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SOF IMO study materials
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SOF IMO: Mathematical Reasoning and Logical Ability - SOF IMO

SOF IMO · Work through your exam, one topic at a time.

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Mathematical Reasoning and Logical Ability - SOF IMO

Mathematical Reasoning and Logical Ability is the backbone of the SOF IMO paper: it checks whether you can spot structure in numbers, codes, patterns and arrangements rather than recall formulas. It supplies most of the Logical Reasoning and Mathematical Reasoning questions, and the hardest variants reappear in the Achievers section. Expect series and analogies, odd-one-out, coding–decoding, direction and ranking puzzles, blood relations, clocks and calendars, Venn diagrams, figure patterns, plus arithmetic and geometry reasoning.

Rules worth automating

  • Number series: test first differences, then second differences, then ratios; if nothing fits, split into two interleaved series and check squares or cubes plus or minus a constant.
  • Coding–decoding: write the alphabet with positions 1–26 and verify the shift letter by letter; watch for reversal and for A=1-style sum codes.
  • Direction sense: draw axes and rotate the facing direction, not the page; net displacement uses Pythagoras.
  • Ranking: total = position from left + position from right − 1.
  • Syllogisms: draw the minimum-overlap Venn diagram; a conclusion is valid only if it holds in every possible diagram.
  • Clocks: angle = |30H − 5.5M|. Calendars: an ordinary year has 1 odd day, a leap year 2.

Worked example

If MANGO is coded as OCPIQ, code APPLE. Compare positions: M(13)→O(15), A(1)→C(3), N(14)→P(16), G(7)→I(9), O(15)→Q(17) - every letter shifts +2. So A→C, P→R, P→R, L→N, E→G, giving CRRNG. The shift is established from all five letters before it is applied; assuming a rule from one letter is the commonest failure.

Traps that cost marks

Odd-one-out items where every option looks related but one breaks a property such as being a perfect square or divisible by 3; counting ranges where endpoints matter (the integers from 15 to 60 number 60 − 15 + 1 = 46); and turns described from a south-facing position, where 'left' is east. Re-read whether the question asks for 'cannot be determined' or 'not necessarily true'.