Logical Reasoning and Analytical Ability: Formal Structure Over Intuition
This domain tests structured reasoning rather than general knowledge. Recurring question types are syllogisms, number and letter series, coding-decoding, blood relations, direction sense, seating and ranking puzzles, assumptions and conclusions, strengthening and weakening arguments, and cause-effect pairs. The reliable strategy is to formalise the statement before answering, and to test a conclusion by trying to construct a counterexample.
Syllogisms and formal logic
- Treat 'All A are B' as a subset relation. Its valid converse is 'Some B are A', valid only where A is non-empty.
- 'Some A are B' converts to 'Some B are A'. It does not imply 'Some A are not B'.
- 'No A is B' converts to 'No B is A'.
- A conclusion follows only if it is true in every diagram consistent with the premises. One counter-diagram is enough to reject it.
Series and coding
- Check successive differences, then ratios, then second differences, then alternating patterns between odd and even positions.
- Letter series: convert to positions, and watch for reversal, skip patterns and vowel-consonant alternation.
- Coding-decoding: test shift, reversal, position swap and letter-to-number mapping in that order; state the rule you used.
Arguments and assumptions
- An assumption is an unstated premise necessary for the argument to work; negate it and see whether the argument collapses.
- A strengthening option makes the conclusion more likely without proving it; a weakening option introduces an alternative cause or a counterexample.
Worked example 1: syllogism
Premises: All officers at this post are trained in risk analysis. Some trained staff are rostered to night duty. Conclusion offered: some officers at this post are rostered to night duty. Invalid. The trained staff on night duty may be people who are not officers at this post; the two groups need not overlap. Only the conversion 'some trained staff are officers at this post' follows.
Worked example 2: direction sense
A patrol moves 6 km north, then 8 km east. Displacement is the hypotenuse of a right triangle: the square root of 36 plus 64, that is 10 km, while the total distance travelled is 14 km. Read the question: distance and displacement are different answers.
Traps that cost marks
- Importing real-world knowledge into a formal syllogism.
- Assuming that some means some but not all.
- Treating a plausible conclusion as a valid one.
- Answering total distance when displacement is asked, or vice versa.
- Drawing only one Venn diagram and stopping there.