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General Aptitude · topic

Deduction, induction, analogy and numerical reasoning

Deduction with conditionals, contrapositive, only if and unless; categorical statements and syllogisms checked with Venn diagrams; induction and counterexamples; analogy and coding rules; number puzzles, arrangements, blood relations, directions, clocks and calendars.

Cheat sheets

GA-14Cheat sheet1 pageIn a paid pack

Deduction: Conditionals and Syllogisms

Deductive logic for GA: the analytical routine (translate, then test every case), conditional statements and their contrapositive, converse and inverse, only if, unless, necessary and sufficient conditions, negations, valid and invalid argument forms, the four categorical statements with Venn diagrams, syllogism checking by least-overlap diagrams and counter-models, complementary (either-or) pairs, and truth-teller puzzles. Every equivalence is checked by truth table and every syllogism by a model search.

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Diagrams from GA-14

Four Venn panels. All A are B: circle A inside circle B. No A is B: two separate circles. Some A are B: overlapping circles with a cross in the overlap. Some A are not B: overlapping circles with a cross in the part of A outside B.
The four categorical forms. A cross marks a region that must contain at least one member. Source: sheet GA-14.
Two Venn panels for the premises All A are B and Some B are C. Case 1: A inside B, C overlaps B away from A, with a cross in the B and C overlap outside A. Case 2: A inside B, C overlaps B and also A, with a cross in the A and C overlap.
All A are B, some B are C. Both models fit, so "some A are C" is possible, not certain. Source: sheet GA-14.

GA-15Cheat sheet1 pageIn a paid pack

Induction, Analogy and Coding

Inductive reasoning and its limits (generalisation, counterexamples, why a pattern that holds for many cases can still fail), how to choose between rules that fit the data, analogy by bridge sentences with a table of relation types, odd-one-out by category, number analogies, and letter and number coding: letter positions, opposite letters, shifts, reversal, alternating shifts and position sums.

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A partial preview of the top of the sheet. The full sheet is in the General Aptitude cheat sheet pack.

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GA-16Cheat sheet1 pageIn a paid pack

Numerical Relations and Reasoning

Number puzzles (digits and reversal, LCM and remainders, divisor counts, trailing zeros, divisibility tests, inclusion-exclusion counts, heads-and-legs), seating puzzles in a row with a worked elimination and a table for left and right in rows and circles, ranking, tournaments, blood relations with a family-tree notation, directions and displacement, clock-hand angles and coincidences, and calendars by odd days. Original examples, each checked by brute force or a date library.

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Partial preview

A partial preview of the top of the sheet. The full sheet is in the General Aptitude cheat sheet pack.

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Diagrams from GA-16

Walking path from a start point: 10 km north, then 6 km east, then 2 km south. A dashed line joins start to end and is labelled 10 km. A compass shows north up.
Net displacement 6 km east and 8 km north: 10 km, about 36.9 degrees east of north. Source: sheet GA-16.