[Reasoning] 4-Statement Syllogism: Approach, Techniques, explained for SBI PO (High level reasoning) and UPSC CSAT paper 2

In Aptitude by Support Staff

  1. Introduction
  2. Recap: 2 statement
  3. Complimentary case
  4. Approaching 4 statement syllogism
  5. Case#1 : Stick, lamps, power, dresses, shirts
  6. Case#2: Bird, Horse, Tiger, Lion & Monkey
  7. Case#3: Bench, Wall, House, Jungle, Road
  8. Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables
  9. Case#5: (Complimentary Pairs): Chair, Handle, Pots, Mats & Buses

Introduction

  • SBI loves asking 4 statement syllogism questions in its PO exam. (usually 5 questions.)
  • In 2012, UPSC asked 3 statement syllogism in CSAT paper II, and nothing prevents UPSC from asking 4-statement syllogism in future, under its BackbreakingTM move.
  • Therefore, anyone who doesn’t want to dig his/her grave in SBI or UPSC, should thoroughly prepare syllogism.
  • Good news is, no matter whether they ask 2 statement syllogism, 3 statement syllogism, 4 statement syllogism or 50 statement syllogism, our UP-UN method continues to work.
  • However, to quickly and accurately solved 4 statement syllogism, first you must master earlier techniques
Two statement syllogism Click me to learn
Three statement syllogism Click me to learn

Recap: 2 statement

Whenever facing two statement syllogism, our standard operating procedure is:

  1. Two statements, must have only three terms
  2. Classify them into UP, UN, PP or PN.
  3. Two statements must be in the Format A to B then B to C, if not then apply the conversion rules
Type of Statement Valid Conversion Path
  1. Universal Positive (UP)
  2. All cats(A) are dogs (B)
  • Only PP
  • Some Cats (A) are dogs. (B)
  • Some dogs (B) are cats. (A)
  1. A to B
  2. B to A
  1. Universal Negative (UN)
  2. No Cats(A) are dogs (B)
  • PN :Some Dogs (B) are not Cats (A).
B to A
  • UN: No Dogs (B) are cats. (A)
  1. Particular Positive (PP)
  2. Some cats (A) are dogs (B)
  • Only PP: Some dogs (B) are cats(A)
B to A
  1. Particular Negative (PN)
  • Not possible.
  1. Now apply the combo rules. Unless specifically mentioned, conversion is A to C.

No conclusion combos

Yes conclusion combos

  1. UP’s politicians hate giving particular statements (both positive and negative). E.g. they donot reveal their clear position on FDI in retail until the 11th hour. (UP+PP/PN=NO)
  2. United Nations hates negativity. (both Universal and particular)(UN+UN/PN=NO)
  3. Pritish Nandy hates everybody. (first statement is PN=NO, Irrespective of second statement.)
  4. Two-negatives=no conclusion.
  5. Two particulars=no conclusion.
  1. If Uttar Pradesh meets Uttar Pradesh, then its size doesn’t increase. (UP+UP=UP)
  2. If Uttar Pradesh meets United Nations then size increases and it becomes United Nations. (UP+UN=UN)
  3. United Nations Secretary Ban Ki Moon is in very positive mood. But he meets another positive person, and his attitude is totally reversed- he becomes particularly negative! (reversed =C to A). (UN+UP/PP=PN)
  4. When Mr.PP observes the universe via NASA telescope, his mood becomes particularly positive or negative depending on the mood of universe.(PP+UP/UN=PP/PN)

Complimentary case

  • Incase you get a no-conclusion combo, BUT any of the answer choice says “either ** or ** follows.” In that case you’ve to check for complimentary cases. (this is critical for SBI PO, since often the 4 statement conclusion have complimentary case situation).
  • For complimentary case to be valid, two conditions must be met:

Condition #1: Two answer choices have same subject and predicate.

Applicable Not applicable
  1. Some Politicians are honest.
  2. No Politicians are honest
  1. Some Politicians are honest.
  2. No Honest are Politicians.
Because both have common subject (politician) and common predicate (honest) In first statement, subject=Politician but in second statement, subject= Honest. Hence complemantary case not possible.

