🚀 New Pattern & Advanced Problems
Master column-matching, statement combination, contradiction detection, missing statement problems, and other advanced syllogism patterns from SBI PO Mains and RBI Grade B
New Pattern & Advanced Problems
Advanced syllogism questions go beyond the traditional "statements → conclusions" format. SBI PO Mains and RBI Grade B feature new pattern questions that test deeper logical reasoning. This lesson walks through every modern format you will encounter.
Type 1: Column Matching
Format: Two columns are provided. Column I contains statements, Column II contains conclusions. Your task is to determine which statement(s) lead to which conclusion(s).
Example:
Column I (Statements): (W) All clouds are rain (X) No rain is a storm (Y) Some storms are thunder (Z) All thunder are lightning
Column II (Conclusions): (p) No cloud is a storm (q) Some lightning are storms (r) Some thunder are lightning (s) No cloud is thunder
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New Pattern & Advanced Problems
Advanced syllogism questions go beyond the traditional "statements → conclusions" format. SBI PO Mains and RBI Grade B feature new pattern questions that test deeper logical reasoning. This lesson walks through every modern format you will encounter.
Type 1: Column Matching
Format: Two columns are provided. Column I contains statements, Column II contains conclusions. Your task is to determine which statement(s) lead to which conclusion(s).
Example:
Column I (Statements): (W) All clouds are rain (X) No rain is a storm (Y) Some storms are thunder (Z) All thunder are lightning
Column II (Conclusions): (p) No cloud is a storm (q) Some lightning are storms (r) Some thunder are lightning (s) No cloud is thunder
Q: Conclusion (p) follows from which combination of statements?
Solve:
Q: Conclusion (r) "Some thunder are lightning" follows from?
- We need a relationship between thunder and lightning
- Statement (Z): All thunder are lightning → thunder inside lightning → Some thunder are lightning ✓
- Answer: (Z) alone
Solving Column Matching Efficiently
-
For each conclusion, identify which two elements are involved
-
Find statements that contain those elements or connect to them through intermediaries
-
Verify the chain from statements to conclusion
Speed trick: Build a relationship map:
clouds ──All──> rain ──No──> storms ──Some──> thunder ──All──> lightning
Then trace the path between the elements in each conclusion.
Type 2: Pick 3 Statements from 6
Format: Six statements are given. You must pick exactly 3 that together make a given conclusion true.
Example:
Statements: (W) All J are K (X) No K is L (Y) Some L are M (Z) All M are N (V) Some J are L (U) No N is J
Q: Which 3 statements make "Some N are not J" definitely true?
Solution:
Try (Y) + (Z) + (U):
- Some L are M → some overlap
- All M are N → M inside N → the L-M overlap is inside N
- No N is J → N separate from J
Wait — if No N is J, then ALL N are not J, which means "Some N are not J" is definitely true ✓
But does this use the right 3? (Y) Some L are M isn't needed if (Z) + (U) already give "No N is J" → "Some N are not J" ✓
Actually, we need N to have members first. (Z) All M are N tells us N is non-empty (if M exists). But we need to confirm M exists... (Y) gives us L-M overlap, confirming M exists.
Hmm, actually for "Some N are not J", we need N to exist and some N to be outside J. From "No N is J" → ALL N are outside J → "Some N are not J" follows as long as N is non-empty.
Simplest: (X) + (Z) + (U) or just (Z) + (U) + any statement confirming N exists.
The key is finding the minimum set of 3 that creates the chain.
Type 3: Contradiction Detection
Format: Given a set of statements, identify which pair of conclusions cannot both be true simultaneously.
Example:
Statements:
- All G are H
- Some H are J
- No J is K
Conclusions: (I) Some G are J (II) No G is J (III) Some H are K (IV) No H is K
Q: Which pair of conclusions cannot be true together?
Analysis:
- (I) "Some G are J" and (II) "No G is J" → These are direct contradictions (Some overlap ↔ No overlap). Cannot both be true.
- (III) "Some H are K" and (IV) "No H is K" → Same contradiction pattern. Cannot both be true.
Answer: (I, II) and (III, IV) are contradictory pairs
Contradiction rules:
| Pair | Contradicts? |
|---|---|
| All X are Y ↔ Some X are not Y | Yes |
| Some X are Y ↔ No X is Y | Yes |
| All X are Y ↔ No X is Y | Yes (these are "contraries" — both can be false, but both cannot be true) |
| Some X are Y ↔ Some X are not Y | No (both can be true simultaneously) |
Type 4: Missing Statement Problems
Format: Given some statements and a target conclusion, find which additional statement would make the conclusion true.
Example:
Given statements:
- All G are H
- _________ (missing)
Target conclusion: No G is J
Options: (a) All J are G (b) No H is J (c) Some H are J (d) All J are H
Solution:
- We need "No G is J"
- We know "All G are H" (G inside H)
- If "No H is J" (H separate from J) → G inside H, H separate from J → G separate from J → "No G is J" ✓
Answer: (b) No H is J
Approach:
- What relationship do we need? (G separate from J)
- What do we already know? (G inside H)
- What would create the needed relationship? (H separate from J would separate G from J)
Type 5: Logically Related Statement Combinations
Format: Multiple statement groups are given. Determine which group produces valid conclusions.
