What would be the most efficient way to approach Q19?

These are tough questions, but definitely possible to master. After you play a binary grouping game, if the game didn't ask one of these questions, pose it to yourself for extra practice (or, if you were asked what's the maximum number IN, then work on the max OUT for a challenge).

For starters, we know we can put L in.

Then, we consider who is a "problem child" - i.e., who forces out a lot of other people. Here it's M, so force M out.

Now, with M out, let's see who is left: W S H P T. Except for T, each of those force out two, and are forced out by two. T is special in that it is related only to M. Since M is already out, let's throw T in. So now we have L and T in.

We're down to considering W S H P.

Let's look at who forces out M already - if we're going to use people who force out two others, we might as well choose the ones that force out M, since M is already out. So let's throw H and P in. That would mean we also have to toss out S and W.

That leaves us with L T H P in and everyone else out.

It's helpful to write out the game's roster for this to help you organize your thinking.

BTW, my diagram for this game looks a bit different than the one posted in that I always have the same element's IN and OUT across from each other. We decided a few months back to encourage students to do that across the board as it usually makes things easier to interpret.

Does that help.

that helped a lot. thanks!

A faster way to approach this problem might be:

You know that:

one of H/S, H/M, M/P, M/T, W/P, W/S, must be out.

The objective is to leave the least # of people out as possible.

Since leaving M out would allow, P,T, and W to possibly be in, the first member out should be M.

With M out, now you just have H/S, W/P, and W/S must be out.

Since leaving W out would allow P and S to be in, then W should be the next selected to be out.

Now that M, W, and H/S needs to be out and there are a total of 7 variables, it means that at the most, 4 variables can be in.

(D) is easily selected.