Condition#2:  The answer choice combo must be either of these three

Answer choice combo example
Uttar Pradesh (UP) + Pritish Nandy (PN)
  1. All Politicians are honest.
  2. Some Politicians arenot honest
PP + Pritish Nandy (PN)
  1. Some Politicians are honest
  2. Some Politicians arenot honest
PP + United Nations (UN)
  1. Some Politicians are honest.
  2. No Politicians are honest

When these two conditions are met, then answer would be “Either (I) or (II) follows.” (to see actual question related to the complimentary pair situation, check the case number 4 and 5 given in the later part of this article.)

Approaching 4 statement syllogism

  • Here you pick up conclusion one at a time, find its parents.
  • Apply chain formula and see if it leads to the given conclusion. (pretty much the same thing that we do in three statement syllogism click me)
  • Anyways without much ado, let’s start solving 4-statement syllogism questions from SBI PO 2010 exam

Case#1 : Stick, lamps, power, dresses, shirts

This is a really cheap and easy question.

Question statements Subject predicate Type
1 1. some sticks are lamps PP
2 2. some flowers are lamps PP
3 3. some lamps are dresses PP
4 4. all dresses are shirts UP
conclusion statements
1 some shirts are sticks PP
2 some shirts are flowers PP
3 some flowers are sticks PP
4 some dresses are sticks PP

Answer choice

  1. None follows
  2. Only 1
  3. Only 2
  4. Only 3
  5. Only 4.

Approach

  • You can start with one conclusion at a time, find its parents and then apply combo rules.
  • But if you look at it carefully: 3 out of 4 question statements are Particular Positive (PP). So if you pick any two of them, PP+PP=no conclusion.
  • Fourth question statement is UP.  UP+PP=PP if this is intermediate conclusion, it won’t give any final conclusion when paired with any other question statement because PP + PP = no conclusion.
  • If situation requires you to convert UP (=can only be converted into PP), then again PP+PP=no conclusion.
  • So with that thought in mind, check four conclusion statement, you’ll see none of their parents can give conclusion.
  • Therefore answer is (A) none follow.

Case#2: Bird, Horse, Tiger, Lion & Monkey

Question statement Subject predicate Type
1 All Birds are Horses UP
2 all Horses are Tigers UP
3 Some Tigers are Lions PP
4 Some Lions are Monkeys PP
conclusion statements
1 Some Tigers are Horses PP
2 Some Monkeys are Birds PP
3 Some Tigers are Birds PP
4 Some Monkeys are Horses PP

Answer choice

  1. Only 1 and 3
  2. Only 1, 2 and 3
  3. Only 2, 3 and 4
  4. Only 1, 2, 3 and 4
  5. None follows.

Approach

  • As you can see conclusion #3 is reappearing in option A to D. so first I’ll check conclusion #3. If it turns out to be false then my effort is saved, I’ll directly tick (E).

Checking conclusion #3

3 Some Tigers are Birds PP

If this conclusion is valid, who’re its parents?

1 All Birds_A are Horses_B UP
2 all Horses_B are Tigers_C UP
  • Ok this is in standard format: A to B then B to C.
  • Apply combo rule: when UP is merged in UP, its size doesn’t increase (UP+UP=UP, A to C). so my conclusion is All birds_A are tigers_C. I’ll reconvert this (UP to PP), so some tigers are birds. This matches with the conclusion number #3.
  • So conclusion #3 is valid. So option E is eliminated.
  • Now I’ll have to check other conclusions as well. Anyways, now let’s check all other conclusions in serial order (1, 2, 4)

Checking conclusion #1

Concl.1 Some Tigers are Horses PP

If this is legit, who’re its parents?

Just one:

Q.Statement 2 all Horses are Tigers UP

I can convert this! (UP to PP) so some tigers are horses. So conclusion #1=valid.

Checking conclusion #2

2 Some Monkeys are Birds PP

If this is valid, who’re its parents?

1 All Birds are Horses UP
2 all Horses are Tigers UP
3 Some Tigers are Lions PP
4 Some Lions are Monkeys PP

I’ll reorder so it makes more sense

4 Some Lions are Monkeys PP
3 Some Tigers are Lions PP
2 all Horses are Tigers UP
1 All Birds are Horses UP
  • Ok we are facing 4 statement chain. We’ve to pick two at a time get intermediate conclusions, pair them with next statement and keep moving.
  • But today is my lucky day, you see first two statements are PP + PP= no conclusion. So we can’t proceed further. And answer choice doesn’t contain any “either or”. So we don’t need to check complimentary case either. That means conclusion #2 is invalid. Our precious time and effort is saved.

