Logical Reasoning
Letter and Symbol Series
3,472 words, 8 sections
Letter and Symbol Series is the second unit of Logical Reasoning in the PMDC MDCAT-2025 uniform curriculum, and its three learning outcomes are arithmetical operations on numbers, geometrical progression on numbers, and series of letters and symbols that follow a given rule. Logical Reasoning is worth 9 of the 180 marks, and this is the heaviest of its chapters: 55 distinct questions across 23 official papers between 2012 and 2026, set by all six boards, Balochistan, DUHS, Federal, KMU, NUMS and UHS, at a mean item difficulty of 2.64, with 503 active questions in the practice bank. The weight is concentrated in Pattern Recognition in Sequences, which holds 42 of the 55 questions over 2014 to 2026; Alphabet Position and Coding takes 7 and Analogies and Classification 6. No textbook exists for this subject, so everything below is built from the sequences the papers actually set. A student who has this material can take any number, letter or mixed sequence, find the rule by testing the gaps and the ratios, and extend it without guessing.
The plain number series is the backbone of the chapter, and nearly all of these items are solved the same way: write the differences between consecutive terms in a line under the series, then read what those differences are doing. A sequence such as 3, 8, 14, 21 looks arbitrary until the gaps are written out as ; the gaps rise by one, so the next gap is and the next term is 29. The sequence itself never announces its rule. The gaps do.
When the first differences are not constant but have a pattern of their own, the method goes one layer deeper and takes the second difference. Take 2, 15, 41, 80. The first differences are $13, 26, 39$, which rise by 13 each time, so the next difference is 52 and the next term is 132. The triangular numbers 1, 3, 6, 10, 15, 21, 28 yield gaps of $2, 3, 4, 5, 6, 7$, so the next gap is 8 and the next term is 36. When the gaps themselves shrink by a fixed amount the rule simply runs downward: 15, 14, 12, 9 falls by $1, 2, 3$, so the next fall is 4 and the next term is 5.
A third family shrinks the rate itself. The series 200, 180, 162, 146, 132 drops by $20, 18, 16, 14$, and that drop is losing two each time, so the next drop is 12 and the next term is 120. The lesson across all three families is the same: never accept the first gap as the rule until the remaining gaps confirm it.
6 more sections in this chapter
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