Reasoning and Problem Solving
Reasoning and Problem Solving
This domain tests deductive and inductive logic plus quantitative problem solving under time pressure. Deductive items supply premises that must entail a conclusion; inductive items ask for the most likely pattern or generalization. Quantitative items cover ratios, percentages, weighted averages, rate/work problems, and data interpretation without a calculator.
Core rules
- In conditional logic, A -> B means if A then B. Valid inferences: A therefore B; not B therefore not A (contrapositive). Invalid: B therefore A; not A therefore not B.
- "All X are Y" does not imply "all Y are X." Treat categorical statements by their actual scope, not by everyday assumptions.
- Percent changes compound and depend on the base. A 20% increase followed by a 20% decrease leaves 96% of the original, not 100%.
- Number series often alternate operations, use squares or primes, or combine two sequences.
Worked example
Premises: "If the package cleared customs, then the manifest was filed. The manifest was not filed." The valid conclusion is that the package did not clear customs, because not-B implies not-A. You cannot conclude that officers were negligent; that fact is outside the premises. If the second premise were "the manifest was filed," you could not conclude the package cleared customs, because that affirms the consequent.
Traps
- Affirming the consequent or denying the antecedent.
- Reversing "all" statements or treating "some" as "all."
- Importing outside knowledge instead of using only the stated premises.
- Averaging percentages without weighting by group size.
- Missing unit conversions, such as hours to minutes or thousands to dollars.