Logical, Analytical & Spatial Reasoning Quick-reference class notes for CSIR-UGC NET / JRF / Ph.D. Part A (General Aptitude)

 

Logical, Analytical & Spatial Reasoning

Quick-reference class notes for CSIR-UGC NET / JRF / Ph.D. Part A (General Aptitude)

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1. Question buckets & rough weight

Theme	Typical tasks	Expected ques.
Logical sequencing	Find next/odd term, rank order, calendar/clock puzzles	3–4
Deductive logic	Syllogism, statement–assumption, course-of-action	2–3
Analytical puzzles	Seating (linear/circular), blood relations, coded directions	3–4
Spatial reasoning	Mirror/water images, paper-fold, 2-D/3-D rotation	2
Venn/diagrammatic	Set membership, minimum/maximum overlaps	1–2

Distribution is inferred from the last ten NET papers.

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2. High-frequency concepts & one-line hacks

1. Syllogism

   • Convert “only A are B” → B ⊂ A.

   • “Some A are B” = intersection, cannot draw subset.

2. Statement–assumption

   • Author’s unstated belief must be implicit and necessary; ignore universal claims like “all/always”.

3. Seating (linear)

   • Draw a single arrow line L→R; fix extreme clues first (“X at one end”).

4. Seating (circular)

   • Facing centre ⇒ left is clockwise; facing outwards ⇒ left is anticlockwise.

5. Blood relation code

   • Translate: M ÷ N = “M is wife of N”, M × N = “M is brother of N”, etc.—build a quick legend.

6. Direction sense

   • Combine successive turns: two lefts + one right = net left.

   • Δx = N–S, Δy = E–W; distance = √(Δx²+Δy²).

7. Mirror image (alphabet)

   • Only four letters look identical (A, H, I, O). Tick them to skip unnecessary drawing.

8. Paper-fold/cut

   • Work backwards: unfold step by step, doubling holes symmetrically.

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3. Micro-formulae & ready reckoners

Topic	Shortcut
Day of week (Zeller)	$h=(q+\lfloor (13(m+1))/5\rfloor +K+\lfloor K/4\rfloor +\lfloor J/4\rfloor +5J)\bmod7$
Clock overlap	Minutes = $\frac{11}{\!–}$ (use 65 × h/11, e.g., 2 h ⇒ 130/11 = 11:49 min)
Cubes after cuts	Total = (n–1)³ small cubes if divided n parts per edge

Memorise the day-of-week values for 1 Jan 1900 (Mon) & 2000 (Sat) to speed Zeller.

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4. Two illustrative problems

• Seating puzzle (circular, inward)
  Clues: A is second left of B, D opposite A, C between B & D. Draw B at 12 o’clock → place A at 10 o’clock → D at 4 o’clock → C at 2 o’clock. Remaining positions auto-fill.

• Spatial fold
  Paper folded thrice (north→south, east→west, west→east) then one hole punched centre. Unfold reverse order: last fold duplicates 2 holes, middle duplicates 4, first duplicates 8 → answer: 8 equally spaced holes.

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5. Rapid practice regime

1. Daily 15-minute mixed-bag: 5 reasoning MCQs timed at 45 s each.

2. Weekly “puzzle sprint”: attempt one full seating/arrangement set (3 Qs) under 7 minutes.

3. For spatial skills, solve 20 mirror-image questions in one sitting—pattern recognition speed increases dramatically after 100 attempts.