Which of the following smartphones is among the top three scorers on all six aspects?
Answer and solution
Correct answer: D
Solution
Answer: D — None of the smartphones
1. To eliminate a phone, find one aspect on which its rank is below third.
2. Alpha is fourth on Design (35). Beta is fourth on Performance (55). Gamma is fifth on Design (25).
3. Delta is fourth on Durability (40), and Epsilon is fifth on Durability (30).
4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.
Detailed setup and verification:
A universal condition such as top three on all six aspects can be rejected by a single counterexample. There is no need to calculate every full ranking for a phone once one failing aspect is found. For example, Design scores 90,65,45,35,25 place Alpha fourth and Gamma fifth.
Performance scores 85,65,60,55,45 put Beta fourth. Durability scores 90,70,50,40,30 eliminate Delta and Epsilon. All five phones have a failing aspect, proving None rather than merely showing that one listed candidate fails.
Verification: 4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
1. To eliminate a phone, find one aspect on which its rank is below third.
2. Alpha is fourth on Design (35). Beta is fourth on Performance (55). Gamma is fifth on Design (25).
3. Delta is fourth on Durability (40), and Epsilon is fifth on Durability (30).
4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.
Detailed setup and verification:
A universal condition such as top three on all six aspects can be rejected by a single counterexample. There is no need to calculate every full ranking for a phone once one failing aspect is found. For example, Design scores 90,65,45,35,25 place Alpha fourth and Gamma fifth.
Performance scores 85,65,60,55,45 put Beta fourth. Durability scores 90,70,50,40,30 eliminate Delta and Epsilon. All five phones have a failing aspect, proving None rather than merely showing that one listed candidate fails.
G Strategy shortcut
Method: One counterexample eliminates each phone; no need to calculate all 30 ranks.Verification: 4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: One counterexample eliminates each phone; no need to calculate all 30 ranks. Verification: 4. Every phone fails on at least one aspect. No smartphone is top three on all six. Answer D. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.