A production manager is reviewing the output data for two manufacturing lines, Line A and Line B, over the past five shifts. The data includes the number of units produced and the number of defects found for each line per shift. **Line A Data:** Shift 1: Produced 100 units, 5 defects Shift 2: Produced 110 units, 4 defects Shift 3: Produced 95 units, 6 defects Shift 4: Produced 105 units, 3 defects Shift 5: Produced 115 units, 5 defects **Line B Data:** Shift 1: Produced 120 units, 6 defects Shift 2: Produced 100 units, 3 defects Shift 3: Produced 110 units, 4 defects Shift 4: Produced 115 units, 5 defects Shift 5: Produced 105 units, 4 defects Consider the following two statements: Statement 1: The average number of defects per unit produced is lower for Line A than for Line B. Statement 2: The total number of units produced is higher for Line B than for Line A. Which of the statements alone is sufficient to determine that Line A has a better overall quality performance (defined as fewer defects per unit) than Line B?

Correct answer: D. Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.

To determine overall quality performance (fewer defects per unit), we need to compare the ratio of total defects to total units produced for each line. For Line A: Total Units = 100+110+95+105+115 = 525. Total Defects = 5+4+6+3+5 = 23. Defects per unit for A = 23/525 ≈ 0.0438. For Line B: Total Units = 120+100+110+115+105 = 550. Total Defects = 6+3+4+5+4 = 22. Defects per unit for B = 22/550 = 0.040. Line A (0.0438) has more defects per unit than Line B (0.040), so Line B has better quality performance. The question asks to determine if Line A has *better* quality performance. Statement 1: 'The average number of defects per unit produced is lower for Line A than for Line B.' If this statement is true, it directly tells us that Line A has fewer defects per unit, thus better quality performance. This statement alone is sufficient. (Note: Based on actual calculation, this statement is false, but in Data Sufficiency, we assume the statement is true and check sufficiency). Statement 2: 'The total number of units produced is higher for Line B than for Line A.' This statement only gives information about total production, not about defects or quality. It does not allow us to determine quality performance (defects per unit). For example, Line B could produce more units but have a much higher number of defects, leading to worse quality. Thus, Statement 2 alone is not sufficient. Therefore, Statement 1 alone is sufficient.