Example:
Group I: All G are H. All H are J. No J is K. Group II: Some G are H. All H are J. Some J are K. Group III: No G is H. All H are J. All J are K.
Q: From which group(s) can we conclude "No G is K"?
Group I: G inside H, H inside J, K separate from J → G inside J → G separate from K → "No G is K" ✓
Group II: Some G are H, All H inside J, Some J overlap K → G-K relationship uncertain → "No G is K" not definite ✗
Group III: G separate from H, H inside J, J inside K → G separate from H, but G could overlap with J or K → "No G is K" not definite ✗
Answer: Only Group I
Type 6: Percentage-Based Advanced
Modern exams use percentages to create complex scenarios:
Statements:
- 90% of G are H (= Some G are H)
- 30% of H are J (= Some H are J)
- 0% of J are K (= No J is K)
- 40% of K are L (= Some K are L)
- 75% of L are G (= Some L are G)
- 100% of G are M (= All G are M)
For syllogism purposes, convert all percentages:
- 0% = No
- 100% = All
- 1%-99% = Some
Then solve normally.
But some questions ask about the PERCENTAGE explicitly:
Q: "Can we say 100% of G are J?"
- We know "Some G are H" and "Some H are J"
- Two "Some" links → No definite conclusion about all G being J
- Answer: Cannot be determined
Q: "Is it possible that 0% of G are K?"
- We need to check if "No G is K" is possible
- G → H (Some), H → J (Some), J → K (No)
- The chain has "Some" breaks, so G-K relationship is uncertain
- "No G is K" is possible ✓
Solving Strategy for New Patterns
Step 1: Identify the question type (Column match / Pick 3 / Contradiction / Missing / Percentage)
Step 2: Convert all statements to standard form (especially percentages and "Only a few" / "Only")
Step 3: Build the relationship chain on rough paper:
G ──All──> H ──No──> J ──Some──> K ──All──> L
Step 4: For the specific question:
- Column match → trace path between conclusion elements
- Pick 3 → find minimum connecting chain
- Contradiction → find opposing pairs
- Missing → identify the gap in the chain
- Percentage → convert and solve normally
Practice Problems
Problem 1: Column Matching
Statements: (W) All flutes are drums (X) No drum is a guitar (Y) Some guitars are violins (Z) All violins are instruments
Conclusions: (p) No flute is a guitar (q) Some instruments are guitars (r) Some violins are instruments
Match:
- (p) needs flute-guitar relationship → (W) + (X): flutes→drums, drums✗guitars → flutes✗guitars ✓
- (q) needs instrument-guitar relationship → (Y) + (Z): Some guitars are violins + All violins are instruments → Some guitars are instruments → Some instruments are guitars ✓
- (r) needs violin-instrument relationship → (Z) alone: All violins are instruments → Some violins are instruments ✓
Problem 2: Missing Statement
Given: _____ . All H are J. Conclusion needed: Some G are J.
Options: (a) No G is H (b) Some G are H (c) All J are G (d) No G is J
Solution:
- Need "Some G are J"
- We have "All H are J" (H inside J)
- If "Some G are H" → Some G overlap with H → that overlap is inside J → "Some G are J" ✓
Answer: (b)
Problem 3: Contradiction
Statements: All J are K. Some K are L. No L is M.
Which pair CANNOT both be true? (a) "Some J are L" and "No J is L" (b) "Some K are M" and "Some K are not M" (c) "All L are K" and "Some L are not K"
Solution:
(a) "Some J are L" ↔ "No J is L" → Contradictory (Some ↔ No) ✓
(b) "Some K are M" ↔ "Some K are not M" → Both CAN be true simultaneously ✗
(c) "All L are K" ↔ "Some L are not K" → Contradictory (All ↔ Some not) ✓
Answer: (a) and (c)
Type 7: "At Least" and "At Most" Keyword Patterns
Modern exams (SBI PO Mains 2023-25, IBPS PO) have introduced "at least" and "at most" phrasing. These are NOT the same as "Some" or "All".
Keyword Conversion Table:
| Exam Keyword | Logical Meaning | Standard Form |
|---|---|---|
| At least some X are Y | Some X are Y (minimum overlap) | Some X are Y |
| At least all X are Y | All X are Y (minimum = all) | All X are Y |
| At most some X are Y | Some or None (maximum = some) | NOT "All X are Y" |
| At most all X are Y | All or Some or None (no constraint) | No useful info |
| At least no X is Y | No X is Y (minimum separation) | No X is Y |
Key Insight: "At least" sets a minimum — the reality could be stronger. "At most" sets a maximum — the reality could be weaker.
"At Least" Examples:
Q: "At least some G are H" — what follows?
- This means: minimum overlap = Some. Could be All G are H.
