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Exactly 2 suppliers: Yes
Exactly 3 suppliers: No
Exactly 5 suppliers: Yes
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
51% (02:17) correct
49%
(02:25)
wrong
based on 988
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
I29-216
General Discussion
06 Oct 2025, 10:30
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1. Exactly 2 Suppliers
To satisfy the rule, both selected suppliers must have strictly lower values in every metric than any excluded supplier.
Comparing the metrics, only Apex and Beacon have strictly lower risk scores in every metric compared to the other four suppliers (Cascade, DeltaCo, Eureka, Forge).
Yes, a group of exactly 2 suppliers (Apex, Beacon) could be selected.
2. Exactly 3 Suppliers
Including Cascade with Apex and Beacon would violate the rule because Cascade does not have strictly lower values than DeltaCo in all metrics
Upon review, no supplier besides Apex and Beacon has all metrics strictly lower than any remaining supplier once a third member is considered.
No, exactly 3 suppliers cannot be selected.
3. Exactly 5 Suppliers
Selecting any 5 would mean excluding only 1 supplier. The rule requires each of the 5 to have strictly lower values in every metric than the excluded supplier.
However, Forge has the worst scores in every metric. If Forge is excluded, all remaining (Apex, Beacon, Cascade, DeltaCo, Eureka) have strictly lower risk scores for every metric compared to Forge.
Yes, exactly 5 suppliers can be selected if Forge is the one excluded.
To satisfy the rule, both selected suppliers must have strictly lower values in every metric than any excluded supplier.
Comparing the metrics, only Apex and Beacon have strictly lower risk scores in every metric compared to the other four suppliers (Cascade, DeltaCo, Eureka, Forge).
Yes, a group of exactly 2 suppliers (Apex, Beacon) could be selected.
2. Exactly 3 Suppliers
Including Cascade with Apex and Beacon would violate the rule because Cascade does not have strictly lower values than DeltaCo in all metrics
Upon review, no supplier besides Apex and Beacon has all metrics strictly lower than any remaining supplier once a third member is considered.
No, exactly 3 suppliers cannot be selected.
3. Exactly 5 Suppliers
Selecting any 5 would mean excluding only 1 supplier. The rule requires each of the 5 to have strictly lower values in every metric than the excluded supplier.
However, Forge has the worst scores in every metric. If Forge is excluded, all remaining (Apex, Beacon, Cascade, DeltaCo, Eureka) have strictly lower risk scores for every metric compared to Forge.
Yes, exactly 5 suppliers can be selected if Forge is the one excluded.
