Reasoning Tricks: Syllogism, Blood Relations, Coding and Direction

Reasoning is the section where a prepared aspirant can score almost full marks, and an unprepared one loses time on questions that should take 30 seconds. The six topics in this guide, syllogism, inequalities, blood relations, coding-decoding, direction and distance, and ranking and order, appear in some form across SSC, railway and bank exams. Reasoning syllabi for these exams commonly list them, but always check the latest notification for the current pattern and marks.

This post gives you, for each topic, the concept, the fastest method that does not break on tricky questions, four or more worked examples with every step shown, and the traps examiners rely on. All examples here are original and have been checked step by step. Work through them with a pen, not just by reading.

How to use this guide

• Read the method, then cover the solution and try each example yourself.
• Do not memorise answers. Memorise the rule that produced them.
• Keep a small notebook of traps. Most wrong answers in reasoning come from the same five or six habits.
• Time target for planning: about 30 to 45 seconds per question once you know the method. This is a practice suggestion, not an official figure.

1. Syllogism

The concept

You are given two or three statements about groups of things, and several conclusions. You must pick the conclusions that follow definitely from the statements, even if they look false in real life. Treat the statements as true and ignore general knowledge.

Every statement is one of four types.

Type	Form	Meaning
A (universal affirmative)	All A are B	A is fully inside B
E (universal negative)	No A is B	A and B do not overlap
I (particular affirmative)	Some A are B	A and B overlap at least a little
O (particular negative)	Some A are not B	At least a part of A lies outside B

Fastest reliable method: rules first, Venn to confirm

Step 1: conversions. These are the hidden statements you can always add.

• All A are B gives Some B are A.
• No A is B gives No B is A. In most exam conventions it also gives Some A are not B and Some B are not A.
• Some A are B gives Some B are A.
• Some A are not B has no conversion.

Step 2: combining two statements through the common (middle) term.

First + Second	Conclusion
All A are B + All B are C	All A are C
All A are B + No B is C	No A is C
Some A are B + All B are C	Some A are C
Some A are B + No B is C	Some A are not C
No A is B + All B are C	Some C are not A
No A is B + Some B are C	Some C are not A
All A are B + Some B are C	No conclusion
Some + Some, No + No, anything + Some are not	No conclusion

Step 3: Venn test for doubtful conclusions. Draw the circles in the way that makes the conclusion false. If you can do that while keeping the statements true, the conclusion does not follow.

Step 4: possibility and either-or. A conclusion that does not follow definitely may still be a possibility if some Venn diagram supports it. If two conclusions have the same subject and predicate and form a contradictory pair (Some are with No, or All with Some are not), and neither follows alone, then either one or the other must be true.

Worked example 1

Statements: All pens are books. All books are tables.

Conclusions: I. All pens are tables. II. Some tables are pens. III. Some books are pens.

Solution: A plus A gives All pens are tables, so I follows. Converting it gives Some tables are pens, so II follows. Converting the first statement gives Some books are pens, so III follows. All three follow.

Worked example 2

Statements: Some roads are lanes. All lanes are paths.

Conclusions: I. Some roads are paths. II. All roads are paths. III. Some paths are roads. IV. Some lanes are roads.

Solution: I plus A gives Some roads are paths, so I follows. Its conversion gives III. Converting the first statement gives IV. II is wrong because only some roads are known to be lanes; other roads may lie outside paths. I, III and IV follow; II does not.

Worked example 3 (either-or)

Statements: Some hills are rivers. Some rivers are lakes.

Conclusions: I. Some hills are lakes. II. No hill is a lake.

Solution: Some plus Some gives nothing, so neither follows alone. Draw it: the hills and lakes circles may overlap or may stay apart while both touch the rivers circle. The two conclusions are an I and E pair on the same terms, so one of them must be true. Either I or II follows.

Worked example 4 (possibility)

Statements: All shirts are coats. Some coats are caps.

Conclusions: I. Some shirts are caps (definite). II. It is possible that all shirts are caps. III. No cap is a coat.

Solution: A plus I gives no conclusion, so I does not follow definitely. For II, put the shirts circle inside coats and let the caps circle cover the whole shirts circle while also sticking out of coats; both statements stay true, so II is a valid possibility. III contradicts the second statement. Only II is correct.

