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ACET (Philippines University Entrance Tests): Abstract Reasoning: Pattern Recognition and Logical Sequences

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Abstract Reasoning: Pattern Recognition and Logical Sequences

Abstract reasoning measures your ability to detect patterns, rules, and relationships in sequences, shapes, and logical puzzles. Common item types include number sequences, letter series, analogies, classification (odd-one-out), and matrix or grid patterns. The core method is systematic: for number sequences, check differences, then ratios, then alternating or interleaved patterns (two sequences woven together). For letter series, convert letters to positions (A=1 … Z=26) and look for constant or increasing jumps, reversals, or alternating directions. For shape patterns, track one attribute at a time: number of sides, rotation, shading, size, and position.

Traps to watch

  • Assuming a single rule when the sequence is interleaved (e.g., odd positions follow one rule, even positions another).
  • Overlooking sign changes or alternating operations (+3, ×2, −3, ×2).
  • In odd-one-out items, more than one feature may differ; find the feature shared by all but one.
  • Misreading rotation direction (clockwise vs. counterclockwise).

Worked example

Sequence: 2, 6, 3, 9, 4, 12, ?. Check interleaving: odd positions 2, 3, 4 (add 1); even positions 6, 9, 12 (add 3). The next term is at position 7 (odd), so 4 + 1 = 5. Rule of thumb: if first differences look erratic, split the sequence into two interleaved strands.