Logic & Acumen

Statements and propositions · true and false statements · facts vs assumptions · premises and conclusions · valid and invalid reasoning · logical consistency · drawing conclusions · identifying contradictions.

Number patterns · arithmetic, geometric and alternating patterns · increasing and decreasing patterns · missing terms · pattern rules · mixed sequences.

Number relationships · odd and even reasoning · factors and multiples · divisibility patterns · number properties · missing-number puzzles · number analogies · number grids.

Translating information into mathematics · choosing appropriate operations · multi-step reasoning · estimation · constraint-based problems · working backward · multiple solution methods · checking reasonableness.

Number, word, symbol and figure analogies · part-to-whole relationships · cause and effect · functional relationships · identifying the relationship rule

Number, word, shape and symbol classification · identifying common properties · finding the odd one out · multiple-rule and abstract classification.

Letter, number and symbol coding · substitution codes · position-based codes · pattern-based coding · mixed letter-number codes · decoding hidden rules.

Alphabet positions · forward and backward sequences · letter patterns · missing letters · letter-number relationships · symbol sequences and substitution.

Given facts and conditions · drawing valid conclusions · if-then reasoning · eliminating impossible choices · multiple-condition reasoning · necessary vs possible conclusions · deductive puzzles.

If-then statements · converse, inverse and contrapositive · necessary and sufficient conditions · compound conditions · logical equivalence.

Understanding sets · membership and subsets · union, intersection and complement · two- and three-set Venn diagrams · Venn diagram word problems.

Premises and conclusions · all/some/no statements · positive and negative statements · testing conclusions · Venn-diagram syllogisms · valid vs invalid conclusions · multi-statement syllogisms.

Position and rank · highest and lowest · before and after · greater and smaller · left-to-right ordering · ranking from multiple clues · relative positions · multiperson problems.

Linear and circular arrangements · facing directions · adjacent and opposite positions · fixed-position clues · conditional seating · multi-condition arrangements.

Cardinal directions · left and right turns · direction changes · distance and direction · relative positions · route tracing · shortest path · multi-step direction problems.

Mental rotation · shape transformations · reflections and symmetry · folding and unfolding · paper folding and cutting · figure completion · spatial relationships.

Figure sequences · missing figures · figure analogies · odd figure out · embedded figures · figure matrices · rotation and transformation patterns.

Cube faces · opposite and adjacent faces · cube nets · folding cubes · painted cubes · dice positions · three-dimensional visualisation

Clock arithmetic · clock angles · time intervals · calendar patterns · days and dates · odd days · repeating calendars · calendar reasoning problems.

Present, past and future ages · age ratios and differences · family relationships · generation relationships · family-tree reasoning · multicondition age problems.

Ratios and proportions · percent reasoning · rates · averages · fractions and decimals · comparison problems · estimation · quantitative word problems.

Tables · bar graphs · line graphs · pie charts · pictographs · comparing data · trends and patterns · multi-chart reasoning.

Understanding what information is needed · sufficient vs insufficient information · one- and two-statement sufficiency · numerical, algebraic, geometric and logical sufficiency

Assignment and scheduling puzzles · grouping and matching problems · distribution problems · ordering constraints · multiple-condition and logicgrid puzzles.

Finding the best solution · minimum and maximum problems · shortest-path reasoning · resource allocation · scheduling optimisation · comparing alternatives · decision strategies

Basic probability · sample spaces · counting possibilities · the fundamental counting principle · permutations and combinations · independent events · conditional reasoning.

Identifying assumptions · evidence vs opinion · strong vs weak arguments · relevant vs irrelevant information · cause vs correlation · identifying bias · detecting contradictions · evaluating claims.

Identifying conclusions and supporting evidence · strengthening and weakening an argument · finding assumptions · evaluating evidence · comparing arguments · drawing justified conclusions.

Understand the problem · organise information · draw a diagram · make a table · look for patterns · work backward · eliminate possibilities · break problems into parts · trial and improvement · verify the solution.

Multi-step logic puzzles · mixed quantitative reasoning · complex pattern recognition · advanced arrangements · multi-layer deduction · strategy and mathematical puzzles · real-world decision problems.