Common traps in syllogism

• Using real-world knowledge. If the statements say all pens are books, accept it.
• Reversing an All statement into All. All A are B does not give All B are A.
• Treating Some as Some but not all. Some only means at least one; it does not exclude all.
• Applying either-or when one conclusion already follows, or when the pair is Some with Some are not (both can be true together).
• Forgetting that a negative statement can be converted, and that doing so may support another conclusion.

2. Inequalities

The concept

You get a chain of relations such as A > B ≥ C = D, and must decide which conclusions are definitely true. In coded versions, symbols like $ or # stand for the relations, and you must decode them first.

Fastest reliable method

1. Decode the symbols once, write them as normal signs, then forget the code.
2. Read the chain left to right. Between any two elements, a conclusion is valid only if every link between them points in one direction.
3. Combining rules: strict plus non-strict in the same direction gives strict (> with ≥ gives >). Equal links do not change the direction. Opposite directions anywhere between two elements means no relation.
4. For a conclusion with ≥ or ≤, it is true if the chain proves either the strict or the equal case.
5. If two conclusions are complementary, such as X > Y and X ≤ Y, or X ≥ Y and X < Y, and neither is proven, then either-or follows.

Worked example 5

Statement: A > B ≥ C = D ≤ E.

Conclusions: I. A > C. II. E ≥ C. III. B > E. IV. A > D.

Solution: I: A > B ≥ C gives A > C, true. II: C = D ≤ E gives C ≤ E, so E ≥ C, true. III: B and E sit on opposite sides of the low point C = D, so no relation; false. IV: A > B ≥ C = D gives A > D, true. I, II and IV follow.

Worked example 6

Statement: P ≤ Q < R ≥ S.

Conclusions: I. P < R. II. Q > S. III. R > P. IV. P ≤ S.

Solution: I: P ≤ Q < R gives P < R, true. III is the same fact written backwards, true. II: Q < R and S ≤ R both point up to R, so Q and S are unrelated; false. IV: P and S are also unrelated; false. I and III follow.

Worked example 7 (coded, with either-or)

Code: $ means ≥, # means <, @ means =.

Statement: M $ N, N # P, P @ Q. Conclusions: I. N < Q. II. M < Q. III. M ≥ Q.

Solution: Decode: M ≥ N < P = Q. I: N < P = Q gives N < Q, true. M and Q lie on opposite sides of the low point N, so no relation is proven. II and III are complementary (M < Q and M ≥ Q cover every case), so I follows, and either II or III follows.

Worked example 8 (the equality trap)

Statement: R ≥ S > T = U ≥ V.

Conclusions: I. R > T. II. S ≥ V. III. R ≥ U. IV. T > V.

Solution: I: R ≥ S > T gives R > T, true. II: S > T = U ≥ V gives S > V, so S ≥ V is true. III: R > T = U gives R > U, so R ≥ U is true. IV: T = U ≥ V gives only T ≥ V, since T could equal V; false. I, II and III follow.

Common traps in inequalities

• Treating ≥ as >. A single ≥ link can allow equality, so only a strict link anywhere in the chain makes the whole result strict.
• Linking two elements across a turning point (two arrows pointing away from, or toward, each other).
• Wrong decoding of the symbol table in a hurry. Write the decoded chain before looking at conclusions.
• Using either-or when one of the two conclusions is already proven.

3. Blood relations

The concept

You are given statements about family links and asked how two people are related. The question tests careful reading more than cleverness.

Fastest reliable method

• Fix the speaker as the starting point. Rewrite phrases like "my mother's only son" as "myself or my brother" based on the speaker's gender.
• Draw a small tree. Use a plus sign for male and a minus sign for female, a horizontal line for spouses, a vertical line for children, and a dotted line for siblings.
• Resolve phrases from the inside out. "The only daughter of my mother" is the speaker if the speaker is female.
• Where gender is not given, the answer has to be a neutral term such as cousin, sibling or nephew or niece. If the options force a gendered word and data is missing, choose "cannot be determined".
• Know the standard terms: your father's or mother's brother is an uncle, their sister is an aunt, their children are your cousins; your sibling's children are your nephew or niece; your spouse's brother is your brother-in-law.

