Types of Sequencing and Arrangement
While a good number of times the statements/conditions given in the LR set will specify the exact positioning of the entities given. However, many times only the relative positioning of the variables will be given.
Let us see some examples of such statements:
Context |
Statement reads as |
Which variables are exactly placed in the sequence? |
M is fourth. |
Which variables are forbidden from a specific position in the sequence? |
M is not fifth. |
Which variables are |
M and N are consecutive. A is next to B. No variable comes between A and B are consecutively in the sequence. |
Which variables cannot be next to, before or |
A does not immediately precede or follow B. A is not immediately before or after B. M and N are not consecutive |
How far apart in the |
Exactly two people come |
What is the relative |
A comes before B in the queue. M comes after N in the queue. |
In the above given examples, we observe two types of sequencing:
Strict Sequencing and Arrangement
In these kinds of sequencing, relative positioning of the variables will be almost fixed. These are the rules which give us the exact position of the variables.
Example :
Directions for questions 1 to 3: Read the following passage below and solve the questions based on it.
During the summer placements at MU, which will run for a single week in June starting from Monday through Friday; Due North Inc. will interview three applicants Omkara, Tyagi, and Keshu. Exactly five interviews will be conducted in this week long schedule with strictly one interview per day.
Further information about the schedule of the interviews is as follows:
- Each applicant is interviewed at least once.
- Omkara is interviewed twice on two consecutive days.
- Tyagi has to meet his girl friend Billo on Wednesday, therefore he cannot be interviewed on Wednesday.
- Keshu is not interviewed on Friday as he has to go to meet Dolly who is Omkara’s wife.
- If Tyagi is interviewed on Monday then Keshu must be interviewed on Tuesday.
Q 1. Which out of the following week’s schedule could be true?
- The person who is interviewed on Tuesday is also interviewed on Thursday.
- The person who is interviewed on Wednesday is also interviewed on Friday.
- The person who is interviewed on Monday is also interviewed on Tuesday.
- Tyagi is interviewed on Monday and Thursday.
Q 2. If in addition to Omkara, one more person is interviewed on two consecutive days, then which of the following could be true?
- Tyagi is interviewed on Monday and Omkara is interviewed on Wednesday.
- Tyagi is interviewed on Tuesday and Friday.
- Tyagi is interviewed on Tuesday and Omkara is interviewed on Friday.
- Keshu is interviewed on Tuesday and Omkara is interviewed on Thursday.
Q 3. If the week’s interview schedule has the same applicant scheduled for Monday and Thursday then on which day must Tyagi be interviewed?
- Monday
- Tuesday
- Wednesday
- Friday
Solution
Scenario
There are three applicants—Omkara (O), Tyagi (T) and Keshu (K) and they are to interviewed for five interviews, Monday through Friday. Looking at the given limitations of exactly one interview per day and with only three applicants for five interviews, some of the applicants must be interviewed more than once.
Rules
The interviews are conducted one per day starting on Monday through Friday. Hence, sketch a weekly schedule with five spaces first.
The first condition says each applicant will be interviewed at least once. The next condition says Omkara is interviewed on two consecutive days–lets have an OO block for two consecutive days. The next two conditions tell about the days on which Tyagi and Keshu cannot be interviewed; mark this information in your diagram. The last condition says that if Tyagi is interviewed on Monday, Keshu must be interviewed on Tuesday.
T (MON) then - K (TUE)
The OO block for Omkara is the only big restricting factor present here. There is nothing that stops its placement on any particular pair of days in the schedule. But since Omkara is interviewed on exactly two days and Tyagi and Keshu are each to be interviewed at least once, you have four out of the five entities. The fifth interview will go to either P or S.
If Tyagi is interviewed on Monday, Keshu is interviewed on Tuesday, then Omkara will be interviewed either on Wednesday-Thursday or Thursday-Friday. Hence, one thing is sure that Omkara is definitely interviewed on Thursday. And if any of this does not happen, then it means that Tyagi would not be interviewed on Monday.
T (MON) then - K (TUE)
- Option (c) is the answer.
- Option (d) is the answer.
- Option (d) is the answer.
Loose Sequencing and Arrangement
In this kind of sequencing, the data given will tell us the relative positioning of one variable with respect to the other variable; without giving the exact position.
