Analytical & Logical Reasoning

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.

  Unwind the phrase left to right, one pencil stroke per link. Start at A, step sideways to a sister, sideways again across a marriage line to her husband, then up one generation to his father — who is A’s sister’s father-in-law.

• Syllogisms. Two premises and a proposed conclusion — “All A are B; some B are C; therefore…?” — where the only question is whether the conclusion is forced, never whether it sounds right. 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

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, and the reason is worth saying out loud: the “some B” in one premise need not be the same B as in the other.

The mammals that happen to be dogs and the mammals that happen to be cats are two subsets of one bigger set, and nothing in the premises forces them to touch. Picture it — a large mammals circle holding a cats circle and a dogs circle that sit well apart. Both premises hold, the conclusion fails, and that settles it: “all A are B” + “some B are C” never implies “some A are C”.

That single counter-picture is also the general method. Whenever a conclusion feels right, try to arrange three circles so every premise holds and the conclusion does not. Manage it and the syllogism is invalid; fail after honest effort and it is valid.

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
• statement-conclusion

The one habit that cracks them all is to externalise the clues rather than juggle them in your head:

• a seat diagram;
• a family tree with squares/circles;
• three Venn circles.

The trap that fools careful students is the syllogism “all A are B” + “some B are C” ⇏ “some A are C” (disjoint subsets). Around a round table “opposite” only exists when the number of seats is even.

Practice

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. The transformations include:

• 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.

Then see what comes out. Here is the thread onward, the last piece of General Aptitude. How do you track the following when the entire puzzle lives only in your mind’s eye?

• a punched hole back through each fold;
• a face around a tumbling cube;
• a figure through its mirror?