So far we’ve done following

Conclusion number Valid/not?
3 Valid
1 Valid
2 Invalid.

Accordingly, Answer choice

  1. Only 1 and 3
  2. Only 1, 2 and 3
  3. Only 2, 3 and 4
  4. Only 1, 2, 3 and 4
  5. None follows

Final answer (A) Only 1 and 3 follow.

Case#3: Bench, Wall, House, Jungle, Road

Question statement Subject predicate Type
1 Some Bench Are Wall PP
2 All Wall Are House UP
3 Some House Are Jungle PP
4 All jungle Are Road UP
Conclusion Statements
1 some Roads Are Benches PP
2 Some Jungles Are Walls PP
3 Some Houses Are Benches PP
4 some Roads Are Houses PP

Answer choices

  1. Only 1 and 2
  2. Only 1 and 3
  3. Only 3 and 4
  4. Only 2, 3 and 4
  5. None follows.

Approach

To save time and effort, I am going to test only 2 and 4. Let’s see if I can get lucky!

Checking conclusion statement #2

2 Some Jungle Are Wall PP

If this is valid conclusion, who’re its parents (question statements)?

2 All Wall Are House UP
3 Some House Are Jungle PP
  • Cool, already in standard format A to B then B to C.
  • And UP’s politicians hate giving particular statements so UP+PP=no conclusion.
  • So conclusion #2 is invalid, that means answer choice A and D are eliminated. Let’s see what is left in the answer choices:
  1. Only 1 and 2
  2. Only 1 and 3
  3. Only 3 and 4
  4. Only 2, 3 and 4
  5. None follows.

Ok now let’s check conclusion #4.

Checking conclusion statement #4

4 some Roads Are Houses PP

If this is valid conclusion, who are its parents (question statements)?

3 Some House Are Jungle PP
4 All jungle Are Road UP
  • Good, already in standard format: A to B then B to C. so directly apply the combo rule.
  • When Mr.PP observes the universe via NASA telescope, his mood becomes particularly positive or negative depending on the mood of universe.(PP+UP/UN=PP/PN)
  • PP+UP=PP. (A to C)
  • Therefore my conclusion is Some Houses are roads. And PP can be converted into PP. So Some roads are houses = also valid.
  • So conclusion #4 is valid. Let’s check our answer choices
  1. Only 1 and 2
  2. Only 1 and 3
  3. Only 3 and 4
  4. Only 2, 3 and 4
  5. None follows.

Final answer: C, only 3 and 4 follows.

Case#4: (Complimentary Pairs): Cups, Bottles, Jugs, Plates & Tables

Question statement Subject predicate Type
1 All Cups are Bottles UP
2 Some Bottles are Jugs PP
3 No Jug is Plate UN
4 some Plates are tables PP
Conclusion Statements
1 Some Tables are Bottles PP
2 Some Plates are Cups PP
3 No Table is Bottle UN
4 Some jugs are cups PP

ANSWER choice

  1. Only 1 follows
  2. Only 2
  3. Only 3
  4. Only 4
  5. Either 1 or 3 follows.

Approach

Let’s start with conclusion 1.

1 Some Tables are Bottles PP

If conclusion 1 is valid then who’re its parents (question statements)?

2 Some Bottles are Jugs PP
3 No Jug is Plate UN
4 some Plates are tables PP

I’ll rearrange the order

2 Some Bottles_A are Jugs_B PP
3 No Jug_B Is Plate_C UN
4 some Plates_C are Tables_D PP
  • Now it is a three statement syllogism.
  • Already in standard format. So, First combine 2+3.
  • PP+UN=PN. (A to C)
  • Some Bottles_A are not plates_C.  (PN)
  • That’s my intermediate conclusion. Now I’ll combine it with question statement number 4.
Intermediate conclusion Some Bottles_A Are not Plate_C PN
Q. statement #4 some Plates_C are Tables_D PP
  • Two particulars = no conclusion.
  • Ok so, conclusion #1=cannot be concluded definitely.
  • But wait, look at answer choice #4: either 1 or 3 follows. So this could be a case of complimentary pairs.
  • Let’s relook at conclusion statement #1 and #3.
Subject Predicate
1 Some Tables are Bottles PP
3 No Table is Bottle UN

Apply the checklist for complimentary case.

