30 syllogism and inequality questions for practice

Reasoning becomes exam-ready when you can prove or disprove a claim under time pressure. This set mixes categorical syllogisms with mathematical inequalities, building sound inference and judgment for Indian SSC, banking, insurance and civil service examinations.

Each syllogism item offers premises and a conclusion. Decide whether it definitely follows, definitely fails, or cannot be established. Inequality items ask for relations using signs, direct chains and reverse reasoning. Treat “some”, “all” and “no” as distinct.

Australian students can fit the drill into commutes across Melbourne and Sydney, using an Opal card or Myki top-up. Expressions such as “no worries”, “have a go” and “fair dinkum” value directness. In an exam, ambiguity receives no automatic benefit.

The goal is active practice, not passive familiarity. Complete items under a fixed limit, mark uncertain responses and explain each answer in one sentence. Separate speed sessions from error analysis so quick guessing does not conceal weak reasoning.

Build a diagram before choosing

For a syllogism, sketch the categories and test the conclusion against matching and non-matching models. If either works, the result is uncertain. For inequalities, use a number line and preserve every sign’s direction.

Keep the routine repeatable: read, map, decide, justify. A guide to finding north captures the principle of fixing a reference point before following a route. In reasoning tests, the diagram plays that role and prevents intuitive leaps.

Coles and Woolworths dominate Australian supermarket retail, but “All Coles stores are supermarkets” does not mean every supermarket is a Coles store. Reversing that statement creates an invalid conclusion.

Syllogism practice questions

For items 1–15, choose T if the final conclusion follows, F if it fails, and C if it cannot be settled.

1. All A are B; all B are C. All A are C.
2. All A are B; all C are B. All A are C.
3. No A is B; all C are B. No C is A.
4. Some A are B; some B are C. Some A are C.
5. All A are B; some B are C. Some A are C.
6. All A are B; no B is C. No A is C.
7. Some A are B; all B are C. Some A are C.
8. No A is B; no B is C. No A is C.
9. Some A are B; no B is C. Some A is not C.
10. All A are B; some C are not B. Some C are not A.
11. No A is B; some B are C. Some C are not A.
12. All A are B; all C are B. Some A are C.
13. Some A are B; no B is C. Some A are C.
14. All A are B; all C are B. No A is C.
15. All A are B; no B is C. Some A are C.

Cricket helps with negative conclusions: a dismissal removes a player from the innings, as “no B is C” excludes overlap. Ask whether the premises make the tested overlap possible or impossible. Items 4, 5, 8, 12 and 14 are traps.

As a current-affairs extension, test the Union Budget deficit target the same way: state the premises, then check whether the conclusion adds an unsupported claim.

Inequality practice questions

For items 16–30, state the relation between A and C using >, <, = or no definite relation.

16. A > B; B > C.
17. A > B; B > C. Express C relative to A.
18. A < B; B < C.
19. A = B; B > C.
20. A > B; B = C.
21. A > B; B < C.
22. A ≥ B; B > C.
23. A > B; B ≤ C.
24. A ≤ B; B > C.
25. A < B; B > C.
26. A ≥ B; B ≤ C.
27. A ≥ B; B = C.
28. A ≤ B; B ≤ C.
29. A = B; B = C.
30. A > B; B < C; C < D. Relate A and D.

Write the whole chain first. In 17, C < A means A > C, but keeping the requested orientation catches direction slips. A weak sign followed by a strict sign yields strict; two weak signs yield only weak.

Answer key and error analysis

Marking without diagnosis wastes effort. For every C answer, name the missing witness or assumption; for every F answer, identify the contradiction. Tag errors as quantifier, diagram, direction or time. A cricket scorecard identifies the cause, while an ATAR-style ranking rewards precision.

The key is:

• Syllogism: 1 T; 2 C; 3 T; 4 C; 5 C; 6 T; 7 T; 8 C; 9 T; 10 T; 11 T; 12 C; 13 F; 14 C; 15 F.
• Inequality: 16 A > C; 17 C < A; 18 A < C; 19 A > C; 20 A > C; 21 no definite relation; 22 A > C; 23 no definite relation; 24 no definite relation; 25 no definite relation; 26 no definite relation; 27 A ≥ C; 28 A ≤ C; 29 A = C; 30 no definite relation.

Compare errors, not just totals. Questions 4 and 12 punish reversed inclusion; 13 and 15 expose impossible overlap. For a separate quantitative interval, try probability problems for exams without weakening this set’s focus.

Common mistakes under time pressure

Three errors lose marks: changing “all” to “some”, reversing a sign, or forcing a relation from chains that never meet. Read the final symbol carefully: item 17 asks for C to A, not A to C.

Use a two-pass strategy. First answer clear items and mark uncertain ones; then attack marked items with fresh diagrams. If time is nearly gone, an omitted response protects the easy score, while a rushed guess can consume time without adding certainty.

Compare the methods and start practising

Use the comparison to choose a review target. Weak syllogism results point to category diagrams; weak inequality results point to sign handling. Record them separately because the remedies differ.

Feature	Syllogism	Inequality
Core task	Test whether a conclusion follows	Compare two quantities
Best tool	Venn diagram	Number line
Main risk	Reversing inclusion or quantifiers	Losing direction or strengthening weak signs
Valid result	Follows, fails or uncertain	>, <, = or no definite relation

If both scores are low, begin with items 1, 7, 16 and 28, which reinforce the basic models. If one is strong, protect it with short mixed blocks rather than abandoning it.

Open a fresh page, set a 25-minute timer and complete all 30 questions now. Check the key and write one reason beside every uncertain or incorrect item, turning this paper into a measurable next session.