Worked example 9

Pointing to a man, Rekha says, "His mother is the only daughter of my mother."

Solution: Rekha is a daughter of her mother. The only daughter of her mother must therefore be Rekha herself. So the man's mother is Rekha, and the man is Rekha's son.

Worked example 10

A is the brother of B. B is the father of C. C is the sister of D, and D is a boy. How is D related to A?

Solution: B is the father of C, and C and D are siblings, so B is also D's father. A is B's brother, which makes A the paternal uncle of D. D is a boy, so D is A's nephew.

Worked example 11

Looking at a photograph, Arjun says, "She is the daughter of my father's only son."

Solution: Arjun is male and is the son of his father. If his father has only one son, that son is Arjun. So the lady is Arjun's daughter. She is Arjun's daughter.

Worked example 12 (chain)

P is the father of Q. Q is the sister of R. R is the mother of S. S is the brother of T. How is P related to T?

Solution: P is the father of Q, and Q is R's sister, so P is also R's father. R is the mother of S, and S and T are siblings, so R is T's mother too. P is the father of T's mother. P is T's maternal grandfather.

Worked example 13 (coded relations)

Code: A + B means A is the mother of B. A – B means A is the brother of B. A × B means A is the sister of B.

Statement: P + Q – R × S. How is P related to S?

Solution: P + Q: P is Q's mother. Q – R: Q is R's brother, so P is also R's mother. R × S: R is S's sister, so R and S have the same parents, and P is S's mother too. P is the mother of S.

Common traps in blood relations

• Assuming gender. "Cousin", "sibling" and "spouse" do not tell you male or female.
• Mixing maternal and paternal sides. "Grandfather" may be either, so write maternal or paternal if the chain tells you.
• Reading "my father's son" as a brother. It can be the speaker himself.
• Skipping the speaker. Always start the tree from the person who is speaking.

4. Coding-decoding

The concept

A word, number or sentence is changed by a hidden rule. You must find the rule from the example and apply it to a new item.

Fastest reliable method

• Write the alphabet with positions: A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13 N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26.
• Compare the word and its code letter by letter, writing the shift for each position. Constant shift, alternating shift, increasing shift, reversal and opposite letters cover most questions.
• Opposite letters (A with Z, B with Y) always have positions that add up to 27. Use this to convert quickly.
• For sentence codes, find the common word between two statements and the common code word between their codes. Repeat for the rest.
• For number codes, test sums, products, squares, and the form n(n+1) or n squared plus or minus a constant.

Worked example 14 (alternating shift)

In a code, CLOUD is written as EMQVF. How is BRAIN written in the same code?

Solution: Compare letter by letter. C to E is +2, L to M is +1, O to Q is +2, U to V is +1, D to F is +2. The rule is +2, +1, +2, +1, +2. Apply it to BRAIN: B+2 = D, R+1 = S, A+2 = C, I+1 = J, N+2 = P. BRAIN is written as DSCJP.

Worked example 15 (increasing shift)

In a code, RAIN is written as SCLR. How is COLD written?

Solution: R to S is +1, A to C is +2, I to L is +3, N to R is +4. The shifts rise by one each time. For COLD: C+1 = D, O+2 = Q, L+3 = O, D+4 = H. COLD is written as DQOH.

Worked example 16 (opposite letters)

In a code, each letter is replaced by its opposite in the alphabet (A with Z, B with Y and so on). Write CAT in this code.

Solution: Opposite letter has position 27 minus the original. C is 3, so 24, which is X. A is 1, so 26, which is Z. T is 20, so 7, which is G. CAT is written as XZG.

Worked example 17 (sentence code)

In a code language, "sun moon star" means "ka ra pa", "moon rise" means "ra to", and "star rise high" means "pa to ni". What is the code for "sun"?

Solution: Statements 1 and 2 share "moon", and their codes share "ra", so moon is ra. Statements 1 and 3 share "star", and their codes share "pa", so star is pa. Then in statement 1, "sun moon star" is "ka ra pa", so sun is the remaining word, ka. (As a check, rise is to, from statements 2 and 3.) Sun is ka.

