A map game requires the arrangement of the game’s elements on a plane according to their relative compass directions (north, south, west, and east). These games, like the circular games we just looked at, are similar to the linear spatial arrangement games we’ve already studied. Like those, we are ordering elements according to their relative positions. The complication is that there are two criteria for ordering: a north-south component and a west-east component. These two ordering processes must be considered simultaneously, which is why these problems are challenging.

 

Summary of strategy for map games

  • Create a roster.
  • Map games require the arrangement of elements onto a plane according to their relative compass directions. Create a quadrant with north at the top, south at the bottom, west to the left, and east to the right.
  • Determine which element to select as your central element – it should be the element for which you have the most information. Place the central element at the center of your quadrant map.
  • Next, place the other elements on the map for which the relationship to the central element is known. Be extremely careful to differentiate between terms such as “further north” and “directly north.”
  • Place on the map any additional elements which relationship to at least one other element is known. Indicate this relationship with an arrow.
  • Read the question and add any additional information to the map. When choosing an answer, be sure that you can draw a map that reflects the most information.

Let’s begin by working through a sample game.

Within a county, there are six cities, L, M, N, O, P, and Q. The location of these cities relative to each other is as follows: Q is further north than P. P is further west than O. L is further north than P. M is further east than P. N is further west than O.

Next LSAT: January 26

As with our previous game types, we can begin with the roster and then summarize the rules. (Roster = L, M, N, O, P, and Q.) Next, we are going to try to construct a diagram to enable us to solve this problem. First, however, we must be sure to read the premise and conditions extremely carefully and precisely. How about when Q is further north than P? Q is more north than P, but does it mean that Q is directly north of P? No. Q may be further west or east than P, and we cannot determine that from the information given to us. Like the circular arrangement games, map games often involve conditions that describe relative spatial arrangements, not fixed positions. We will construct a map that indicates the relative positions of the elements.

Well, according to our diagrams, there are only two open seats that would allow Ben and Antonia to be sitting next to each other. However, since we cannot know who is on which side, that is, whether Ben is to the right of Antonia or vice versa, we could place the two of them into either of the two open positions, creating two arrangements for each of our diagrams, for a total of four arrangements. Rather than creating two additional schemes, however, it may be more useful to simply add this information as A/B and B/A for the two seats. These terms represent the possibility that either A or B is sitting in one position and either B or A is in the second position.

Now that we have this information placed onto our diagram, let’s work through each answer choice one at a time, remembering that we are looking for the condition that must be true. Choice A places Antonia between Ben and Denise. Is this possible? Yes. Since we are looking for the condition that must be true, however, we must also see if we could arrange the elements in an alternate way. Here are two possibilities: the left diagram allowing the positioning described in choice A and the right diagram showing an arrangement in which this condition is not met:

Therefore, we can eliminate choice A.

In choice B, Ben is across from Carlos. Is this possible? Yes. Can we come up with an arrangement in which this condition is not met? Again, yes. We can see these two possibilities by looking at the previous diagrams, so we can eliminate choice B. In choice C, Carlos is between Felicity and Gavin. Is this possible? In looking at our diagram, we can see that this cannot work. Felicity and Gavin are directly across from each other; there are three seats in between them. In choice D, Ben is between Antonia and Denise. Again, by looking at the previous set of possible diagrams, we can see that this is a possible arrangement, though not the only arrangement we could construct. Therefore, we can eliminate choice D. In choice E, we are told that the empty chair is between Eduardo and Carlos. Is this possible? Can we place all the elements onto the diagram and have the empty chair between Eduardo and Carlos? Yes. Is it necessary to have this placement? In this case, the answer is yes. You can see this by looking at the above two diagrams. (It remains true if you place A and B together onto the original alternative diagram we created, as well.) Therefore, choice E is the correct answer because this arrangement must always be true.

Now that we have constructed this map, let’s look at the questions.

Question One

(1) A person leaving N and driving in a southwest direction on a single, straight road, might pass by which of the following cities, in the order given?

(A) M, L, O
(B) L, P, M
(C) L, M, Q
(D) O, M, P
(E) L, P, Q

If our map indicated exact locations, it would appear that the only other city that could be encountered on a southwest route from city N would be city P. This is not one of the choices. We know that it is west of O. A road leading from N in the southwest direction could never encounter O. We can eliminate all answer choices that include O, choices A and D. Next, let’s tackle the remaining answer choices, one at a time, using what we know about the relationships between P and the other cities.

Choice B offers L, P, and M. L is north of P, so encountering L before P would make sense if a person were to travel in a southwestern direction. If we look at our map, we see that M is east of P, not west. Thus, this linear sequence of cities would be impossible, and we can eliminate choice B. Next let’s look at choice C: Q, M, then L. This one does not contain any of our fixed elements, that is, it does not contain our central element, nor does it contain the other two elements for which we have relative location information.

Let’s look at the last choice, E, which has the sequence L, P, and Q. Again, let’s start by looking at the relationship between L and P. We know that L is north of P, which is consistent with L being encountered first. What about P and Q? We know that Q is actually north of P, which is not consistent with it being encountered after P on a southwestern route, and we can eliminate this possibility.

To confirm that choice C is correct, let’s see if we can rearrange the map to reflect the necessary route (southwest from N) while still maintaining the appropriate relationships between the central element, P, and the surrounding cities.

We can maintain the necessary relationships to P (and that of N to O, represented still by the arrow) and allow a southwestern route from N to contact these three cities in the order described in choice C.

To confirm that choice C is correct, let’s see if we can rearrange the map to reflect the necessary route (southwest from N) while still maintaining the appropriate relationships between the central element, P, and the surrounding cities.

We can maintain the necessary relationships to P (and that of N to O, represented still by the arrow) and allow a southwestern route from N to contact these three cities in the order described in choice C.

Question Two

(2) If city Q is located directly north of city N, then which of the following statements must be true:

(A) City P is further south than city O.
(B) City Q is further west than city P.
(C) City O is further east than city Q.
(D) City N is further north than city P.
(E) City L is further south than city O.

To begin addressing this question, first add the new information to the map; that is, we must either reposition city N or reposition city Q. When we do this, we must also draw an arrow indicating their known relative positions (that city Q is directly north of city N).

Does our new map indicate that Q is east of L? Or that Q is north of O? No. The only spatial relationships that we know of are the relationships of the cities and the relationships between N and O, and Q respectively. Keep in mind that the correct answer will reflect either a relationship described in the original conditions or it will reflect the new condition given in the question.

We know that Q is north of P, so Q is north of both N and P. From that, can we deduce anything about the relationship of N and P? No, so we can eliminate choice D for this reason. We do know that N is west of O. If Q is north of N, it too must be west of O (and O is east of Q). This is the correct choice, C, the only answer choice that describes a relationship that we can confirm as true given the information provided.

Next LSAT: January 26

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Prep Guide

Table of Contents  Chapter 1  Chapter 2  Chapter 3  Chapter 4  Ordering Games  Characteristic Games  Grouping Games  Networking Games  Spacial Games  Maps  Chapter 5