Which option lists all the smartphones that are among the top two scorers on the greatest number of aspects?
Answer and solution
Correct answer: C
Solution
Answer: C — Alpha, Gamma and Delta
1. Rank phones separately within each aspect. Durability top two: Gamma, Alpha. Coverage: Alpha, Gamma. Performance: Alpha, Delta.
2. Design top two: Delta, Epsilon. Support: Delta, Beta. Price: Gamma, Beta.
3. Counts: Alpha 3, Beta 2, Gamma 3, Delta 3, Epsilon 1.
4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.
Detailed setup and verification:
Create one tally mark per top-two appearance, not one per win. Alpha qualifies on Durability, Coverage, Performance; Gamma on Durability, Coverage, Price; Delta on Performance, Design, Support. Each has three appearances. Beta qualifies on Support, Price and Epsilon only on Design.
There are six aspects and two places per aspect, so the total number of tally marks must be 12. The counts 3+2+3+3+1=12 verify that none was omitted or double-counted. The answer must name every phone tied for the highest tally.
Verification: 4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
1. Rank phones separately within each aspect. Durability top two: Gamma, Alpha. Coverage: Alpha, Gamma. Performance: Alpha, Delta.
2. Design top two: Delta, Epsilon. Support: Delta, Beta. Price: Gamma, Beta.
3. Counts: Alpha 3, Beta 2, Gamma 3, Delta 3, Epsilon 1.
4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.
Detailed setup and verification:
Create one tally mark per top-two appearance, not one per win. Alpha qualifies on Durability, Coverage, Performance; Gamma on Durability, Coverage, Price; Delta on Performance, Design, Support. Each has three appearances. Beta qualifies on Support, Price and Epsilon only on Design.
There are six aspects and two places per aspect, so the total number of tally marks must be 12. The counts 3+2+3+3+1=12 verify that none was omitted or double-counted. The answer must name every phone tied for the highest tally.
G Strategy shortcut
Method: Mark only the top two per column and tally. A/G/D each have 3 appearances.Verification: 4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: Mark only the top two per column and tally. A/G/D each have 3 appearances. Verification: 4. The maximum count is 3 and all three attaining phones are Alpha, Gamma, Delta. Answer C. No tie convention is required because aspect scores are distinct. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.