Bunuel
A logistics company reviewed 2,000 shipments that arrived later than scheduled and grouped them according to shipping distance. For each distance group, the table shows the percentage of delayed shipments for which each listed factor was recorded as contributing to the delay. A shipment could have more than one contributing factor.
Contributing
factor | Under 100 km (300 shipments) | 100–300 km (400 shipments) | 300–700 km (500 shipments) | 700–1,200 km (450 shipments) | Over 1,200 km (350 shipments) |
|---|
| Weather | 12% | 18% | 26% | 34% | 48% |
| Traffic congestion | 42% | 39% | 31% | 22% | 14% |
| Sorting delay | 24% | 29% | 33% | 37% | 41% |
| Vehicle problem | 8% | 10% | 13% | 17% | 22% |
| Incorrect address | 18% | 15% | 12% | 10% | 8% |
| Staffing shortage | 16% | 19% | 21% | 18% | 15% |
| Documentation issue | 5% | 7% | 9% | 12% | 16% |
| Other | 6% | 5% | 7% | 6% | 8% |
For each of the following conclusions, select
Supported if the conclusion is supported by the information in the table. Otherwise, select
Not supported.
Official Solution:• More than 550 of the delayed shipments were associated with weather.Calculate the number of shipments associated with weather in each distance group:
300 * 12% = 36
400 * 18% = 72
500 * 26% = 130
450 * 34% = 153
350 * 48% = 168
Thus, the total number of shipments associated with weather was:
36 + 72 + 130 + 153 + 168 = 559
Since 559 > 550, the statement is supported.
Answer:
Supported.
• Less than 65% of the delayed shipments associated with traffic congestion were also associated with a staffing shortage.First, find the total number of shipments associated with traffic congestion:
300 * 42% = 126
400 * 39% = 156
500 * 31% = 155
450 * 22% = 99
350 * 14% = 49
Total:
126 + 156 + 155 + 99 + 49 = 585
The table does not tell us the actual overlap between traffic congestion and staffing shortage. The minimum possible overlap is 0 because, within each distance group, the two percentages add to less than 100%, so no overlap is required.
To determine whether the statement must be true, we need to check the
maximum possible overlap. For each distance group, the maximum overlap is the smaller of the number of shipments associated with traffic congestion and the number associated with a staffing shortage. This is because the overlap cannot contain more shipments than either of the two groups.
Under 100 km:Traffic congestion: 300 * 42% = 126
Staffing shortage: 300 * 16% = 48
Maximum overlap = 48
100–300 km:Traffic congestion: 400 * 39% = 156
Staffing shortage: 400 * 19% = 76
Maximum overlap = 76
300–700 km:Traffic congestion: 500 * 31% = 155
Staffing shortage: 500 * 21% = 105
Maximum overlap = 105
700–1,200 km:Traffic congestion: 450 * 22% = 99
Staffing shortage: 450 * 18% = 81
Maximum overlap = 81
Over 1,200 km:Traffic congestion: 350 * 14% = 49
Staffing shortage: 350 * 15% = 52.5
Maximum overlap = 49
Thus, the maximum possible overlap is:
48 + 76 + 105 + 81 + 49 = 359
As a percentage of the 585 shipments associated with traffic congestion:
359/585 ≈ 61.4%
Even the maximum possible overlap is less than 65%. Therefore, fewer than 65% of the shipments associated with traffic congestion could also have been associated with a staffing shortage.
Answer:
Supported.
• For exactly half of the contributing factors listed in the table, the percentage of delayed shipments associated with that factor increased with each successive distance group.Check each of the 8 contributing factors from left to right:
• Weather: increases in every successive group
• Traffic congestion: does not
• Sorting delay: increases in every successive group
• Vehicle problem: increases in every successive group
• Incorrect address: does not
• Staffing shortage: does not
• Documentation issue: increases in every successive group
• Other: does not
Thus, 4 of the 8 contributing factors show an increase with each successive distance group.
Therefore, exactly half of the contributing factors satisfy the condition.
Answer:
Supported.