8.3 Abstract, Symbolic & Figural Reasoning

Number Series

A number series asks for the next term that continues a hidden rule. Work through a fixed checklist, cheapest test first.

Worked example (alternating): In 2, 4, 8, 10, 20, 22, ? the operations cycle +2, x2, +2, x2, +2, x2. From 22 the next step is x2, giving 44. When a single difference or ratio fails, suspect an alternating pattern and test the operations two at a time.

Worked example (second differences): 2, 3, 5, 8, 12, ? has differences 1, 2, 3, 4, so the next difference is 5 and the answer is 17. If the first differences are not constant, look at the differences of the differences.

Letter Series

Convert letters to their position values (A=1, B=2, ... Z=26) and the hidden rule usually becomes an ordinary number pattern.

• Skip forward: A, C, E, G, ? -> positions 1, 3, 5, 7 (skip one each time) -> I (9).
• Skip backward: Z, X, V, T, ? -> 26, 24, 22, 20 -> R (18).
• Mirror pairs: AZ, BY, CX, ? -> each pair sums to 27 (A+Z = 1+26), so after C(3) the partner is 27-4 = 23 = W and the letter is D(4): answer DW.
• Two-track letters: A, B, D, G, K, ? -> gaps grow +1, +2, +3, +4, so from K(11) add 5 -> P (16).

Figure & Abstract Reasoning

Figural items show a sequence of shapes; you must pick the next figure. Isolate the one feature that changes each step. The four transformation rules:

1. Rotation — the figure turns a fixed angle, usually 90 degrees clockwise or counter-clockwise. Example: an arrow points UP, RIGHT, DOWN, ... — that is a 90-degree clockwise turn each step, so the next is LEFT, then back to UP.
2. Reflection — the figure flips across a mirror line (left-right or top-bottom); a shape facing right now faces left.
3. Addition / subtraction of elements — dots, sides, or lines increase or decrease by a set count: a box with 1, 2, 3 dots continues to 4 dots; a polygon gaining one side each step goes triangle -> square -> pentagon.
4. Shading / size change — shading rotates among positions, or a shape alternates small-large-small.

Often two features change together (for example, an arrow rotates 90 degrees while a dot count increases by one). Track each feature in its own column, project both forward, then find the option that satisfies both.

Symbolic Reasoning & Coding

Coding-decoding items replace letters with other letters or symbols by a fixed rule; find the shift.

• Caesar shift: if CAT is written DBU, every letter advanced +1 (C->D, A->B, T->U). To code DOG, apply +1: EPH. To decode, reverse the shift (-1).
• Reverse alphabet: if A maps to Z and B to Y, the code is the 27-minus-position mirror; CAB becomes XZY.
• Symbol substitution: a legend assigns each letter a symbol; solve by direct look-up, checking that repeated letters use the same symbol.

A Reliable Routine

For any abstract item: (1) state the rule in words before touching the choices; (2) confirm the rule holds across all given terms, not just the first two; (3) if one rule fails, test alternating or two-feature patterns; (4) generate the next term yourself, then match it to an option rather than reading options first. This self-generate-then-match habit prevents the exam's look-alike distractors from steering you.

Figure Analogies and Odd-One-Out

Some figural items are analogies: figure A : figure B :: figure C : ?. Solve them exactly like word analogies — describe the transformation from A to B (rotate 90 degrees, add a dot, shade the top half), then apply the same transformation to C. If A-to-B removes one side of a polygon, then C-to-answer must also remove one side.

Odd-one-out items give four or five figures and ask which breaks the shared rule. Identify the property common to the majority (all have an even number of sides, all arrows point inward), then flag the single figure that violates it.

Number Analogy

Number analogies apply the same bridge logic to digits: 2 : 8 :: 3 : ?. If the rule is "x4," then 2 x 4 = 8 and 3 x 4 = 12; if the rule is "n cubed," then 2 becomes 2^3 = 8 and 3 becomes 27. Because two rules can fit a single pair, confirm the rule is consistent with a second relationship in the item before committing.

Quick Checklist

• Numbers: test difference, ratio, squares/cubes, then alternating.
• Letters: convert to position value, then check skip or mirror.
• Figures: rotate, reflect, add/remove elements, shade.
• Codes: find the fixed shift, then apply or reverse it.