- "Some G are H" → ✓ Follow (guaranteed minimum)
- "All G are H" → ? Doubtful (possible, not guaranteed)
- "No G is H" → ✗ Not possible
Q: "At least all G are H" — what follows?
- This means: minimum = All G are H. G is definitely inside H.
- Same as "All G are H" — use normal "All" rules.
"At Most" Examples:
Q: Statement says "At most some G are H" — what follows?
- This means: maximum overlap = Some. It's NOT the case that All G are H.
- "Some G are not H" → ✓ Follow (since not all G are H, some must be outside)
- "All G are H" → ✗ Not possible (violates the "at most" limit)
- "Some G are H" → ? Doubtful (there might be zero overlap — "at most some" allows "None")
- "No G is H" → ? Doubtful (possible — zero is ≤ some)
This is tricky! "At most some" means the overlap is anywhere from 0% to partial — it could be zero!
Practice Problem:
Statements:
- At least some rivers are lakes
- All lakes are reservoirs
- At most some reservoirs are dams
Conclusions:
- Some rivers are reservoirs → ?
- All rivers are reservoirs → ?
- All reservoirs are dams → ?
- Some lakes are not dams → ?
Solution:
-
"At least some rivers are lakes" = "Some rivers are lakes" (minimum). Some rivers are lakes + All lakes are reservoirs → Some rivers are reservoirs → ✓ Follow
-
"All rivers are reservoirs" → Doubtful (we only know "some rivers are lakes", not all) → Does not follow
-
"All reservoirs are dams" → "At most some" means NOT all → ✗ Definitely False
-
"Some lakes are not dams" → Lakes inside reservoirs. "At most some reservoirs are dams" means some reservoirs might not be dams. But we can't guarantee the lake portion is in the non-dam part. → Doubtful, does not follow (but IS a possibility)
Common Mistakes
- Column matching: Not checking the full chain. Two statements might seem sufficient but miss an intermediate link.
- Pick 3: Selecting statements that don't connect. All 3 must form a continuous chain.
- Contradiction: Confusing "contraries" (both can be false) with "contradictories" (one must be true). For syllogism: All↔Some not and Some↔No are true contradictories.
- Missing statement: Not considering the direction. "All G are H" and "All H are G" are different!
- Percentage traps: Treating 90% as "All" instead of "Some". Any percentage 1-99% = Some.
Summary Cheat Sheet
| Concept / Topic | Key Details / Explanation |
|---|---|
| Type 1: Column Matching | Column I = statements, Column II = conclusions. Identify which statements form the chain needed for each conclusion. Build a relationship map (A──All──>B──No──>C) and trace paths. |
| Column matching strategy | For each conclusion, identify the two elements involved → find statements containing those elements or intermediaries → verify the chain. |
| Type 2: Pick 3 from 6 | Given 6 statements, pick exactly 3 that together make a target conclusion true. Find the minimum connecting chain. All 3 must be continuous. |
| Pick 3 key insight | For "Some N are not J": if "No N is J" is achievable through 3 statements, then "Some N are not J" follows automatically (all not → some not). Confirm N is non-empty via the third statement. |
| Type 3: Contradiction Detection | Find which pair of conclusions cannot both be true. Use contradiction rules: All ↔ Some Not (contradictory), Some ↔ No (contradictory), All ↔ No (contrary — both can be false, but cannot both be true). |
| Contrary vs Contradictory | Contradictory: exactly one must be true (All↔SomeNot, Some↔No). Contrary: both can be false but not both true (All↔No). |
| "Some X are Y" + "Some X are not Y" | These are NOT contradictory — both CAN be true simultaneously (partial overlap satisfies both). |
| Type 4: Missing Statement | Given some statements + target conclusion, find which additional statement completes the chain. Work backwards: what gap needs to be filled to connect the elements? |
| Missing statement approach | 1) What relationship is needed? 2) What is already known? 3) What would bridge the gap? — Usually a statement connecting the middle element to the target. |
| Type 5: Logically Related Groups | Multiple statement groups given; determine which group produces the target conclusion. Apply chain analysis to each group separately. |
| Type 6: Percentage-Based | Convert all percentages: 0% = No, 100% = All, 1-99% = Some. Then solve normally. "Can 100% of G be J?" = Can "All G are J" follow? Apply chain rules. |
| "At least some X are Y" | = Some X are Y (minimum). Some X are Y → ✓. All X are Y → Doubtful. No X is Y → impossible. |
| "At least all X are Y" | = All X are Y (minimum = all). Same as standard "All" rules. |
| "At most some X are Y" | = NOT All X are Y. Maximum is partial overlap. Some X are not Y → ✓ (definite). All X are Y → impossible. Some X are Y → Doubtful (could be zero). No X is Y → Doubtful (zero is ≤ some). |
| "At most" is tricky | "At most some" allows ZERO overlap. So "Some X are Y" is only possible, not definite. "No X is Y" is also possible. |
| General strategy for new patterns | 1) Identify question type. 2) Convert all statements. 3) Build relationship chain on rough paper. 4) Trace/fill/find/verify based on type. |