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Analytical & Logical Reasoning

Seating puzzles, blood relations, and syllogisms — the skill is drawing a diagram, not holding everything in your head.

7 min read Intermediate GATE DA Lesson 113 of 122

What you'll learn

  • The four puzzle shapes GATE recycles: seating/ordering, blood-relations, syllogisms, statement-conclusion
  • Drawing beats memorising — sketch the situation before deducing
  • Why 'all A are B' and 'some B are C' do NOT imply 'some A are C'
  • Using a Venn diagram to test syllogism validity in 20 seconds

Before you start

You read the question once. Five people, a round table, “A is between B and C”, “D is opposite A” — and your brain immediately tries to track all of it at once. That never works. The students who solve these in 90 seconds aren’t smarter; they just draw the diagram.

Analytical reasoning rewards externalising the puzzle. A four-clue puzzle becomes trivial the moment it leaves your head and lands on rough paper. (It’s the same move you make sketching a tricky SQL join or a tangle of if conditions — externalise the constraints, then read off the answer.)

The four shapes GATE recycles

  • Seating / ordering. People around a table or in a row. Draw the seats; pencil each name in as clues land.
  • Blood relations. “A’s sister’s husband’s father…” Draw a family tree with squares for males, circles for females, lines for marriage and parenthood.
  • Syllogisms. “All A are B; some B are C; therefore…?” Test by Venn diagram, not by gut feel.
  • Statement-conclusion. Given a statement, which conclusions necessarily follow? Reject any that need extra assumptions.

A round-table puzzle, drawn out

round tableABCDE?E?dashed: A ↔ D axis
Place A and D (opposite). B and C flank A. E sits in one of the two remaining seats — which one needs an extra clue.

Five friends A, B, C, D, E sit around a round table. A is between B and C. D is opposite A. Where does E sit?

Walk it through.

  1. Place A anywhere (call it the top).
  2. D opposite A — bottom seat.
  3. A between B and C — B and C take the two seats flanking A.
  4. E is the only person left, and two seats remain: one between B and D, one between C and D.

Without a fifth clue (e.g. “E is to D’s right”), the puzzle is under-determined (the clues allow more than one valid answer) — E could be in either of the two remaining seats. GATE will always give you enough clues to pin it down; recognising “I’m missing a clue” tells you to re-read for one you skimmed past.

Syllogisms — when intuition lies

The trap that catches even careful students:

All cats are mammals. Some mammals are dogs. Therefore some cats are dogs?

That looks plausible for half a second. It’s wrong. The mammals that are dogs need not overlap with the mammals that are cats. Two subsets of a bigger set can be completely disjoint.

The rule of thumb: “all A are B” + “some B are C” never implies “some A are C”. When in doubt, draw three overlapping circles (A, B, C) and try to arrange them so the premises hold but the conclusion fails. If you can, the syllogism is invalid.

How GATE asks this

A mix of MCQ and NAT. The MCQs are usually pure deduction puzzles (“who sits where?”, “what is X’s relation to Y?”, “which conclusion follows?”). The NATs are usually numeric (“how many people sit between A and B going clockwise?”, “what is the minimum number of people in the room?”). Two distinct skills, same toolkit — externalise the puzzle, then deduce.

Quick check

Quick check

0/5
Q1Six people P, Q, R, S, T, U sit in a row of six chairs (left to right). Q is at the left end. R is immediately to the right of Q. S is exactly in the middle of the row, with three people on each side… wait, a row of 6 has no exact middle, so S is in seat 3 or 4. Given U is in seat 6, how many distinct valid arrangements are there if T sits immediately right of S? Compute the number of valid arrangements.numerical answer — type a number
Q2Pointing to a photograph, Ravi says, 'She is the daughter of my grandfather's only son.' How is the woman in the photograph related to Ravi?
Q3Which of the following syllogisms are VALID? (select all that apply)select all that apply
Q4Five boxes B1 … B5 are stacked vertically. B3 is just above B5. B1 is at the top. B4 is just below B1. Which box is at the bottom?
Q5Seven students sit in a row. A is three seats left of B. C is immediately right of B. How many distinct seats can A occupy?numerical answer — type a number

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