Analytical Aptitude

Syllabus: Analytical Aptitude: Logic - deduction and induction; analogy; numerical relations and reasoning.

Deduction, induction and validity

A conclusion is valid only if it must follow — not if it merely could. Draw the Venn diagram in every way the premises allow; if a single arrangement breaks the conclusion, it does not follow. Real-world truth is irrelevant, which is what makes these questions feel odd.

$\text{All A are B}\ \not\Rightarrow\ \text{All B are A}$
the converse is not implied
$\text{All A are B}\ \Rightarrow\ \text{Some B are A}$
valid, and easy to miss
$\text{Some A are B}\ \Rightarrow\ \text{Some B are A}$
"some" is symmetric
$\text{No A is B}\ \Rightarrow\ \text{No B is A}$
$\text{two particular premises}\Rightarrow\text{no definite conclusion}$
two "some" statements never combine
$P\to Q:\ \neg Q\to\neg P\ \text{(valid)};\ \ Q\to P\ \text{(invalid)}$
contrapositive is valid; converse is the classic fallacy

Where marks are lost

Induction generalises from examples and is never certain; deduction is. If a question asks which conclusion definitely follows, an inductively reasonable option is still the wrong answer.

Analogy and numerical relations

Name the relationship in a short sentence before looking at the options — X is the tool used by Y, X is a part of Y, X is the cause of Y. Then apply that sentence to each option and keep the one that fits exactly, including direction.

$\text{name the relation first}$
tool:worker, part:whole, cause:effect, degree, function.
$\text{direction matters: }A\!:\!B\ \text{must map as}\ C\!:\!D,\ \text{not}\ D\!:\!C$

Arrangements and puzzles

Start from the most constrained statement, not the first one. Build a grid and enter only what is forced; where two possibilities remain, carry both branches and let a later clue kill one. Guessing early and backtracking wastes more time than carrying two cases.

$\text{linear: fix the ends first}$
the ends have the fewest neighbours
$\text{circular}$
Fix one person, then place everyone relative to them — that removes the rotational ambiguity.
$\text{facing inward}\Rightarrow\text{left/right reverse from the reader's view}$

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