

Kindly refer the image below:
There are 7 branches with and overall decrease in the entire period, 1/1/2011 to 12/31/2011, Which constitutes 46.67% of total number of branches.

A. 33%
  B. 47%  
C. 53%
D. 60%
E. 73%

kntombat · Answer

the answer to the second question is B. I wasn't able to solve the first question.

Sajjad1994 · Answer

Official Explanation

Statement 1:    –$3,500.   The problem first specifies that it is talking about only the branches that had an increase in variable costs during the second half of the year. This description corresponds to those points with a positive y-coordinate (i.e. above the x-axis).

There are 9 branches above the x-axis. From this group only, find the one with the median change in cost during the first half of the year (the x-axis). The median is the 5th data point from either end of the x-axis (the physical middle). Count over 5 from the left or 5 from the right; the median branch is the point at approximately (-3.5, 19). Because the change in variable cost during the earlier period is given by the x-coordinate (in thousands), the median branch experienced a change of  -3.5 × $1000 = -$3,500.

Statement 2:  47%.   To find branches with a net decrease in costs, it will help to understand what each quadrant represents.

Quadrant I (upper right): These branches had an increase over both periods (3 branches fall into this category).
Quadrant II (upper left): These branches had a decrease during the first period but an increase during the second (6 branches).
Quadrant III (lower left): These branches had a decrease during both periods (1 branch).
Quadrant IV (lower right): These branches had an increase during the first period but a decrease during the second (5 branches).

None of the branches that have an increase during both periods will have a net overall decrease, so ignore the branches in Quadrant I (3 branches). All branches that have a decrease during both periods will have a net overall decrease, so count all branches in Quadrant III (1 branch).

Now, address the more complicated situations—an increase in one period but a decrease in the other. To arrive at a net overall decrease, you need a larger dollar decrease than increase. For Quadrant II (decrease in first period but increase in second), the x-coordinate (period 1) must have a larger magnitude than the y-coordinate (period 2). This is the case for 3 points: (-7, 5.5), (-15.5, 5.5), and (-16, 0.5). For each of these points, the decrease outweighs the increase (do not calculate the actual values).

Finally, for Quadrant IV (decrease in the second period but increase in the first), the y-coordinate (period 2) must have a larger magnitude than the x-coordinate (period 1). This is the case for 3 points (2.5, -4.5), (0.5, -7.5), and (11, -17). For each of these points, the decrease again outweighs the increase.

A total of 1 + 3 + 3 = 7 branches out of the 15 have a net decrease. 7/15 is slightly less than 1/2 or 50%; 47% is the best estimate.

Alternatively, if you feel very comfortable with coordinate plane problems, you could find all the points satisfying the expression x + y < 0 (i.e. the sum of the changes is negative). Rearrange in order to graph: y < –x. Where does that line appear on the coordinate plane? This is the equivalent of graphing the line y = –x and then shading underneath that line. Any points underneath the line satisfy that inequality.

There are 7 points located below that line out of 15 total branches, so the best estimate is a little bit less than 1/2, or approximately 47%.

Answer: B and B

pudu · Answer

please someone explain the first problem. I'm unable to understand it.....

DmitryFarber · Answer

pudu

We can break the question into pieces.

1) We're asked to look at branches that had an increase in the 2nd half of the year. The explanation of the graph says that the y-axis represents the change in the 2nd half of the year, so the question is asking us to look at the entries above the x-axis. These all have positive y values, meaning that they had an increase in costs.

2) Out of that set, find branch with the median change in the 1st half of the year. There are 9 entries above the y-axis, and we want the middle one, so that's the 5th one. If you look at the highest-up dot, you can see that it has 4 to the left of it and 4 to the right, so it's the median.

3) Find that branch's change in costs for the first half of the year. In other words, find its x value. It's between -5 and 0, and the graph tells us we're counting in thousands of dollars. So the change in cost was around -$3,000. B is a match.

I hope that helps clarify, but please follow up if there's something that still doesn't make sense.

Hdatta001 · Answer

`can anyone explain the second problem?

cheshire · Answer

check the most helpful reply, it does a really good job of breaking it down.

Each of 15 branches of a regional department store chain are plotted

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Graphs and Tables (G&T) Questions

Each of 15 branches of a regional department store chain are plotted

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards