#21 - Local, Could Be True

[Administrator]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?f=107&t=7219)

The correct answer choice is (B)

The stem establishes that exactly three subzones are designated for each use (H, I, R) for a total of nine designated subzones. Since no zone contains three H subzones, we can begin our analysis by separating the three H subzones into two groups (regardless of the actual development zones they are in):

oct12_game_4_#21_diagram_1.png

Second, consider the designation of the three I subzones. Due to the I H rule, we can infer that all three I subzones must all be designated within the only zone that does not contain any H’s, an inference that eliminates answer choice (A):

oct12_game_4_#21_diagram_2.png

Third, recall that no more than 1 R is allowed in any zone containing an H subzone (third rule), and so at most 2 R’s can be distributed between the zones containing H. Therefore, at least one R must be added to the group of three I subzones:

oct12_game_4_#21_diagram_3.png

Next, we need to comply with the first rule of the game, which prohibits one of the zones (Z1) from containing any R subzones. Clearly, then, the two unassigned R subzones cannot be evenly split between the zones containing H’s: if they were, then each of the three groups would contain an R subzone in violation of the first rule. Additionally, the two remaining R’s cannot both be added to either zone containing an H, in compliance with the third rule. Accordingly, one of these R’s must be added to the group of 3 I’s and 1R, eliminating answer choice (D):

oct12_game_4_#21_diagram_4.png

Finally, let’s examine the placement of the remaining R. According to the last rule, no zone can contain an I subzone along with 3 R subzones. Therefore, the remaining R cannot be added to rightmost of the three vertical groups above, and must instead be added to one of the remaining two groups, eliminating answer choice (E):

oct12_game_4_#21_diagram_5.png

While we cannot determine exactly which development zone each block corresponds to, it is clear that the zone containing I subzones must be either Z2 or Z3. This eliminates answer choice (C), leaving us with answer choice (B), which could be true and is therefore correct.

[Lsatcat]

Dear instructors:

I was able to get through most of the questions in section 3, game 4 (questions 18-23) by applying the rules to each question. However,
I got stuck on question 21 and was hoping you might have suggestions as to how I might approach that question efficiently.

Many thanks!

[Jason Schultz]

Hi lsatcat,

The Millville zoning game is an undefined grouping game, and what hung me up are the confusingly named "zones" and "subzones." I find it helped to visualize it better if you analogize zones to neighborhoods, and subzones to streets. With that in mind, you have (I)ndustry, (R)etail, or (H)ousing on each street, subject to the rules on what can be in each neighborhood.

Question 21 is a double local rule question - the question itself gives you one local rule (You have RRR, HHH, and III to place) and then gives you another local rule in each question to see if you can create a solvable game.

There is no shortcut to this, unfortunately, so it's best to save this question for last in the section to avoid burning time for the other ones. However, since you are looking for any setup which creates a legal solution you can stop and pick that answer once you've found it without continuing. That answer is B.

A is out because the local rule requires you to place 3 Housing streets. With "exactly" one Industrial street accounted for in Z3, you cannot place the Houses without stacking all three of them together (violating rule 2) or putting them with an industrial (violating rule 4).

C is out because without the ability to place a retail in Z1 (rule 1) or a House (rule 4), you cannot fill out the game without having two Retails with a House (rule 3).

D is out because with "exactly" one Retail on Z2, that means the other two are on Z3 and there's nowhere to put the Houses.

E is out because three Retails together prevent you from adding an Industrial (rule 4) or a house (rule 3), leaving you with no way to place the other three Houses and Industrials.

[Blueballoon5%]

Hello, I got this question wrong with the phrasing of the word "exactly." I interpreted "exactly" in answer choice B to mean that ONLY 2 housing uses occupied this space. Please let me know why this isn't the case.

Thank you!

[Adam Tyson]

"Exactly" can mean only, but it may not, depending on the use and context.

"I have exactly one option" means I have only one option.

"I have exactly two dogs" means I have only two dogs, but it does NOT mean I have only two PETS.

It's the latter that is causing you a problem here, I suspect. In answer B, "Exactly two subzones in Z2 are designated for housing" does not mean that those must be the ONLY subzones in that zone. There could also be a subzone designated for retail. The "exactly" applies to Housing, but it does not apply to things other than housing.

Don't swap the word "only" for the word "exactly" and you won't have that problem. Just treat that word as meaning exactly what it means - that is the exact number, no more and no less, of the thing mentioned, which tells you nothing about any other things (like other pets or other subzones, etc.)

Keep at it, Blueballoon5%!