CAT Logical Reasoning (Lr) Flashcards

24 sample cards from the Logical Reasoning (Lr) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. In number/letter series, what are the common patterns to check?

   Constant difference (arithmetic), constant ratio (geometric), differences of differences (second-order), prime numbers, squares/cubes, alternating series, and Fibonacci-type (each term = sum of previous two).

2. What is the next term and rule for the series 2, 6, 12, 20, 30, ...?

   Next term is 42. Rule: differences are 4, 6, 8, 10, 12 (increasing by 2); equivalently term n = n(n+1).

3. What is a syllogism, and what are its three components?

   A syllogism is a logical argument deriving a conclusion from two premises. Components: major premise, minor premise, and conclusion, each using quantifiers (All, Some, No, Some-not).

4. State the four standard categorical (syllogism) statement types and their letters.

   A: Universal affirmative (All S are P). E: Universal negative (No S is P). I: Particular affirmative (Some S are P). O: Particular negative (Some S are not P).

5. In syllogisms, what immediate conversions are valid?

   'All A are B' converts to 'Some B are A'. 'No A is B' converts to 'No B is A'. 'Some A are B' converts to 'Some B are A'. 'Some A are not B' has NO valid conversion.

6. What is the 'possibility' rule for the conclusion 'Some A are B' when premises give 'All A are B'?

   If 'All A are B' is given (definite), then 'Some A are B' is definitely true, and 'Some A are not B' is a possibility (not certain). Definite conclusions take priority over possibility cases.

7. In syllogisms, what is the rule when both premises are negative or both are particular?

   No definite conclusion can be drawn if both premises are negative, or if both premises are particular (Some). At least one premise must be universal and one affirmative for a valid definite conclusion.

8. What is 'binary logic' (truth-teller/liar puzzles), and the two main person types?

   Binary logic puzzles feature people who are either always truth-tellers (every statement true) or always liars (every statement false). Some variants add 'alternators' who alternate true/false statements.

9. What is the standard method to solve a truth-teller/liar puzzle?

   Assume one person's type (truth-teller or liar), trace the implications of all statements, and check for contradictions. If a contradiction arises, the opposite assumption holds. Test each case systematically.

10. In binary logic, if person A says 'I am a liar', what type can A be?

    A cannot consistently be either a pure truth-teller or pure liar (it is a paradox). In standard puzzles this means A is an alternator, or the scenario is impossible for pure types.

11. In a knockout (single-elimination) tournament with n players, how many matches are played to determine a winner?

    n - 1 matches, since every match eliminates exactly one player and all but the winner must be eliminated.

12. In a round-robin tournament with n teams where each plays every other once, how many total matches occur?

    nC2 = n(n-1)/2 matches.

13. In a round-robin league, how are total points/wins constrained, and why is this useful?

    Total wins across all teams = total matches played (each match yields one win, assuming no draws). This conservation lets you back-solve unknown results from a points table.

14. In tournament/game logic puzzles with a points table, what columns must always be reconciled?

    Matches played, Won, Lost, Drawn (W+L+D = played), and Points (using the scoring rule, e.g. 2 for win, 1 for draw). Goals for/against may also need balancing.

15. What defines a 'numerical puzzle' in LR, and give a common example type.

    Puzzles where numeric values (ages, scores, amounts) must be deduced from quantitative clues and constraints. Examples: age problems, sum/product constraints, magic squares, and budget distributions.

16. In a 3x3 magic square using numbers 1-9, what is the magic constant (sum of each row/column/diagonal)?

    15. (Total 1+...+9 = 45; divided by 3 rows = 15.) The centre cell must be 5.

17. What is the general formula for the magic constant of an n x n magic square using 1 to n^2?

    Magic constant = n(n^2 + 1)/2.

18. What is 'data arrangement with figures', and what extra dimension does it add?

    Puzzles where arrangement is described via or combined with a diagram/figure (floor plans, seating maps, network/route maps, Venn-like figures). The figure adds spatial/positional constraints beyond pure logical clues.

19. In a multi-floor building arrangement puzzle, how do you interpret 'A lives immediately above B'?

    A's floor number = B's floor number + 1 (adjacent floors, A higher). 'Above' (not immediate) only means A's floor > B's floor.

20. What is the recommended order of operations for tackling any LR set under time pressure?

    1) Read all clues, 2) identify the puzzle type, 3) note the most restrictive/definite clues first, 4) build a framework (grid/line/circle/tree), 5) place definite clues, then test possibilities by elimination.

21. What is the difference between a 'fixed' clue and a 'floating' clue in arrangement puzzles, and which do you use first?

    A fixed clue pins an item to a definite position or definite relationship; a floating clue gives relative info that can shift. Always apply fixed/definite clues first to reduce the solution space.

22. In coding-decoding, how do you decode a 'positional/conditional' code where rules depend on whether letters are vowels or consonants?

    Identify each character's category (vowel/consonant, first/last position), apply the stated conditional rule to each, and watch for special cases (e.g. 'if the word begins with a vowel, swap first and last codes').

23. In selection puzzles, how do you treat the constraint 'Exactly one of A and B must be selected'?

    It is an exclusive-or (XOR): either A is in and B is out, or B is in and A is out; both-in and both-out are invalid. Split into two cases and test each.

24. In circular arrangements with people facing both inward and outward, what is the key thing to confirm for each individual before applying left/right clues?

    Confirm each person's individual facing direction first, because left/right reverse depending on whether that specific person faces the centre or away. Treat each person's orientation separately.

What this deck covers

Logical Reasoning (Lr) flashcards FAQ