Example :
Directions for questions 4 to 5: Read the following passage and solve the questions based on it.
Eight parties—Forward Block, Hindustan Party, Janta Party, Lokmat, New Socialist party, Praja party, Socialist party and TDP, contested in the last general election. The number of seats won by these parties vary largely. While announcing the final results, The election commission expressed the following observation regarding the number of seats won by these parties in terms of their popularity (the more the popularity, the more is the number of seats won by the party and vice versa).
(While doing the ranking, take the first to be being the party with the maximum seats won and the eighth to be the party with minimum seats won.)
- No two parties won the same number of seats.
- The Socialist party and the Forward block are each less popular than the TDP.
- The Socialist party is more popular than the Janta party.
- The Lokmat and the New Socialist party are each less popular than the Forward block.
- The Hindustan party and the Lokmat are each less popular than the Janta party.
- The Praja party is less popular than the Lokmat.
- The Praja party is not the eighth in rank.
Scenario
When planning the diagram for the sequencing first, decide if it should be drawn horizontally or vertically. To draw the diagram here, we will think of the rankings in terms of top to bottom.
Unlike the problems done in the strict sequencing section, writing 1 to 8 or creating eight spaces will not serve the purpose owing to the fact that no exact information regarding the positioning of variables, e.g., (The Praja party is not eighth) is given.
Rules
Start visualizing. Let us name each party with its first letter as in the Forward Block is F etc.
The first condition states that S and F are both less popular than T. Here we do not know anything about the space between these two entities, just the order. Draw T above both S and F by keeping in mind that nothing is said about the relationship between S and F.
The second condition: S is more popular than J
Next condition: Both L and N are less popular than F
Next condition: Both H and L are below J
Next condition: P is less popular than L
Last condition: P is not the eighth. “P ≠8” or “P is not the last”
Let us now start joining the information. If we connect S from condition 2 to condition 1, this is exactly what we get:
After joining the rules, we have the relationship bet- ween more parties.
Which is higher, F or P? Of course F is higher, and we know we can determine the relationship between them because we can travel from one to the other in one direction.
Flaw Detector—Now have a look at F and H. Can we say that F is higher then H? The answer is—No. It is all because of the fact that to go from F to H, we would have to “travel” along the tree in more than one direction (first up then down, or first down then up). By doing this there is no definite relationship. F could be ranked higher than H or H could be higher than F. Which party is ranked last? Either H or N.
Lets now consider the questions.
Q 4. Which of the following could be the order of the parties listed from winning the maximum number of seats to the minimum number of seats?
- T, F, S, L, J, N, P, H
- S, T, F, N, J, L, P, H
- T, S, J, H, F, P, L, N
- T, S, J, F, L, N, P, H
(All the parties are being denoted by their first letter).
Solution 4. Option (d) is the answer.
To start with, this could be seen as the complete and accurate list, since all parties are taken into consideration in each answer choice.
Now, start going through the options.
Apply each condition to the given options. Option (b) violates condition (i) by making S more popular than T, therefore option (b) must be incorrect. Condition (ii) and (iii) do not help eliminate any options, but (a) violates condition (iv) by making L more popular than J, and is hence, incorrect. Option (c) gives P a higher popularity than L, a violation of condition (v). We have eliminated three options. So the remaining option (d) has to be the correct answer.
Q 5. If the Forward block is more popular than the Socialist Party and the Hindustan party is more popular than the Praja Party, then which of the following must be true of the number of seats won by different parties in the election?
- The Hindustan Party is sixth.
- The Lokmat is sixth.
- The Lokmat is seventh.
- The New Socialist Party is eighth.
Solution 5. Option (d) is the answer.
Let us again use the first letter of the parties as their symbol.
This “if” question places two additional conditions on the order of popularity. The first condition places F above S. The second condition places H above P. Re-draw your sketch to incorporate these new conditions:
Going through the options against the backdrop of the introduction of new facts like F is assigned to position 2 and the elimination of H as a possibility for the last position (leaving only N available for that slot) in the new sketch, option (d) is correct. Since both H and L could be in the sixth position, (a) and (b) do not have to be true, although these are probably true. Also, if L is placed at the seventh position, then P would have to be in the last position. And this violates the last condition, making option (c) incorrect.