Official ExplanationStep 1: Understand the Prompt and QuestionFirst StatementAccording to the forecasts, the team with the median sales in Q1 will also have the median sales in Q2The statement says that the same team has the median sales in both Q1 and Q2. Glance back up at the blurb; how many sales teams are there? Nine. (You don’t have to count—the blurb says that there are nine teams. Always check the blurb first before you try to count the total number of rows; if it’s a longer table, chances are the blurb will tell you.)
Step 2: Plan Your ApproachTo find the median, the numbers have to be listed in order, so you’re definitely going to sort this thing. Finding the median for Q1 will be easy, since the Q1 column shows the actual sales figures.
Q2, though, is trickier, as it shows only the percentage increase or decrease from Q1. You do have a calculator, so maybe you just have to calculate the forecasted sales for each sales team in Q2? There are nine rows. That’s a lot of work. So stop! Don’t do annoying math. This is why you Plan before you Solve.
First, sort by Q1 sales to find that median, then examine the data to think about the best approach for the Q2 data.
Step 3: Solve the problemHere’s the table sorted by Q1 (and without Q3 or Q4, since they don’t matter for this statement):
Attachment:
2.jpg [ 72.71 KiB | Viewed 13996 times ]
The median for Q1 is the fifth one from the top or the bottom: Team G. Go back to your Plan stage for a minute and remind yourself of the question: Does Team G have the median for both Q1 and Q2? In other words, does Team G stay in the fifth position or does its position change? Team G’s sales will decrease a little bit, but not that much—a little over 5%. The numbers for each team are far enough apart that you can use benchmarks to estimate the change:
10% of $2,140 = $214
Half of that = 5% = $107
$2,140 – $107 ≈ $2,000
Next, eyeball the data to see which other teams might change positions relative to Team G. (To eyeball is to look and think logically about the data; you won’t be doing any actual calculations, even at an estimation level.)
Teams D, A, and B are already below $2,000 in Q1 and they all decrease further, so they will still stay below Team G in the Q2 list. No need to calculate anything for them.
Team C, by contrast, increases, so it could jump past Team G. You might have to do some calculations, so jot down Team C on your scratch paper as a reminder. Next, take a look at the teams that have Q1 sales greater than those of Team G. They are already higher than $2,000 and all four increase in Q2, so they will stay above Team G in that quarter.
The only possibility is that Team C will swap places with Team G. Eyeballing the data saves a lot of time that would have been wasted with unnecessary calculations! Jot down the numbers you need, then figure out how to do the calculations.
Finally, plug the calculations into your calculator to solve:
Attachment:
1.jpg [ 38.06 KiB | Viewed 13427 times ]
Team C does indeed pass Team G in Q2, so Team C is now the team with the median sales volume. Is it not true that the same team is in the median position for both quarters.
The correct answer for statement 1 is False.Here is statement 2:Of the teams that are projected to see a quarterly increase in Q3, more than half are expected to see an additional quarterly increase in Q4.The statement says that the same team has the median sales in both Q1 and Q2.
This time, the statement focuses on Q3 and Q4. When you see something like of the teams that (fall into a certain category), the statement is giving you a qualifier: It wants you to consider only a subset of the categories given in the table.
In this case, the desired subset is those teams that will have a Q3 increase. You don’t technically have to sort in order to see which teams have positive percentages in Q3, but do so anyway. Sorting by Q3 will group those teams together so that you don’t inadvertently include teams that you don’t want. Before you do that, though, jot down what the statement wants you to find.
Here’s one way to do that:
Attachment:
4.jpg [ 39.82 KiB | Viewed 13306 times ]
Note it in any way that makes sense to you. Here’s the data sorted by the Q3 column:
Attachment:
5.jpg [ 95.83 KiB | Viewed 13290 times ]
Only five of the teams will have a quarterly increase in Q3: Teams G, E, F, H, and A. Of just those teams, three also have an increase in Q4: Teams G, E, and F.
Therefore, three out of five of the teams increase in both quarters. This is greater than 50%, so this statement is true.
The correct answer for statement 2 is True.Here is the third statement:The number of teams projected to see a quarterly decrease in both Q2 and Q3 is greater than the number of teams projected to see a quarterly decrease in both Q3 and Q4
This is very similar to statement 2: You’re looking for two adjacent quarters with the same trend. You have to do it for two groupings this time, not just one. Jot this down in a form that makes sense for you; here’s one way to do that:
Is # (Q2 and Q3) ↓ more than # (Q3 and Q4) ↓ ?
Make sure to evaluate each part separately so that you don’t, for example, mistakenly carry over Q2 data into the examination of Q3 and Q4. And you’ll again minimize your chances of a careless error if you sort as you go.
First, sort by Q2:Attachment:
6.jpg [ 67.48 KiB | Viewed 13108 times ]
Two teams are projected to have a decrease in both Q2 and Q3: Teams B and D.
Next, sort by Q3:Attachment:
7.jpg [ 71.4 KiB | Viewed 13049 times ]
Again, two teams are projected to have a decrease in both Q3 and Q4; Teams B and D again.
It is not the case that the number of teams with decreased sales in both Q2 and Q3 is greater than that in both Q3 and Q4.
The correct answer for statement 3 is False.