Non-Verbal Reasoning — SSC CGL

Non-verbal questions look like puzzles but behave like arithmetic: every sub-type has one mechanical rule. Mirrors flip left–right. Water flips top–bottom. Opposite dice faces never touch. Folded paper multiplies cut-outs symmetrically. Learn the rule per sub-type and these become the fastest marks in the reasoning section — no vocabulary, no reading time.

1. What SSC actually asks

Tier 1: 3–5 questions · Tier 2: 3–5 questions, spread across:

2. Mirror and water images

Mirror (vertical mirror at the right): left and right swap; top and bottom stay. Letters with vertical symmetry are unchanged: A H I M O T U V W X Y.

Water image: top and bottom swap; left–right order stays. Letters with horizontal symmetry survive: B C D E H I K O X.

Clock mirror shortcut: mirror time = 11:60 − given time (or 23:60 −). Mirror of 4:30 → 11:60 − 4:30 = 7:30. Water image of a clock ≈ 6:30 ± trickier — SSC almost always asks the mirror version.

Elimination discipline: in figure options, first check one distinctive element (an arrow, a dot's corner). Its mirrored position eliminates 2–3 options instantly — never compare whole figures element by element.

3. Paper folding & cutting

The paper is folded (shown left-to-right), holes/cuts are punched, then unfolded. Rule: unfold in reverse order; every unfold mirrors the punches across that fold line.

• One fold → each punch appears 2×; two folds → 4×.
• Punch positions mirror across the fold — a hole near the fold edge stays near the crease when unfolded; a hole near the outer edge lands far from the crease.
• Symmetry check: the final pattern must be symmetric about every fold line. Options violating any fold's symmetry die immediately.

4. Dice and cubes

Standard dice fact: opposite faces of a die sum to 7 (1–6, 2–5, 3–4) — but only if stated/standard. For general dice, use:

1. Two-view rule: if two views share a common face, the faces adjacent to it in both views are all adjacent to it — the one number never seen with it is its opposite.
2. Never-together rule: faces appearing together in any view are adjacent, never opposite.

Painted cube arithmetic (cube cut into $n^3$ small cubes after painting all faces):

For $n=4$: 8 corners, 24 edge-cubes, 24 face-cubes, 8 core. (Check: 64 (correct).)

Open dice (nets): in a cross-shaped net, faces separated by one square (same row/column) are opposite. Mark opposites first; then any "which face is opposite X" or "can this cube be formed" question is a lookup.

5. Figure series and analogies

The transform menu (test in order):

1. Rotation — element rotates 45°/90°/135° clockwise or anti-clockwise each step. Distinguish rotation vs mirror: a rotated flag keeps its chirality (handedness); a mirrored one reverses it.
2. Position stepping — an element hops corners/sides in a fixed cycle (often skipping one more position each step).
3. Element count — sides/dots/lines increase or decrease arithmetically (a pentagon → hexagon → heptagon series).
4. Appearance/disappearance — elements toggle on a cycle; new element enters each step, oldest leaves.
5. Combination — two of the above running simultaneously (track each element separately, exactly like interleaved number series).

6. Counting figures

Count by size class, never by staring:

• Triangles in a triangle grid: count unit triangles, then 4-unit, then 9-unit (both orientations).
• Squares in an n×n grid: $1^2+2^2+\cdots +n^2$. A 4×4 grid has $30$ squares. Rectangles in an n×n grid: ${\left(\genfrac{}{}{0ex}{}{n+1}{2}\right)}^2$ — for 4×4: ${\left(\genfrac{}{}{0ex}{}{5}{2}\right)}^2=100$.
• Triangles formed by diagonals of a quadrilateral: a square with both diagonals = 8 triangles.
• Write counts per class and add — the options are engineered to catch one missed class.

7. Solved PYQ-style examples

Q1. The mirror image of "QUALITY" — which letters stay visually unchanged? Solution. Letters with vertical symmetry: U, A, I, T, Y stay; Q and L flip. (Any option showing Q unflipped is eliminated first.)

Q2. A clock shows 2:40. Its mirror image shows? Solution. 11:60 − 2:40 = 9:20.

Q3. A paper is folded twice (right-to-left, then top-to-bottom) and one hole is punched. How many holes on unfolding? Solution. Two folds → $2^2=$ 4 holes, symmetric about both fold lines.

Q4. Two views of a die: view 1 shows 1, 2, 3; view 2 shows 2, 4, 6. What is opposite 2? Solution. Faces seen adjacent to 2: 1, 3 (view 1), 4, 6 (view 2). The only number never adjacent to 2 is 5 → opposite.

Q5. A 3×3×3 cube is painted and cut. How many small cubes have exactly one painted face? Solution. $6(n-2{)}^2=6\times 1=$ 6.

Q6. How many squares in a 3×3 grid of unit squares? Solution. $9+4+1=$ 14.

8. Exam protocol

1. Identify the sub-type, recall its one rule, apply — never "visualise harder".
2. Mirror/water: pick one distinctive element and eliminate options by its position.
3. Folding: check symmetry about every fold line; count = punches × 2^folds.
4. Dice: mark opposite pairs first from the views/net.
5. Counting: size classes on paper with running totals.
6. Non-verbal questions are 20–40 second marks once the rule fires — bank the cluster early.