FREE PREVIEW Week 2 4 lessons

Reasoning: Logic and Arrangements

Order and ranking, alphanumeric sequences, linear and circular seating, floor puzzles, syllogism (with possibility and 'only a few' cases) and direct and coded inequalities. These carry the most marks in bank prelims and mains.

Lessons in this module

Order, Ranking and Alphanumeric Sequences

Lesson • 5 quiz questions

Read notes ↓

Seating Arrangement and Simple Puzzles

Lesson • 5 quiz questions

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Syllogism (with Possibility and 'Only a Few')

Lesson • 5 quiz questions

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Inequalities (Direct and Coded)

Lesson • 5 quiz questions

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Lesson notes

1. Order, Ranking and Alphanumeric Sequences

Ranking questions give a person's position from one or both ends of a row or class and ask for the total, the other rank or the number of people between two persons. Alphanumeric sequence questions give a mixed line of letters, numbers and symbols.

Ranking formulas with examples

Total = position from left + position from right - 1. Ravi is 15th from left and 20th from right, so total = 15 + 20 - 1 = 34.
Rank from bottom = total - rank from top + 1. In a class of 40, 12th from top is 40 - 12 + 1 = 29th from bottom.
People between two persons: convert both to the same end. Row of 30, A is 10th from left, B is 12th from right. B is 30 - 12 + 1 = 19th from left, so people between = 19 - 10 - 1 = 8.
Interchange type: A is 8th from left and B is 12th from right. They swap places and A becomes 15th from left. A's new place is B's old place, which is 15th from left and 12th from right, so total = 15 + 12 - 1 = 26.
Trap: if the two persons' positions overlap (left rank + right rank is more than the total), count the overlap, not the gap.

Comparison of heights, marks or ages

Write each clue as a small chain using > and join the chains. Example clues: A is taller than B, C is shorter than B, D is taller than A, E is shorter than C.
Chains: A > B, B > C, D > A, C > E. Joined: D > A > B > C > E.
So D is the tallest, E is the shortest and B is in the middle.
If a clue is missing, two persons may not be comparable. Then the correct answer is 'cannot be determined'.

Alphanumeric sequence

Example line: R 4 # K 7 M $ 2 P @ 9 B 5 % E (15 elements).
'How many letters are immediately followed by a number?' Check every letter: R4, K7 and B5 qualify; M$ and P@ do not. Answer 3.
'Which element is 4th to the right of the 9th from the left?' The 9th from left is P. Add 4: 9 + 4 = 13th from left, which is 5.
To count from the right, convert: position from left = total + 1 - position from right.
Read words like 'immediately preceded by' and 'immediately followed by' slowly; swapping them is the most common mistake.

Quick facts

Total in a row: left + right - 1
Rank from bottom: total - top rank + 1
Between two persons: difference of positions - 1
From left: total + 1 - from right

💡 Always draw a short line with dots for ranking questions and mark the two persons. A picture shows at once whether they overlap.

📝 5-question quiz on this lesson: enrol free to take it and track your score.

2. Seating Arrangement and Simple Puzzles

Seating arrangement questions place people in a row or around a table using clues. Puzzles place people on floors, in months or with different items. The skill is to fix sure positions first and then test the remaining cases.

Directions in a row and a circle

Row facing North: their right is your right and their left is your left. Row facing South: their right is your left.
Circle facing the centre: left = clockwise, right = anticlockwise. Facing outside, it is the opposite.
'Immediate right' means next seat. 'Second to the right' means skip one seat.
In a circle of 6 or 8, the person 'opposite' is half the circle away (3 seats in a circle of 6).
Fix definite clues first (ends, middle, opposite), then clues with 'immediately', then negative clues ('not adjacent').

Worked example: linear row

P, Q, R, S and T sit in a row facing North. R is in the middle. Q is immediately to the right of R. S is second to the left of R. P is at one of the ends.
Number seats 1 to 5 from left. R = 3, so Q = 4 and S = 1.
P must be at an end; seat 1 is taken, so P = 5. T gets the last seat, 2.
Final row from left to right: S, T, R, Q, P. P is at the extreme right end.

Worked example: circle and floor puzzle

A, B, C, D, E, F sit around a round table facing the centre. A is opposite D. B is immediately to the right of A. C is second to the left of B. E is not an immediate neighbour of C.
Going clockwise from A: B is right of A, so B is anticlockwise of A. C, second to the left of B, is clockwise of A. The clockwise order is A, C, F, D, E, B, so F sits opposite B.
Floor puzzle: J, K, L, M, N live on floors 1 (bottom) to 5 (top). M is on the top floor. K is on an even floor above L. N is immediately above J. L is not on floor 1.
M = 5. If K = 2, L must be on floor 1, which is not allowed, so K = 4 and L is on 2 or 3. If L = 2, floors 1 and 3 are left, but J and N need two floors next to each other. So L = 3, J = 1 and N = 2.
Final from bottom: J, N, L, K, M. Check each clue once more before answering.

Quick facts

Facing North: right = your right
Facing South: right = your left
Facing centre: left = clockwise
Opposite in 6 seats: 3 seats away
Order of clues: definite, then immediate, then negative

💡 When a clue gives two cases, draw both diagrams side by side. A later clue usually kills one case.

📝 5-question quiz on this lesson: enrol free to take it and track your score.

