Logic games that require sequencing can be fully diagrammed before you start to answer any question. A typical fact pattern and list of constrains for a sequencing game follows.

**Logical game:**

Anna, Bill, Claire, Dave, Emily, Frank, and Gina are all working on their mathematics final. Each student hands his or her test to the professor at different times. The order in which their tests are submitted is governed by the following constrains:

Anna turns in her test before Bill.

Claire turns in her test after Bill.

Claire turns in her test before Dave.

Emily turns in her test after Dave.

Gina turns in her test before Emily and after Frank.

Frank turns in her test after Bill.

The technique that you should use to map out sequencing problems is very similar.

## Technique that you used to solve formal logic problems

**1.** Transcribe the Constrains. In a sequencing problem, the constrains can be arranged sequentially. For instance, “Anna turns in her test before Bill” can be transcribed as; A>B. One you have read through all seven constraints, transcribe them into symbols as follows:

**A 2.B 3.C<D**

When first transcribing the constraints, be careful to do two things. First, make sure that your “greater-than” signs consistently denote the same direction. Many test takers make careless errors by using a greater-than sign to represent “after” at the beginning of the problem and then switching to a “less-than” sign to represent “after” later in the problem. This is a serious mistake, so be sure to use a consistent ordering method in which you know the direction that each sign represents. Second, pay attention to “before “ versus “after” and to the use of the words not and sometimes. Test makers will throw in a “not after” or a “not before” just to try to confuse you. Also, they will mix up saying “before” and “after” when referring to the same variables, hoping that you will confuse the two words. Finally, if the word sometimes is used, then the constraint really means nothing, because just as a variable could sometimes come before another, it could also sometimes come afterward. To sum up, figuring out the correct order of the variables before you begin transcribing is the most difficult step in solving sequence problems, if you take the time to determine the correct order, the rest of the problem will be easy.

**2. Add Logic Chains.** Consolidate the seven constraints through logic chain addition. Constraints 1 through 4 can be added together to make a linear chain:

A < B < C < D < E

Constraints 5 through 7 can be added to the linear chain to form a connecting chain that look like this:

A < B < C < D < E

< <

F < G

This all-encompassing chain represents all the variables in the problem.

**3. Figure Out What You Deduce Correctly.**

Before moving on the questions, you should ask yourself what the chain and its variables mean. That is, what can you deduce from the chain? Several deductions are clear”. A is less than E, F and G are less than E, and B is less than G. However, there are several fallacious deductions that people often make when confronted with a chain like this. Hence are a couple of incorrect deductions: F is less than D, G is greater than C, and D is equal to G. When a chain branches like this, it is of the utmost importance to realize that you can deduce nothing about the order of a variable that is not connected in a direct chain. Watch out for branched chains and beware of making these false deductions.

Here is another chain. For practice, ask yourself the following question. What are some false deductions that a test maker would like to trick a test taker into making based on this diagram of the variables?

N < P < L

< <

M < K < O < J

Here are some examples of false deductions:

**N < K 3.N < J****N < O 4.J < N**

The principle is that there has to be a direct sequential link between the variables. If you are ever unsure of the sequential relationship, then start at one variable and try to make it to the next variable without either jumping the chain or having the sign change from “greater than” to “less than.” For example, take N < O. Starting at N and trying to connect to O, you would have move greater to P, but then you would have to go less to O, By trying to go to other direction, you would go less to M, then you would have to move greater to K and then to O. Making an assumption by switching from less to greater is impossible. Try to follow the order of logic of the correct deductions described next. Hence are some examples of correct deductions:

- M < L
- K < P
- M < J

See how you could start at M and consistently use the same chain to move greater to L. The following logic game will help you practice these techniques. Remember the order of operations. First, be careful while transcribing the constraints. Second, use logic chain addition. Finally, ask yourself what you can correctly deduce from your chain.

## Important Examples for Logical Games

Eight Olympic sprinters ran a 100-meter dash and finished in the following order:

Adam finished before Bill.

Frank finished before Evan.

Bill finished before Charles.

Dave finished after Charles and Bill.

Ham finished after George.

Evan finished before Charles and Dave.

George finished after Bill.

**1. Which of the following is a possible order for the finishers to finish in from first to last?**

(A) Frank, Evan, Adam, Bill, George, Ham, Charles, Dave

(B) Dave, Charles, Evan, Frank, Ham, George, Bill, Adam.

(C) Adam, Evan, Frank, Bill, George, Ham, Charles, Dave.

(D) George, Frank, Adam, Evan, Bill, Ham, Charles, Dave,

(E) Adam, Bill, Frank, Evan, Charles, Dave, Ham, George.

**Answer:** (A) Looking at your diagram, it is clear that Frank, Evan, Adam, Bill, George, Ham, Charles, and Dave is a possible order. It is possible that Evan finishes before Adam, and it is possible that George and Ham finish before Charles. The rest of the ordering is mandated by the constraints.

**2. If Ham finishes after Charles, then how many runners must finish before Charles?**

(A) Two

(B) Three

(C) Four

(D) Five

(E) Six

**Answer:** (C) If Ham finishes after Charles, then two runners must finish after Charles- Ham and Dave. It is possible that George finishes either before or after Charles. However, four people are required to finish before Charles- Adam, Bill, Evan, and Frank.

**3. Which one of the following statements must be true?**

(A) George finishes after Charles.

(B) Ham finishes before Dave.

(C) Frank finishes after Adam.

(D) Charles finishes after Dave.

(E) Ham finishes after Bill.

**Answer:** (E) Ham must finish after Bill. The order choices are only possibilities, except for D, which is impossible.

**4. If George finishes after Dave, and Frank finishes after Bill, how many different orders could the racers finish in?**

(A) None

(B) One

(C) Two

(D) Three

(E) Four

**Answer:** (B) There would only be one possible order- Adam, Bill, Frank, Evan, Charles, Dave, George, and finally Ham.

**5. If Evan finished before George, then which of the following must be true?**

(A) George must finish after Charles.

(B) Frank must finish after Bill.

(C) Ham must finish after Frank.

(D) Dave must finish after Ham.

(E) Adam must finish first.

**Answer:** (C) This constraint would set up a chain that would look like this: F < E < G < H. Based on this chain, it is clear that Frank must finish before Ham.

## Logical Games Questions from Previous Year Exams

- Logical Games

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