Worked example 18 (number pattern)

If 5 is coded as 30, 6 as 42 and 7 as 56, what is the code for 9?

Solution: 5 × 6 = 30, 6 × 7 = 42, 7 × 8 = 56. The code of n is n × (n+1). For 9: 9 × 10 = 90. The code is 90.

Worked example 19 (letter to number)

If MANGO is written as 13-1-14-7-15, write LEMON in the same code.

Solution: Check the rule: M is 13, A is 1, N is 14, G is 7, O is 15, so each letter is replaced by its position. LEMON: L is 12, E is 5, M is 13, O is 15, N is 14. LEMON is 12-5-13-15-14.

Common traps in coding-decoding

• Checking only the first letter. A rule that works for one letter may fail on the next, so test every position.
• Forgetting wrap-around. Shifting Y by +3 goes to B, not past Z.
• Reversing the direction of the shift when decoding. If the code is +2, decoding means going -2.
• In sentence codes, assuming the order of code words matches the order of words. Always find matches by common elements.

5. Direction and distance

The concept

A person moves in steps with left and right turns, and you must find the final distance from the start, the direction of the start from the end, or the direction someone faces.

Fastest reliable method

• Fix north at the top of the page. Draw each leg on an x-y grid, east as +x and north as +y.
• Track the facing direction. A right turn is 90 degrees clockwise (facing north, right gives east; facing east, right gives south; facing south, right gives west; facing west, right gives north). A left turn is the reverse.
• Add up east-west and north-south movement separately. If the two net movements are x and y, the straight-line distance is the square root of x squared plus y squared. Remember the triplets 3-4-5, 5-12-13, 8-15-17.
• For shadow questions: in the morning the sun is in the east, so shadows fall to the west. In the evening shadows fall to the east. At noon in most of India the shadow points roughly north, but exam problems usually avoid this.
• For turns by angle, measure clockwise from north: N is 0, NE is 45, E is 90, SE is 135, S is 180, SW is 225, W is 270, NW is 315.

Worked example 20

A man walks 8 km north, turns right and walks 6 km, then turns right again and walks 8 km. How far and in which direction is he from the start?

Solution: North 8 km. Turning right from north faces east: 6 km east. Turning right from east faces south: 8 km south. Net north-south movement is 8 - 8 = 0. Net east is 6 km. He is 6 km due east of the start.

Worked example 21

A girl walks 5 m south, turns left and walks 12 m. How far is she from the start and in which direction?

Solution: Facing south, a left turn faces east (south to east is anticlockwise). So she is 5 m south and 12 m east of the start. Distance is the square root of 25 + 144, which is the square root of 169, or 13 m. She is 13 m from the start, towards the south-east.

Worked example 22

Ravi walks 20 m east, turns left and walks 15 m, turns left and walks 20 m, then turns left and walks 5 m. How far is he from the start and in which direction?

Solution: East 20. Left from east faces north: 15 north. Left from north faces west: 20 west. Left from west faces south: 5 south. East-west: 20 - 20 = 0. North-south: 15 - 5 = 10 north. He is 10 m north of the start.

Worked example 23 (shadow)

One morning just after sunrise, Neha stood facing a pole, and its shadow fell exactly to her right. Which direction was she facing?

Solution: In the morning the sun is in the east, so the shadow falls to the west. The west is on her right. If she faces south, her right hand points west (facing north, right would be east). She was facing south.

Worked example 24 (turns by angle)

A person facing north-east turns 90 degrees clockwise, then 135 degrees anticlockwise. Which direction does he face now?

Solution: North-east is 45 degrees. Clockwise 90 gives 135, which is south-east. Anticlockwise 135 gives 135 - 135 = 0, which is north. He faces north.

Common traps in direction and distance

• Mixing up left and right when the person is facing south or west. Always update the facing direction before each turn.
• Reporting only the distance. Check whether the question asks for the direction of the start from the end, which is the opposite of the direction of the end from the start.
• Adding the legs instead of finding the net displacement.
• Wrong shadow side. Morning shadow falls west; evening shadow falls east.

6. Ranking and order

The concept

You are given positions in a row, queue or class, and asked for total strength, someone's position from the other end, or the number of people between two persons. Simple but easy to lose a mark on through an off-by-one error.

