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shunheJanuary 8, 2020
Hi @claire_crites,
For guidance on this question: we need to find a pair of employees who can serve as managers together. There's a quick shortcut way to do this problem and there's a more thorough, longer way to do it. Let me give you the quick way first.
Note that there are rules pertaining to F and G, but nothing in the rules pertains to H, K, or L. This essentially means that for our purposes, H, K, and L are interchangeable. I like to mark when pieces don't have rules attached to them by writing out all the letters and circling the letters without rules. When multiple pieces don't have any rules attached to them, we can switch time around with each other and face no consequences. There's nothing that differentiates them in anyway. Now, we've gotten rid of (A) and (B). Notice that two of the answer choices involve G and one of the interchangeable pieces. (C) has G and K, and (D) has G and L. But K and L should be interchangeable, which means that these two answer choices are basically telling us the same thing. We know, however, that only one answer choice can be right, and so we can eliminate both of them and pick (E), which has two of the interchangeable parts. When using this tactic, make sure that the parts are truly interchangeable. It can definitely save you a lot of time though.
Now for the long way, where we actually walk through it. We've eliminated (A) and (B). Can G and K or L serve as managers together? We know that G supervise two employees, and that supervised employees hold different positions than supervisors. There are 5 total pieces, so if G supervises two of them, there could be 3 or 4 total layers (not necessarily in the following order, and people on higher layers supervise the layer directly beneath them):
President G Two supervisees of G Last person
President G + someone else Two supervisees of G
Ex hypothesi, G is a manager, so G isn't the president. We can only have one president, and G supervises exactly two employees, which accounts for four people (the president isn't supervised, so isn't one of the two employees G supervises). The last person is either on the same level as G or on their own level. If they're on the same level as G, then they can't be a manager since there's no one left to supervise, and the two employees G supervises can't be managers, since they don't have anyone to supervise, so we know that the last person has their own layer. There's 2 possibilities (since, once again, only the president isn't supervised):
President Last person G Two supervisees of G
President G Two supervisees of G Last person
In the first scenario, neither the two supervisees of G nor the last person can be managers because each supervised employee holds a different position than his or her supervisor. In the second scenario, the two supervisees of G can't be a manager for the same reason, and the last person can't be a manager because then they don't supervise anyone, but each manager supervises at least one employee. So we know that it can't be G and one of the others, so we can eliminate (C) and (D). Hope this helps!
