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.
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?
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?
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
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Question 1 of 23
1. Question1 points
Read the below passage carefully and answer the following questions:
At a small company, parking spaces are reserved for the top executives: CEO, president, vice president, secretary, and treasurer with the spaces lined up in that order. The parking lot guard can tell at a glance if the cars are parked correctly by looking at the color of the cars. The cars are yellow, green, purple, red, and blue, and the executives names are Alice, Bert, Cheryl, David, and Enid.
# The car in the first space is red.
# A blue car is parked between the red car and the green car.
# The car in the last space is purple.
#The secretary drives a yellow car.
# Alice's car is parked next to David's.
# Enid drives a green car
# Bert's car is parked between Cheryl's and Enid's.
# David's car is parked in the last space.
Who is the secretary?Correct
Cheryl cannot be the secretary, since she's the CEO, nor can Enid, because she drives a green car, and the secretary drives a yellow car. David's, the purple car, is in the last space. Alice is the secretary, because her car is parked next to David's, which is where the secretary's car is parked.Incorrect
Cheryl cannot be the secretary, since she's the CEO, nor can Enid, because she drives a green car, and the secretary drives a yellow car. David's, the purple car, is in the last space. Alice is the secretary, because her car is parked next to David's, which is where the secretary's car is parked.
Question 2 of 23
2. Question1 points
What color is the vice president's car?Correct
The vice president's car cannot be red, because that is the CEO's car, which is in the first space. Nor can it be purple, because that is the treasurer's car, which is in the last space, or yellow, because that is the secretary's. The president's car must be blue, because it is parked between a red car (in the first space) and a green car, which must be the vice president's.Incorrect
The vice president's car cannot be red, because that is the CEO's car, which is in the first space. Nor can it be purple, because that is the treasurer's car, which is in the last space, or yellow, because that is the secretary's. The president's car must be blue, because it is parked between a red car (in the first space) and a green car, which must be the vice president's.
Question 3 of 23
3. Question1 points
Five cities all got more rain than usual this year. The five cities are: Last Stand, Mile City, New Town, Olliopolis, and Polberg. The cities are located in five different areas of the country: the mountains, the forest, the coast, the desert, and in a valley. The rainfall amounts were: 12 inches, 27 inches, 32 inches, 44 inches, and 65 inches.
# The city in the desert got the least rain; the city in the forest got the most rain.
# New Town is in the mountains.
# Last Stand got more rain than Olliopolis.
# Mile City got more rain than Pol berg, but less rain than New Town.
# Olliopolis got 44 inches of rain.
# The city in the mountains got 32 inches of rain; the city on the coast got 27 inches of rain.
Which city got the most rain?Correct
Olliopolis got 44 inches of rain. Last Stand got more rain than that, so it got 65 inches, which is the most.Incorrect
Olliopolis got 44 inches of rain. Last Stand got more rain than that, so it got 65 inches, which is the most.
Question 4 of 23
4. Question1 points
How much rain did Mile City get?Correct
Olliopolis got 44 inches of rain, Last Stand got 65, and Polberg got 12. New Town is in the mountains, and the city in the mountains got 32 inches of rain. Therefore, Mile City got 27.Incorrect
Olliopolis got 44 inches of rain, Last Stand got 65, and Polberg got 12. New Town is in the mountains, and the city in the mountains got 32 inches of rain. Therefore, Mile City got 27.
Question 5 of 23
5. Question1 points
Where is Olliopolis located?Correct
The city that got the least rain is in the desert. New Town is in the mountains. Last Stand got more rain than Olliopolis, so it cannot be the city with the least rain; also,Mile City cannot be the city with the least rain. Olliopolis got 44 inches of rain. Therefore, Polberg is in the desert and got 12 inches of rain.Incorrect
The city that got the least rain is in the desert. New Town is in the mountains. Last Stand got more rain than Olliopolis, so it cannot be the city with the least rain; also,Mile City cannot be the city with the least rain. Olliopolis got 44 inches of rain. Therefore, Polberg is in the desert and got 12 inches of rain.
Question 6 of 23
6. Question1 points
Five roommates Randy, Sally, Terry, Uma, and Vernon each do one housekeeping task mopping, sweeping, laundry, vacuuming, or dusting one day a week, Monday through Friday.
# Vernon does not vacuum and does not do his task on Tuesday.
#Sally does the dusting, and does not do it on Monday or Friday.
# Terry does his task, which is not vacuuming, on Wednesday.
# The laundry is done on Friday, and not by Uma.
# Randy does his task on Monday.
What task does Terry do on Wednesday?Correct
Terry does not dust, mop, do laundry, or vacuum. Therefore, Terry does the sweeping on Wednesday.Incorrect
Terry does not dust, mop, do laundry, or vacuum. Therefore, Terry does the sweeping on Wednesday.
