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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

Last lesson promised a puzzle with almost no numbers, where the failure mode is juggling the whole tangle in your head. Here it is. You read once — five people, a round table, “A is between B and C,” “D is opposite A” — and your brain instantly tries to hold all of it at once. That never works. The students who solve these in ninety seconds are not smarter; they simply draw the diagram.

Analytical reasoning rewards externalising the puzzle. A four-clue knot becomes trivial the moment it leaves your head and lands on rough paper, where the eyes can do the bookkeeping the working memory cannot. (It is the same move you make sketching a tricky SQL join or a tangle of if conditions — get the constraints out of your head, then read the answer off the page.)

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 — 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, never by gut feel.
  • Statement-conclusion. Given a statement, which conclusions necessarily follow? Reject any that need an extra assumption.

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, pencilling each clue onto the diagram:

  1. Place A anywhere — call it the top seat.
  2. D opposite A — the 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 (say “E is to D’s right”), the puzzle is under-determined — the clues allow more than one valid answer, and E could sit in either remaining seat. GATE will always give you enough clues to pin it down, so the feeling “I’m missing a clue” is your cue to re-read for one you skimmed past.

Syllogisms — when intuition lies

Here is the deduction your gut will get wrong every time:

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

It looks plausible for half a second. It is 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 skills, one toolkit — externalise the puzzle, then deduce.

In one breath

Analytical reasoning recycles four shapes — seating/ordering, blood relations, syllogisms, and statement-conclusion — and the one habit that cracks them all is to externalise the clues (a seat diagram, a family tree with squares/circles, three Venn circles) rather than juggle them in your head; the trap that fools careful students is the syllogism “all A are B” + “some B are C” ⇏ “some A are C” (disjoint subsets), and around a round table “opposite” only exists when the number of seats is even.

Practice

Quick check

0/5
Q1Recall — Which of the following syllogisms are VALID? (select all that apply)select all that apply
Q2Apply — Pointing 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?
Q3Apply — Five 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?
Q4Trace — Seven 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
Q5Create — Six people P, Q, R, S, T, U sit left-to-right in a row of six chairs. Q is at the left end; R is immediately right of Q; U is at the right end; and T sits immediately right of S. How many distinct valid arrangements are there?numerical answer — type a number

A question to carry forward

Notice what saved you in every puzzle here: you could externalise it. A seat diagram, a family tree, three Venn circles — each turned the words into a picture your eyes could read off. The clues lived in language, and language could be drawn.

The final GA bucket takes the words away and hands you the picture instead — then mangles it. A square of paper folded twice and punched; a cube flattened into a paper cross; a shape held up to a mirror. There is nothing to deduce in sentences, and often nothing useful to draw, because the puzzle is the transformation itself. You have to mentally perform the fold, the rotation, the reflection, and see what comes out. Here is the thread onward, the last piece of General Aptitude: how do you track a punched hole back through each fold, a face around a tumbling cube, a figure through its mirror — when the entire puzzle lives only in your mind’s eye?

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