Logical Reasoning & Problem Solving Flashcards

Three jars are labelled 'Red Marbles', 'Blue Marbles', and 'Mixed'. Every label is incorrect. Without looking inside, you reach into the jar labelled 'Mixed' and draw one marble — it is red. What does the jar labelled 'Red Marbles' actually contain?

Answer: Only blue marbles

Since all labels are wrong, the jar labelled 'Mixed' must contain only one colour. Drawing a red marble confirms it holds only red marbles. The jar labelled 'Blue Marbles' cannot contain blue (wrong label), and since red is already accounted for, it must hold the mixed collection. That forces the jar labelled 'Red Marbles' to contain only blue marbles. Every assignment is determined by elimination — no guessing required.

Identify the next number in the sequence: 4, 9, 25, 49, 121, 169, ___

Answer: 289

Each term is the square of a consecutive prime number: 2²=4, 3²=9, 5²=25, 7²=49, 11²=121, 13²=169. The next prime after 13 is 17, and 17²=289. The gaps between terms are not arithmetic or geometric — the underlying pattern is membership in the set of prime numbers.

A school surveyed 200 students about two extracurricular activities. 120 students play chess, 90 participate in debating, 40 do neither activity, and 15 belong to a separate photography club. How many students participate in BOTH chess and debating?

Answer: 50

Students in at least one activity = 200 − 40 = 160. By the inclusion-exclusion principle: |Chess ∪ Debate| = |Chess| + |Debate| − |Chess ∩ Debate|, so 160 = 120 + 90 − x, giving x = 50. The photography club figure (15) is a deliberate distractor — it has no bearing on the calculation.

A research report claims: 'University students who highlight their textbooks extensively score higher on end-of-year examinations. Therefore, highlighting is an effective study strategy that directly causes better exam performance.' Which statement, if true, most seriously undermines this conclusion?

Answer: Students who are already highly self-motivated tend to both highlight more and invest significantly more time in overall exam preparation

Option B identifies a confounding variable — academic self-motivation independently drives both greater highlighting behaviour and better exam results. This severs the proposed causal link: it is not the highlighting causing performance gains, but a third factor causing both. Option A shows exceptions but does not disprove the general causal claim. Option C introduces a contradictory mechanism without explaining the observed correlation. Option D raises an external validity concern but does not attack the causal reasoning itself.

Pipe A fills a tank in 6 hours, Pipe B fills the same tank in 9 hours, and Pipe C drains it in 18 hours. All three pipes are opened simultaneously at time zero. After exactly 1 hour, Pipe A is closed while B and C remain open. How many additional hours are required to completely fill the tank after Pipe A is closed?

Answer: 14 hours

Phase 1 (all three pipes, 1 hour): combined rate = 1/6 + 1/9 − 1/18 = 3/18 + 2/18 − 1/18 = 4/18 = 2/9 per hour. After 1 hour, 2/9 of the tank is filled; 7/9 remains. Phase 2 (B and C only): net rate = 1/9 − 1/18 = 2/18 − 1/18 = 1/18 per hour. Time to fill 7/9 at 1/18 per hour = (7/9) ÷ (1/18) = (7/9) × 18 = 14 hours.

A formal logical system has four rules: (1) If A, then B. (2) If B, then C. (3) If not-D, then not-C. (4) If D, then E. Assuming A is true, which of the following conclusions is INVALID?

Answer: D must be false

Starting from A: Rule 1 gives B; Rule 2 gives C. Rule 3 states 'if not-D, then not-C' — its contrapositive is 'if C, then D', so C being true forces D to be true. Rule 4 then gives E. The full chain is A → B → C → D → E, making all five propositions true. Concluding that D is false directly contradicts this chain and is therefore the invalid conclusion.