Fastest reliable method

• Total = (rank from one end) + (rank from the other end) - 1.
• Rank from the other end = Total - rank from this end + 1.
• People between two persons in the same row, both counted from the same end = difference of positions - 1.
• If two people swap places, the person takes the other's original position, so use that to find the total.
• For comparison orderings, write a single chain with the tallest, heaviest or oldest on the left, and reason about the middle position only after the whole chain is fixed.

Worked example 25

Rahul ranks 12th from the top in a class of 40. What is his rank from the bottom?

Solution: Rank from bottom = 40 - 12 + 1 = 29. He is 29th from the bottom.

Worked example 26 (interchange)

Mira is 15th from the left and Nisha is 18th from the right in a row. After they interchange positions, Mira becomes 22nd from the left. How many people are in the row?

Solution: After the swap, Mira stands where Nisha stood, so Nisha was 22nd from the left. Total = 22 + 18 - 1 = 39. Check: Nisha's position from the left is 39 - 18 + 1 = 22, which matches. There are 39 people.

Worked example 27 (persons between)

In a queue of 30 people, Kiran is 8th from the front and Lata is 10th from the back. How many people are between them?

Solution: Lata from the front = 30 - 10 + 1 = 21. People between = 21 - 8 - 1 = 12. There are 12 people between them.

Worked example 28 (order by comparison)

A is taller than B. C is shorter than B but taller than D. E is taller than A. Who is in the middle when they stand in order of height?

Solution: E is taller than A, A is taller than B, B is taller than C, C is taller than D. The order, tallest to shortest, is E, A, B, C, D. Among five people, the middle is the third. B is in the middle.

Worked example 29 (two-ended rank)

In a class, Anil ranks 7th from the top. Bala is 5 ranks below Anil and is 31st from the bottom. How many students are in the class?

Solution: Bala's rank from the top is 7 + 5 = 12. Total = 12 + 31 - 1 = 42. There are 42 students.

Common traps in ranking and order

• Forgetting the minus 1 in Total = left + right - 1.
• Counting the two persons themselves while counting the people between them.
• Misreading "5 ranks below" as 5 places from the bottom.
• Declaring a middle position before checking that all comparisons are in one chain.

Study plan for these six topics

This is a planning suggestion; adjust it to your own schedule.

1. Week 1: syllogism and inequalities. Do 15 questions a day with the rules table above on your desk.
2. Week 2: blood relations and ranking. Draw a tree or number line for every question, no mental shortcuts.
3. Week 3: coding-decoding and direction. Write the alphabet with positions at the top of every coding page.
4. Week 4: mixed sets under a timer, then review every wrong answer and label the trap.

Frequently asked questions

Which of these topics gives the quickest marks? Inequalities, ranking and direction questions are the most mechanical. Once you know the rules, they take well under a minute.

Do I need Venn diagrams for every syllogism? No. Use the rules table for speed, and draw a Venn diagram only for doubtful conclusions, possibility questions and either-or cases.

Does "Some A are B" mean some A are not B? Not necessarily. Some means at least one, and it does not exclude all.

When is either-or correct in syllogism? When the two conclusions share the same subject and predicate, form a contradictory pair, and neither follows individually.

Why does a chain with ≥ not always give a strict result? Because ≥ allows equality. You get a strict result only if at least one strict link is present in the same direction.

What if a blood relation question does not give gender? Use a neutral term such as cousin or sibling, or choose "cannot be determined" if the options need a gender.

How do I find the opposite letter fast? Subtract the position from 27. For example, G is 7 and its opposite is the letter at 20, which is T.

Is the direction of the start from the end the same as the end from the start? No. It is the opposite. If he ends up north-east of the start, the start is south-west of him.

How many people are in a row if I know the positions from both ends? Add the two positions and subtract 1.

How much should I practise daily? As a planning suggestion, 20 to 30 questions on one or two topics plus review is more useful than 100 unreviewed questions.

Practise under exam conditions

Methods stay shaky until you test them against the clock. Take sectional tests on these topics and then full-length mocks on Pareeksha to check speed and accuracy together. After each test, note which trap cost you marks and revisit that section of this guide.