Question 7 of 23
7. Question1 points
What day does Uma do her task?Correct
Uma does the mopping, which is done on Thursday.Incorrect
Uma does the mopping, which is done on Thursday.
Question 8 of 23
8. Question1 points
What task does Vernon do?Correct
Vernon does not vacuum, dust, or sweep. Randy does the vacuuming, Sally does the dusting, Terry does the sweepingâ€”leaving laundry and mopping for Uma and Vernon. Uma does not do laundry; therefore, she must mop, and Vernon does the laundry.Incorrect
Question 9 of 23
9. Question1 points
When does Sally do the dusting?Correct
Dusting must be done on Tuesday, Wednesday, or Thursday. However, the mopping is done on Thursday, and Terry does his task on Wednesday. Therefore, Sally does the dusting on Tuesday.Incorrect
Dusting must be done on Tuesday, Wednesday, or Thursday. However, the mopping is done on Thursday, and Terry does his task on Wednesday. Therefore, Sally does the dusting on Tuesday.
Question 10 of 23
10. Question1 points
What day is the vacuuming done?Correct
Dusting is on Tuesday, sweeping is on Wednesday, mopping is on Thursday, and laundry is on Friday. Therefore, the vacuuming is done on Monday.Incorrect
Dusting is on Tuesday, sweeping is on Wednesday, mopping is on Thursday, and laundry is on Friday. Therefore, the vacuuming is done on Monday.
Question 11 of 23
11. Question1 points
Aditya, Bala, Chinmay, Darsh, Eliza and Farida stay in different areas namely Matunga, Mulund, Sion, Dadar, Kurla and Bhandup. Each of them has different musical instruments- Guitar, Keyboard, Violin, Tablas, Flue and Octopad not necessarily in the same order. The one having Flute stays in Dadar and the one having Tablas stay in Kurla. Eliza doesn’t stay in Matunga or Kurla. Chinmay plays Keyboard and stays in Sion. Darsh doesn’t stay in Dadar. The one who plays Violin doesn’t stay in Mulund. Eliza plays Guitar. Neither Darsh nor Farida play Octopad. The one playing octopad doesn’t live in Bhandup. Darsh plays Tablas. The one staying in Bhandup plays Violin. Aditya stays in Matunga.
Who plays the octopad?Correct
Question 12 of 23
12. Question1 points
Which of the following is definitely true?Correct
None of theseIncorrect
None of these
Question 13 of 23
13. Question1 points
Who stays in Mulund?Correct
Question 14 of 23
14. Question1 points
Which of the following statements is incorrect?Correct
Both (A) & (B) are correcIncorrect
Both (A) & (B) are correc
Question 15 of 23
15. Question1 points
Seven girls- Sona, Tina, Reena, Sheena, Meena, Beena & Neena teach seven activities- Painting, singing, dancing, cooking, swimming, shooting and skating not necessarily in the same order from Monday-Friday. Each girl teaches a different activity. Not more than two activities are taught on any day. Cooking is taught by Tina on Tuesday. Sheena teaches on Friday but neither singing nor dancing. Sona teaches skating on the day on which painting is taught. Reena teaches swimming on Monday. Beena teaches painting but neither on Thursday nor on Friday. Neena teaches on Thursday. Singing and cooking are taught on the same day.
Skating is taught on which day?Correct
Question 16 of 23
16. Question1 points
Which of the following pairs of girls teach on Tuesday?Correct
Question 17 of 23
17. Question1 points
Which activity is taught on Friday?Correct
Question 18 of 23
18. Question1 points
Which activity is taught by Neena?Correct
Question 19 of 23
19. Question1 points
There is a group of friends – Ramesh, Suresh, Ritesh, Paresh, Mitesh, Mangesh, Dinesh studying in the same class. Each one of them speak a different language- English, Marathi, Hindi, Gujarati, Bengali, Tamil and Malyalam. Each of them secured different marks in the examination. Ritesh who scored second highest marks speaks neither English nor Guajarati. Mitesh who secured the least marks neither speaks neither Tamil nor Marathi. Paresh who speaks Hindi, secured more marks than Dinesh and Suresh. Suresh speaks Bengali. Ramesh secured more marks than Paresh. Suresh’s marks are more than Mitesh but less than Dinesh. Ramesh speaks Malyalam and has not scored the highest marks. The one who speaks Gujarati has secured the highest marks. Ritesh does not speak Marathi.
In which language does Dinesh speak?Correct
Question 20 of 23
20. Question1 points
In which language does Mitesh speak?Correct
Question 21 of 23
21. Question1 points
Who secured third lowest marks?Correct
Question 22 of 23
22. Question1 points
Who speaks Gujarati?Correct
Question 23 of 23
23. Question1 points
When all the students are arranged according to their marks in descending order, what will be the position of Ramesh from the top?Correct
None of theseIncorrect
None of these