# If three subzones are designated for each use, then which one of the following is allowed?

on July 17 at 07:33AM

more efficient way to get to the right answer

it seems pretty inefficient to have to draw out every scenario presented in the answer choices, i don't see how that could be reasonably done in the amount of time alloted. it seems like a time suck. so is that the best strategy for answering this question? there isn't a more efficient method?

Shunhe on July 17 at 04:55PM

Hi @marissa,

Thanks for the question! So instead of just trying out each of the answer choices, I recommend taking the hypothetical and seeing what inferences you can draw from it, which will help you eliminate answer choices without trying them out. I’ll show you what I mean.

In this question, we’re asked to assume that three sub zones are designated for each use, and then asked what could be true. OK, well then let’s just do that! What has to follow if we make three sub zones designated for each use. Well, we know that the designations are talking about H, I, and R, so basically we know three sub zones are going to be for H, I, and R each (so we’ll have HHHIIIRRR).

OK, so we know there’s three zones. Where can we go from here? Well, we know that industrial sub zones are not allowed in any zone in which a sub zone is designated for housing; in other words, I and H can’t be in the same zone. We also know that no more than two sub zones for housing are allowed in any particular zone. Which means that since we have three sub zones for housing, there’s only two possible distributions:

2-1-0
1-1-1

But when you think about it, the 1-1-1 distribution isn’t possible, because I can’t be anywhere H is, so if H is in all the zones, then I can’t go anywhere in the game! So we know that the Hs have to be 2-1-0, and then the Is have to be in the remaining sub zone, (since they can’t be where H is). So we know that so far, we have (not necessarily in this order, and with the zones going horizontally)

I I I
H H
H

Now is there anything else we can get from this game? Well, we know that R can’t be in zone 1. So we also have to have a 2-1-0 for R. We can’t have a 3-0-0 distribution because we know that we can’t have more than one R whenever there’s an H, and we can’t have and I with three Rs. So we know that the two Rs have to go with I. So we know

I I I R R
H H
H

And then we just have to place one more R somewhere.

Now look at the answer choices. (A) can’t be true because the I’s have to all be in the same zone, (C)’s wrong because I and R are together but we can’t have Rs in Zone 1, (D)’s wrong because III goes with 2 R’s, and (E)’s wrong because we can’t have all three R’s together. Which leaves (B), and this is completely possible based on our diagram above. And that way we don’t have to go through and try out all of the answer choices.

Hope this helps! Feel free to ask any other questions that you might have.