Consider the following three comparative statements about how many movies three people saw during the past year: I. During the past year, Josh saw more movies than Stephen. II. Stephen saw fewer movies than Darren. III. Darren saw more movies than Josh. Based only on statements I and II, the truth status of statement III is:

Difficulty: Easy

Correct Answer: The third statement cannot be determined from the first two statements.

Explanation:


Introduction / Context:
This logical reasoning question tests your ability to compare quantities using relational statements and decide whether a third statement is necessarily true, necessarily false, or simply not decidable from the given information. Such questions are common in aptitude exams to check clear thinking rather than arithmetic skill.


Given Data / Assumptions:


    • Josh, Stephen and Darren are being compared only by the number of movies they saw during the past year.

    • Statement I: During the past year, Josh saw more movies than Stephen (so Josh > Stephen).

    • Statement II: Stephen saw fewer movies than Darren (so Darren > Stephen).

    • Statement III: Darren saw more movies than Josh (Darren > Josh). We must judge this using only I and II.


Concept / Approach:
We translate each English sentence into an inequality and then see what relationships are forced. If the information does not uniquely determine the relationship between Darren and Josh, then the third statement is not logically fixed and will be classified as “cannot be determined from the first two statements”.


Step-by-Step Solution:
Step 1: From Statement I, Josh > Stephen. Step 2: From Statement II, Darren > Stephen. Step 3: Combining these, we only know that both Josh and Darren individually saw more movies than Stephen. Step 4: There is no direct comparison given between Josh and Darren in Statements I and II. Step 5: It is possible that Darren > Josh, Josh > Darren, or even Darren = Josh, while still keeping Josh > Stephen and Darren > Stephen true. Step 6: Since all these different scenarios fit Statements I and II, the truth of Statement III is not uniquely determined.


Verification / Alternative check:
Consider numerical examples. Let Stephen = 5 movies. If Josh = 9 and Darren = 12, then I and II are true and III (Darren > Josh) is also true. But if Josh = 12 and Darren = 9, then I and II are still true, yet III is now false. Since both possibilities exist while keeping I and II valid, we cannot fix the truth of III from the given information alone.


Why Other Options Are Wrong:
Option A (“always correct”) is wrong because we just found a case where Josh saw more movies than Darren, making III false while I and II remain true.
Option B (“always incorrect”) is wrong because we can choose numbers where Darren clearly saw more movies than Josh, making III true while I and II remain true.
Option D (“unrelated”) is wrong because Statement III is clearly about the same three people and the same comparison of movie counts as in I and II; it is logically connected even if not deducible.


Common Pitfalls:
A common mistake is to assume that if two people each saw more than a third person, then one of them must have seen more than the other in a fixed way. Another error is to think that if a relationship is not explicitly stated, it must be false. In logical reasoning, “not stated” or “not deducible” is very different from “false”. Always check whether multiple numerical examples can satisfy the given premises but give different truth values for the statement under test.


Final Answer:
Thus, the third statement's truth cannot be fixed by the first two statements alone, so the correct choice is The third statement cannot be determined from the first two statements.

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