Hi!
Dimochka presents a great mathematical explanation, but let's focus on efficiency, remembering one key rule:
To get the point on a DS question, you don't need to actually answer the question - you just need to determine whether it's possible to do so.
Keeping this rule in mind will save you a lot of time in DS!
Along those lines, let's tackle the question, starting with Step 1 of the Kaplan Method for DS: analyze the stem.
Each employee on a certain task force is either a manager or director. What percent of the employees on the task force are directors?
We see a "what" question, so we know we're being asked for a value. We think: for sufficiency, we need one and only one possible value.
We also note that we have a percent question, so we jot down the relevant formula:
% = part/whole = #directors/#(directors+managers)
Next, we think about THE most powerful rule in data sufficiency: # of equations vs # of unknowns. Right now we have 1 equation and 3 unknowns. What do we need to solve? 2 more distinct and linear equations OR 1 equation that gives us the exact ratio in the equation above.
Step 2 of the Kaplan Method for DS: Evaluate the Statements
(1) we can certainly turn this statement into a linear equation. Let's go through a short checklist:
- does it introduce any new variables? NO
- is it identical to the original equation? NO
- does it give us the exact ratio we want? NO
only 1 standard equation, but we needed 2... insufficient.
(2) identical kind of statements as (1); (1) was insufficient, so this definitely will be as well.
TOGETHER: 2 distinct linear equations + the original equation means that we have 3 equations for our 3 unknowns... SUFFICIENT, choose (C)!
* * *
As an aside, if we wanted to solve, a graphical approach is the fastest way to do so for this type of weighted average question.
A fancy word for the method we're about to use is "alligation" (I just learned that it had a special name a little while ago!). Of course, understanding how it works is far more important to knowing what it's called.
When you have 2 subgroups and an overall average, plot the subgroup averages and the overall average on the number line. Using the info from both statements, we have:
Managers ---------- all ----------------------------- directors
Next, write in the known information:
Managers ------5000------ all ---------------15000-------------- directors
Finally, you can now write out the ratio of the parts:
Managers/Directors = 15000/5000 = 3/1
and we quickly see that directors make up 1 in 4 parts, i.e. 25% of the whole.
In generic terms, the ratio always works out as:
group 1 average---------------x-------------overall average--------y--------group 2 average
group 1/group 2 = y/x
This method is extremely useful both in problem solving and data sufficiency!
