Logic, Analytical and Quantitative Reasoning
What to master
Three families of items appear. Deductive logic: syllogisms, conditional reasoning (if P then Q; contrapositive; inverse and converse errors), and quantifiers (all/some/none). Analytical reasoning: ordering, grouping, and scheduling puzzles solved by building a diagram and applying constraints. Quantitative reasoning: percentages, ratios, averages, rates (work, speed, mixtures), and simple probability.
Traps to expect
- Converse and inverse errors: from "if P then Q" you may infer "if not Q then not P" (contrapositive), but not "if Q then P" nor "if not P then not Q".
- Percentage base changes: a 20% rise followed by a 20% fall does not return to the original value; always recompute on the new base.
- Averages: adding a value changes the mean; the sum matters, not the count alone.
- Some/none: "some A are B" does not imply "some A are not B" unless existence is stated.
Rule of thumb
For conditionals, negate and swap to get the valid contrapositive. For percentages, convert to multipliers (a 20% rise is ×1.2; a 20% fall is ×0.8) and multiply in sequence. For puzzles, write the constraints as a list and eliminate options one by one.
Worked example
A price rises 20% then falls 20%. Multipliers: 1.2 × 0.8 = 0.96, a net 4% decrease, not zero change. The trap is assuming the two changes cancel; recomputing on the changed base shows they do not.