  1. Two answer choices have same subject and predicate?= YES
  2. The answer choice combo must be either of these three
    1. Uttar Pradesh (UP) + Pritish Nandy (PN)
    2. PP + Pritish Nandy (PN)
    3. PP + United Nations (UN)

Yes, it is combo number III (PP+UN). So final answer is either 1 or 3 follows.

Case#5: (Complimentary Pairs): Chair, Handle, Pots, Mats & Buses

Question statements are Type
1. Some chairs are Handles PP
2. All Handles are Pots UP
3. All Pots are Mats UP
4. Some Mats are Buses PP
Conclusion Statement
1. Some buses are handles PP
2. Some mats are chairs PP
3. No bus is handle UN
4. Some mats are handles PP

Answer choices

  1. Only 1,2,3 follow
  2. Only 2,3 and 4 follow
  3. Either 1 or 3 AND 2 follow
  4. Either 1 or 3 AND 4 follow
  5. Either 1 or 3 AND 2 and 4 follow

Approach

Take a look at c,d,e all of them contain “Either 1 or 3”. So we’ve to check for complimentary cases. Given conclusions

1. some buses are handles pp
3. no buses is handle un
  • Ok this both have some subject and predicate.
  • And they’re in form of PP+UN. So, Yes, they’re fit for complimentary case= Either 1 or 3 follows. Let’s see our answer choices again:
  1. Only 1,2,3 follow
  2. Only 2,3 and 4 follow
  3. Either 1 or 3 AND 2 follow
  4. Either 1 or 3 AND 4 follow
  5. Either 1 or 3 AND 2 and 4 follow
  • So answer can be C/D/E. Let’s Start with answer choice C.
  • C says “either 1 or 3 AND 2”
  • We have already checked that either 1 or 3 is valid.
  • Now let’s test conclusion statement number 2
2. some Mats Are chairs PP

If this is valid then who’re its parents (question statements)?

1. some Chairs(A) are Handles(B) PP
2. all Handles(B) are Pots(C) UP
3. all Pots(C) are Mats(D) UP

Ok now let’s pair up 1 and 2

1. some Chairs(A) Are Handles(B) PP
2. all Handles(B) Are Pots(C) UP
  • Are they in standard format A to B B to C? yes.
  • Apply rules. PP + UP.
  • When Mr.PP observes the universe via NASA telescope, his mood becomes particularly positive or negative depending on the mood of universe.(PP+UP/UN=PP/PN)
  • Therefore, PP + UP = PP (A to C)
  • Intermediate Conclusion statement is Some chairs(A) are pots(C)
  • Combine intermediate conclusion with q.statement #3.
Some chairs(A) are pots(C) PP
3. all Pots(C) are Mats(D) UP
  • Are they in std. format? yes they’re in standard format, (A to C C to D)
  • Apply rules. PP + UP = PP (A to D).
  • Our conclusion: Some chairs (A) are mats(D)==>convert Some mats are chairs (PP to PP).
  • Conclusion statement #2 said: some mats are chairs.
  • Yes so conclusion statement #2 is legit. So far our situation is
  1. Only 1,2,3 follow
  2. Only 2,3 and 4 follow
  3. Either 1 or 3 AND 2 follow
  4. Either 1 or 3 AND 4 follow
  5. Either 1 or 3 AND 2 and 4 follow
  • Now let’s check conclusion statement #4.
4.some mats are handles PP

Find its parents.

2. all Handles_A Are Pots_B UP
3. all Pots_B are Mats_C UP
  • 2+3= already in std format, UP+UP =UP merged with UP, size doesn’t hence.
  • So UP+UP=UP (A to C) very easy. Conclusion will be All handles are mats (UP).
  • But fourth conclusion is some mats are handles. No problem, we’ll convert our conclusion (rule UP–>PP).
  • So, All handles are mats (UP) => Some mats are handles.
  • Therefore, conclusion number 4 is also correct. Therefore Final answer: (e)  Either 1 or 3 AND 2 and 4 follow.

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