Paper IPaper I · General Mental Ability

Logical Reasoning

Syllogisms, statements and conclusions, seating arrangement, puzzles, and ranking, with worked examples and practice

CAPF wiki5 min read15 sections
At a glance
PaperPaper ISubjectGMASyllabusGeneral Mental Ability: logical reasoningImportanceHigh
GMAReasoningSyllogismStatements ConclusionsSeating ArrangementPuzzlesRankingPaper 1

This is the analytical core of the reasoning section: deduce what must be true from given statements. Unlike verbal reasoning, the answer is rarely a guessed pattern; it is forced by the rules of inference. Draw a diagram and stay strict about what "follows".

Core tools

Sub-type Method
Syllogism Draw Venn diagrams; a conclusion holds only if it is true in every possible diagram
Statements and conclusions Accept the statements as true; a conclusion follows only if it must be true, not merely could be
Seating arrangement Draw the row or circle; fix the most constrained person first
Puzzles (matching) Build a grid; mark each clue as yes or no, eliminate
Ranking Convert "from top" and "from bottom" into one line; use the total formula

Ranking formula

If a person is rank a from one end and b from the other in a line of N people, then N = a + b - 1 (the person is counted from both ends, so subtract one).

Syllogism quick rules

  • Two particular statements (some) together give no definite conclusion.
  • Two negative statements together give no definite conclusion.
  • "All A are B" allows "some B are A" (the converse-particular) but not "all B are A".
  • Watch for "possibility" conclusions, which can be true even when a definite conclusion is not.

Worked examples

Example 1: Syllogism

Statements: All pens are books. All books are tables. Conclusions: (i) All pens are tables. (ii) Some tables are pens.

Pens sit inside books, which sit inside tables, so every pen is a table; (i) follows. Since all pens are tables, certainly some tables are pens; (ii) follows. Both follow.

Example 2: Syllogism with "some"

Statements: Some doctors are engineers. All engineers are graduates. Conclusion: Some doctors are graduates.

The doctors who are engineers must be graduates (since all engineers are graduates). So at least those doctors are graduates. The conclusion follows.

Example 3: Statement and conclusion (does not follow)

Statement: Many students failed the test. Conclusion: The test was very hard.

The failure could be due to poor preparation, not difficulty. The conclusion is possible but not forced. It does not follow.

Example 4: Linear seating

Five recruits A, B, C, D, E stand in a row. C is to the immediate right of B. A is at one end. D is between C and E. Where does each stand (left to right)?

A is at an end; place A at the far left. B then C are adjacent (C just right of B). D is between C and E, so the order C, D, E holds. The row is A, B, C, D, E.

Example 5: Ranking

In a line of students, Ravi is 7th from the front and 12th from the back. How many students are in the line?

N = a + b - 1 = 7 + 12 - 1 = 18 students.

Example 6: Circular seating

Four officers P, Q, R, S sit around a square table, one per side, all facing the centre. P is opposite R. Q is to the immediate left of P. Where is S?

P and R face each other across the table. Q sits immediately to P's left. The only remaining side is for S, who is therefore opposite Q (and to P's right).

Example 7: Matching puzzle

Three friends, X, Y, Z, like one sport each: cricket, hockey, football. X does not like cricket. Z likes football. Who likes what?

Z likes football. X does not like cricket and football is taken, so X likes hockey. Y is left with cricket.

Shortcut tips

  • For syllogisms, the safest method is to draw the diagram that makes the conclusion false; if you cannot draw such a diagram, the conclusion follows.
  • In statements and conclusions, reject anything requiring outside knowledge or an assumption; only what is logically forced counts.
  • In seating, always place the most-constrained clue first (someone at an end, or two people fixed relative to each other).
  • For circular tables, decide first whether members face the centre or outward; "left" and "right" flip with the facing direction.
  • For ranking, if positions overlap (sum exceeds N + 1) the person is double-counted; if they fall short, there is a gap.

Practice questions

  1. Statements: All cats are animals. All animals are living things. Does "All cats are living things" follow?
  2. Statements: Some books are pens. No pen is a pencil. Does "Some books are not pencils" follow?
  3. In a row of 25 children, Meena is 9th from the left. What is her position from the right?
  4. Five boxes are stacked. A is above B, B is above C, D is at the bottom, E is at the top. Give the order top to bottom.
  5. Statement: The college cancelled the picnic. Conclusion: It was raining. Does it follow?
  6. P, Q, R, S, T sit in a row. T is at the right end. Q is second from the left. P is to the immediate left of T. Where is each?
  7. In a queue, Sita is 5th from front and 8th from back. How many are in the queue?
  8. Statements: All roses are flowers. Some flowers are red. Does "Some roses are red" follow?
  9. Four people sit around a table facing the centre. W is opposite Y. X is to the left of W. Where is Z?
  10. Statements: No teacher is rich. All rich people are happy. Does "Some happy people are not teachers" follow?

Answer key

Reveal the answer key and full worked solutions
  1. Yes; cats are inside animals, which are inside living things, so all cats are living things.
  2. Yes; the books that are pens cannot be pencils (no pen is a pencil), so some books are not pencils.
  3. From right = 25 - 9 + 1 = 17th.
  4. Top to bottom: E, A, B, C, D.
  5. Does not follow; the cause is not given, so rain is only one possibility.
  6. T at right end; P immediately left of T; Q second from left. Order left to right: _, Q, _, P, T with R and S filling the blanks consistent with the clues, for example R, Q, S, P, T.
  7. N = 5 + 8 - 1 = 12.
  8. Does not follow; the red flowers need not be roses.
  9. With W opposite Y and X to W's left, Z takes the remaining side, opposite X.
  10. Yes; rich people are happy and none of them is a teacher, so those happy people are not teachers.

See also

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