Generically speaking, there are four types of analytical reasoning problems. Having said this, it is important for the examinee to understand that some analytical reasoning problems are combine problem types.
The problem types are as follows:
- Ordering: These problems require the examinee to place the "players" of the question in a certain sequence.
- Selection: These problems require the examinee to compose a smaller group of "players" from a larger group based on certain criteria.
- Allocation: These problems require the examinee to allocate the provided "players" into identified groups.
- Connection: These problems require the examinee to connect some of the "players" in the set of conditions based on some criteria or characteristic.
Ordering
- As the name implies, analytical reasoning
- ordering problems require the examinee to place the "players" provided the set of conditions in a particular sequence.
- The ordering problem could require the examinee to place people, places, or things in sequence.
- Furthermore, the structure of the sequence required by the question could be a straight line, a circle, or some other configuration.
- Because of the broad possibilities posed by analytical reasoning ordering problems examinees are wise to read the set of conditions very carefully and establish what can be definitively known. These facts will eventually form the foundation for answering the various questions based on the set of conditions.
Examinees will be expected to provide information on some variation of the following requests in a given analytical reasoning (games) problem:
- Determine the location within the sequence of a particular player;
- Identify all potential positions within the sequence that a particular player may occupy;
- Identify all potential positions within the sequence that a particular player may not occupy;
- Determine which players may or must be next to/across from each other in the sequence;
- Determine which players cannot be next to/across from each other in the sequence;
- Identify all players that must come earlier or later in the sequence than a given player;
- Identify the number of positions separating two players within the sequence.
Now that the basics have been fleshed out, consider the following example:
State Q has eight prominent towns within its borders. These towns are 1, 2, 3, 4, 5, 6, 7, and 8. There are five routes, A, B, C, D, and E, available in state Q that connect towns 1 through 8. The following is a description of the five routes:
Route A connects 1 and 4 and passes only through 3.
Route B connects 2 and 4.
Route C begins at 2 and travels to 7 passing through 5.
Route D connects 5 and 8.
Route E connects 6 and 7.
Where two towns are connected by a route, no other town is on that route.
Examinees will quickly notice that there is a great deal of information provided in analytical reasoning (games) problems. The above problem is a typical type of question that appears on the LSAT. Most experts advise that the best approach to tackling these problems is to transform the information provided in the set of conditions into a picture format so that the picture(s) can be revisited when answering the various questions based on the set of conditions. This strategy would greatly increase an examinee's odds of answering many of the types of questions that are likely to arise. Consider the following question based on the above set of conditions
1. Which two towns can be reached directly from more than one other town?
Trying to answer this question having only read the set of conditions might seem impossible. With all of the routes drawn out, it is easy to see that towns 3, 4, 2, 5, and 7 can all be reached directly from more than one other town.
Selection
The common thread uniting all analytical reasoning selection problems is that the set of conditions will provide the examinee with a group of "players" out of which a smaller group must be selected. Like all of the analytical reasoning problems, the topics utilized in these selection problems can run the gamut.
Another important feature for examinees to understand when addressing an analytical reasoning selection problem is that a careful initial reading of the set of conditions is critical. Like all analytical reasoning problems, selection problems will provide the examinee with a list of players and certain facts or criteria unique to each player. Along with this introduction, the parameters of the problem will be introduced. For example, the problem may read like this:
Boss must select three managers to attend the seminar.
Analytical reasoning selection problems will require the examinee to answer one or more of the following questions:
- Identify the players that must be selected based on the criteria/facts provided;
- Identify the players that are eligible for selection based on the criteria/facts provided;
- Identify the players that are ineligible for selection based on the criteria/facts provided;
- Assuming some specific player or players are selected, identify the players that must be selected;
- Assuming some specific player or players are selected, identify the players that cannot be selected;
- Given certain facts, identify the number of players eligible for selection.
Having established the background for analytical reasoning selection problems, consider the following example:
There are five friends that all live in the same neighborhood. Their names are Amy, Betty, Cathy, Dora, and Eve. Five parties are planned in the neighborhood for the coming season which all of the aforementioned friends can attend, subject to the following restrictions:
If Amy attends a party, then Dora cannot attend that party.
If Betty attends a party, then either Cathy or Dora, but not both, attends that party.
If Cathy attends a party, then Eva does not attend that party.
If Eva attends a party, then either Amy or Betty, but not both, attends that party.
It is easy to see that the examinee is bombarded with a glut of information right from the start in analytical reasoning selection problems. Most authorities agree that the key to addressing these problems is to actively read the set of conditions and determine the various relationships. Depending on what works best for the examinee, it may prove helpful to draw out certain pictures that denote players that are restricted from being together, forced to be together, or can be together. This may assist the examinee to speedily tackle typical questions that flow from the set of conditions. For example, utilizing the set of conditions above, consider this question:
If Dora attends one of the parties, then which one of the following could be a complete and accurate list of the other friends who could also attend that party?
Without having established some method of memorializing the various restrictions provided in the set of conditions, the examinee may find that they must revisit the set of conditions and waste precious time.
Allocation
Analytical reasoning allocation problems will require the examinee to answer one or more of the following questions:
- Identify which players must be included in a certain group/category;
- Identify which players could be included in a certain group/category;
- Identify which players are ineligible for inclusion in a certain group/category;
- Determine the number of players that are to be placed in a certain group/category; and
- Determine which players have to be, cannot be, or could be paired with other specific players.
Connection
Analytical reasoning connection problems will require the examinee to answer one or more of the following questions:
- Identify which player(s) must connect with the various characteristics;
- Identify which player(s) could be connected with the various characteristics;
- Identify which player(s) are excluded from connecting with the various characteristics;
- Identify which players must, must not, or can, share characteristics with the other players.
Consider the following analytical reasoning (games) connection problem:
There are four children: Will, Xena, Yarba, and Zoe. These children are afraid of the following creatures: snakes, lizards, and spiders consistent with the following:
Each of the children is afraid of at least one of the creatures;
No child is afraid of all three creatures;
At least two, but not all four of the children are afraid of snakes;
If Will is afraid of a creature, then Xena is afraid of that creature;
If a child is afraid of snakes, then that child is also afraid of lizards;
Yarba is afraid of snakes.
From the problem posed above it is easy to see how even the most diligent examinee can get very crossed up before even reading the specific questions associated with the set of conditions. Again, the key for making sense of analytical reasoning (games) connection problems is to first identify the players. In this case that would be Will, Xena, Yarba, and Zoe. The next step is to identify the characteristics. In this case, that would be the creatures that cause the various children to be frightened, or snakes, lizards, and spiders. It is very helpful for examinees to chart out how the characteristics apply to each player. It is important to note that the set of conditions may give direct correlations between players and the characteristics (e.g. Yarba is afraid of snakes) or indirect correlations between players and the characteristics (e.g. If Will is afraid of a creature, then Xena is afraid of that creature).
