Analytical Aptitude

Analytical questions test whether a conclusion follows from the given information. Convert statements into a compact representation, then check every inference against it. For numerical relations, inspect differences, ratios, alternating terms, and position effects systematically; test a proposed rule on every supplied term.

Deduction and induction

Idea. Deduction applies stated rules to reach a conclusion that must follow if the premises are true. Induction finds a pattern from examples and proposes a likely rule; it does not guarantee that the rule is the only possible one. For “all,” “some,” and “none,” keep the quantifier exactly as strong as given.

Solved examples.

1. Question. All calibrated sensors pass inspection. Sensor P is calibrated. What follows? Solution. (1) The universal rule applies to every calibrated sensor. (2) P meets its condition. (3) Therefore P passes inspection. Answer. P passes inspection. Trap. This does not imply every inspected sensor is calibrated.
2. Question. Some reports are delayed. All delayed reports require review. Must some reports require review? Solution. (1) At least one report is delayed. (2) Every delayed report requires review. (3) The delayed report therefore belongs to the reviewed group. Answer. Yes, at least one report requires review. Trap. “Some” means one or more, not most or all.
3. Question. No metal samples are transparent. Some tested objects are metal samples. What must be true? Solution. (1) Each metal sample is not transparent. (2) At least one tested object is a metal sample. (3) That object is not transparent. Answer. At least one tested object is not transparent. Trap. The conclusion concerns some tested objects, not all of them.
4. Question. If the alarm is active, the indicator is red. The indicator is not red. What follows? Solution. (1) Let A mean active and R mean red. Rule is $A\Rightarrow R$. (2) We know $\neg R$. (3) By modus tollens, $\neg A$. Answer. The alarm is not active. Trap. From $A\Rightarrow R$ and R alone, one cannot infer A.
5. Question. Over five days, a plant grew 2, 4, 6, 8, then 10 mm. Is “growth rises by 2 mm each day” a deduction or induction? Solution. (1) The observation is a finite list. (2) A constant difference of 2 fits the observations. (3) Other future patterns could also fit those five values. Answer. Induction suggests the pattern but does not prove it continues. Trap. Observed regularity is not certainty about unobserved cases.

Logical relations and case analysis

Idea. Translate “if P then Q” as implication, “P only if Q” as $P\Rightarrow Q$, and “P if Q” as $Q\Rightarrow P$. To test a conclusion, try to construct a case satisfying all premises but violating the conclusion. If such a case exists, the conclusion does not follow.

Solved examples.

1. Question. A person enters only if registered. Nila entered. What follows? Solution. (1) “Enters only if registered” means entry implies registration. (2) Nila entered. (3) Apply the implication. Answer. Nila is registered. Trap. “Only if” introduces a necessary condition.
2. Question. Either the lab is open or the key is with the guard, possibly both. The lab is closed. What follows? Solution. (1) “Either” here allows both. (2) Since lab open is false, the disjunction can hold only if the key condition is true. Answer. The key is with the guard. Trap. Do not assume exclusive-or unless stated.
3. Question. If a file is encrypted, it requires a key. File F requires a key. Must F be encrypted? Solution. (1) Premise says encryption is sufficient for requiring a key. (2) Other reasons may also require a key. (3) A non-encrypted protected file is a counterexample. Answer. No. Trap. This is affirming the consequent.
4. Question. Three boxes A, B, C are ordered. A is before B; C is after B. Which is last? Solution. (1) A precedes B. (2) B precedes C. (3) Transitivity gives A before B before C. Answer. C. Trap. Combine pairwise constraints before selecting a position.
5. Question. Exactly one of X and Y is true. X is false. What is Y? Solution. (1) “Exactly one” excludes both true and both false. (2) Given X false, the true member must be Y. Answer. Y is true. Trap. “At least one” alone would not be enough for this inference.

Analogy

Idea. An analogy compares relations, not surface similarity. Express the first pair as a verb phrase—“tool is used to perform action,” “part belongs to whole,” or “cause produces effect”—then test whether the second pair has the same direction and relation.

Solved examples.

1. Question. Thermometer : temperature :: barometer : ? (A) pressure (B) rain (C) wind (D) height Solution. (1) A thermometer measures temperature. (2) A barometer measures pressure. Answer. (A). Trap. Match the function, not an associated weather outcome.
2. Question. Seed : plant :: egg : ? (A) nest (B) bird (C) feather (D) shell Solution. (1) A seed can develop into a plant. (2) An egg can develop into a bird. Answer. (B). Trap. The relationship is developmental, not container-to-object.
3. Question. Compiler : source program :: translator : ? (A) target language (B) source text (C) dictionary (D) speaker Solution. (1) A compiler acts on a source program to produce a representation. (2) A translator acts on source text. Answer. (B). Trap. Identify the input relation rather than a possible output.
4. Question. Choose an analogous relation: “sparrow is to bird as salmon is to ___.” Solution. (1) Sparrow is a member of the broader class bird. (2) Salmon is a member of a broader class. Answer. Fish. Trap. Preserve category direction: specific first, general second.
5. Question. Lock : key :: question : ? (A) answer (B) paper (C) reader (D) ink Solution. (1) A key is the means that opens a lock. (2) An answer resolves a question. (3) Both pairs link a problem or barrier to its resolution. Answer. (A). Trap. Analogy relations may be functional rather than exact object similarity.

Numerical relations and reasoning

Idea. For number series, calculate first and sometimes second differences; test ratios and alternating subsequences. For a relation puzzle, define symbols and track constraints without changing their direction. A rule is acceptable only if it explains all given terms.