3. Syllogism (with Possibility and 'Only a Few')

A syllogism gives two or more statements and some conclusions. You must accept the statements as true, even if they are strange, and decide which conclusions must follow. Bank exams also ask 'possibility' and 'only a few' questions.

Method using Venn diagrams

Draw a circle for each word. 'All A are B': circle A fully inside B. 'No A is B': circles apart. 'Some A are B': circles overlap.
Draw the simplest diagram first, then try to break each conclusion with another valid diagram.
A definite conclusion follows only if it is true in every possible diagram.
Example: All dogs are animals. All animals are living beings. So all dogs are living beings, and some living beings are dogs. Both follow.
Example: Some pens are books. No book is a bag. The pens that are books cannot be bags, so 'Some pens are not bags' follows. 'Some bags are pens' does not follow, because bags may be away from pens.

Possibility cases

'A possibility' conclusion is true if you can draw at least one valid diagram where it happens.
Example: All roses are flowers. No flower is a tree. Then no rose can be a tree, so 'Some trees being roses is a possibility' is false.
Example: All phones are devices. Some devices are toys. 'Some phones are toys' does not follow definitely, but it is a possibility.
A possibility is false if it breaks a given statement or a definite conclusion.

'Only a few' and either-or

'Only a few A are B' means some A are B AND some A are not B. So 'All A are B' is never true or possible.
Example: Only a few teachers are singers. All singers are dancers. 'Some teachers are dancers' follows. 'All teachers can be singers' is not possible.
Either-or case: when neither conclusion follows alone but one of them must be true. The pair must have the same two words, and be like 'Some A are B' and 'No A is B', or 'All A are B' and 'Some A are not B'.
Example: Some cats are dogs. No dog is a rat. I: Some cats are rats. II: No cat is a rat. Neither is sure, but one must be true, so the answer is 'Either I or II follows'.

Quick facts

All A are B: A inside B
No A is B: no overlap
Some A are B: at least one common
Only a few A are B: some are, some are not
Either-or pair: Some + No, same two words

💡 Do not use real-world knowledge. Only the given statements matter, even if they say 'All cows are birds'.

📝 5-question quiz on this lesson: enrol free to take it and track your score.

4. Inequalities (Direct and Coded)

Inequality questions give a chain of relations such as P > Q ≥ R = S and ask which conclusions are definitely true. Coded inequalities replace the signs with symbols like @, #, $ that you must decode first. They are quick marks in bank prelims.

Rules for joining signs

Between two letters, read the signs on the path. If all signs point the same way (> and ≥, or < and ≤), a relation exists.
If the path has > or < anywhere, the result is strict (> or <). If it has ≥ and = only, the result is ≥ (and = if all signs are =).
If the path has signs facing opposite ways (like > and <, or ≥ and ≤), there is no definite relation.
Example: P > Q ≥ R = S < T. P to S: >, ≥, = all point one way with a strict sign, so P > S is true. Q to T: ≥, =, < face opposite ways, so T > Q is not definite.
When two chains share a letter (J < K ≤ L and L > M ≥ N), join them at that letter before comparing.

Either-or in inequalities

If neither conclusion is true alone but together they cover all cases, the answer is 'Either I or II is true'.
The two conclusions must use the same two letters, for example A > C and A = C, when the chain gives A ≥ C.
Example: A ≥ B = C ≤ D. A and C are joined by ≥ and =, so A ≥ C. I: A > C, II: A = C. Answer: Either I or II.
If one conclusion is already definitely true, there is no either-or.

Coded inequalities

Example code: A @ B means A > B; A # B means A < B; A $ B means A = B; A % B means A ≥ B; A & B means A ≤ B.
Step 1: Rewrite the statement with real signs. M % N $ O @ P becomes M ≥ N = O > P.
Step 2: Rewrite each conclusion. I: M @ P means M > P. II: N @ P means N > P.
Step 3: Check normally. M ≥ N = O > P gives M > P and N > P, so both are true.
Trap: the code changes in every question set. Never carry a code from one set into another.

Quick facts

>, ≥, =: same direction, result strict if any > present
> with <: no relation
≥ only: either > or = (either-or pair)
Coded: decode first, then solve

💡 Draw an arrow along the chain with your finger. The moment the direction flips, stop: there is no relation.

📝 5-question quiz on this lesson: enrol free to take it and track your score.

Other modules in Railway Exams Prep: RRB NTPC & Group D

Start Here: Railway Exams (RRB NTPC and Group D)FREE PREVIEW → Quantitative Aptitude: Number BasicsFREE PREVIEW → Quantitative Aptitude: Arithmetic IFREE PREVIEW → Quantitative Aptitude: Arithmetic IIFREE PREVIEW → Quantitative Aptitude: Advanced and DataFREE PREVIEW → Reasoning: Verbal BasicsFREE PREVIEW → Reasoning: Analytical and Non-VerbalFREE PREVIEW → General ScienceFREE PREVIEW → Environment and Ecology (Karnataka focus)FREE PREVIEW → Ancient IndiaFREE PREVIEW → Medieval IndiaFREE PREVIEW → Colonial Rule and the Freedom StruggleFREE PREVIEW → The Constitution of IndiaFREE PREVIEW → How India Is GovernedFREE PREVIEW → India's Economic Journey and PoliciesFREE PREVIEW → Indian Geography for National ExamsFREE PREVIEW → Static GK for National ExamsFREE PREVIEW → Computer KnowledgeFREE PREVIEW → Final AssessmentFREE PREVIEW →

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