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14 Oct 2025, 06:40
Kudos
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Exactly 2 suppliers: Yes
Exactly 3 suppliers: No
Exactly 5 suppliers: Yes
A manufacturer evaluated 6 suppliers - Apex, Beacon, Cascade, DeltaCo, Eureka, and Forge - on six quality risk metrics numbered 1 through 6. These metrics measure adverse outcome rates, and smaller values indicate better performance on every metric.
Selection rule: if any suppliers are excluded, then every selected supplier must have strictly lower values on all six metrics than every excluded supplier.
Assuming the rule above, for each of the following numbers, select Yes if a group with exactly that number of suppliers could be selected. Otherwise, select No.
| Risk score (lower is better) | ||||||
| Supplier | Metric 1 | Metric 2 | Metric 3 | Metric 4 | Metric 5 | Metric 6 |
|---|---|---|---|---|---|---|
| Apex | 0.8 | 0.9 | 0.7 | 0.6 | 0.4 | 0.8 |
| Beacon | 0.9 | 0.8 | 0.8 | 0.7 | 0.5 | 0.9 |
| Cascade | 1.4 | 1.3 | 1.2 | 1.1 | 0.9 | 1.6 |
| DeltaCo | 1.6 | 1.5 | 1.4 | 1.2 | 1.0 | 1.5 |
| Eureka | 2.4 | 2.1 | 2.2 | 1.9 | 1.7 | 2.5 |
| Forge | 2.7 | 2.5 | 2.4 | 2.1 | 1.9 | 2.8 |
Selection rule: if any suppliers are excluded, then every selected supplier must have strictly lower values on all six metrics than every excluded supplier.
Assuming the rule above, for each of the following numbers, select Yes if a group with exactly that number of suppliers could be selected. Otherwise, select No.
| Yes | No | |
| Exactly 2 suppliers | ||
| Exactly 3 suppliers | ||
| Exactly 5 suppliers |
ShowHide Answer
Official Answer
Exactly 2 suppliers: Yes
Exactly 3 suppliers: No
Exactly 5 suppliers: Yes
14 Oct 2025, 06:40
Kudos
Bookmarks
Official Solution:
We apply strict lower-is-better dominance: if any suppliers are excluded, then every selected supplier must be strictly lower on all six metrics than every excluded supplier. To derive the answers, anchor on a single metric to force separation, then verify full six-metric dominance. Start with Metric 5. Apex has the lowest Metric 5 value (0.4) and Beacon has the next lowest (0.5). Any excluded supplier must therefore have Metric 5 greater than 0.5 if Apex and Beacon are selected. Then we confirm that Apex and Beacon are lower on all six metrics than each excluded supplier.
• Exactly 2 suppliers
With Metric 5 anchored at 0.4 and 0.5, select Apex and Beacon. For each excluded supplier, Apex and Beacon are strictly lower in all six metrics.
Answer: Yes
• Exactly 3 suppliers
The next lowest value on Metric 5 after 0.4 and 0.5 is Cascade’s 0.9. So if a third supplier could be added, based on Metric, it would have to be Cascade. Check full dominance: Cascade must be strictly lower than every excluded supplier. But DeltaCo has Metric 6 = 1.5 while Cascade has Metric 6 = 1.6, so Cascade does not dominate DeltaCo. Thus a three-supplier selection fails.
Answer: No
• Exactly 5 suppliers
Using the same Metric 5 anchor, include Apex, Beacon, Cascade, DeltaCo, and Eureka, excluding only Forge. Verify full dominance against Forge: for each selected supplier, every metric is lower than Forge’s row. Hence all five selected suppliers dominate the lone excluded supplier.
Answer: Yes
Correct answer:
Exactly 2 suppliers "Yes"
Exactly 3 suppliers "No"
Exactly 5 suppliers "Yes"
Bunuel
We apply strict lower-is-better dominance: if any suppliers are excluded, then every selected supplier must be strictly lower on all six metrics than every excluded supplier. To derive the answers, anchor on a single metric to force separation, then verify full six-metric dominance. Start with Metric 5. Apex has the lowest Metric 5 value (0.4) and Beacon has the next lowest (0.5). Any excluded supplier must therefore have Metric 5 greater than 0.5 if Apex and Beacon are selected. Then we confirm that Apex and Beacon are lower on all six metrics than each excluded supplier.
• Exactly 2 suppliers
With Metric 5 anchored at 0.4 and 0.5, select Apex and Beacon. For each excluded supplier, Apex and Beacon are strictly lower in all six metrics.
Answer: Yes
• Exactly 3 suppliers
The next lowest value on Metric 5 after 0.4 and 0.5 is Cascade’s 0.9. So if a third supplier could be added, based on Metric, it would have to be Cascade. Check full dominance: Cascade must be strictly lower than every excluded supplier. But DeltaCo has Metric 6 = 1.5 while Cascade has Metric 6 = 1.6, so Cascade does not dominate DeltaCo. Thus a three-supplier selection fails.
Answer: No
• Exactly 5 suppliers
Using the same Metric 5 anchor, include Apex, Beacon, Cascade, DeltaCo, and Eureka, excluding only Forge. Verify full dominance against Forge: for each selected supplier, every metric is lower than Forge’s row. Hence all five selected suppliers dominate the lone excluded supplier.
Answer: Yes
Correct answer:
Exactly 2 suppliers "Yes"
Exactly 3 suppliers "No"
Exactly 5 suppliers "Yes"
17 Mar 2026, 02:37
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It is kind of a trap to feel if 3 suppliers is a No then 5 suppliers mostly must be no too, in the heat of the moment. But then you realise that 5 of the top picks supersedes the only leftover and in such a question the lesser number of suppliers, the more volatile and more checks needed!
Bunuel
