A manufacturer evaluated 6 suppliers - Apex, Beacon, Cascade, DeltaCo,

Question

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.

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 .

Bunuel · Accepted Answer

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

paragw · Answer

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.

Dereno · Answer

There are 6 suppliers and their quality metrics is rated under 6 categories- metrics 1 to metrics 6. Where a smaller value is a better performance indicator.

The selected supplier must have lower values on all six metrics than the excluded supplier.

EXACTLY 2 supplier  :

The selected supplier are Apex and Beacon - they have metrics which is lower than all the other six metrics of the remaining 4 suppliers. Hence,  YES .

EXACTLY 3 supplier :

The top three suppliers are Apex, Beacon and Cascade. The third supplier - Cascade has a lower metrics than remaining suppliers in all the 5 metrics. Except - Metric 6 which has a higher value of 1.6 compared to Delta Co 1.5. Hence, doesn’t qualify.

Hence,  NO .

EXACTLY 5 supplier :

The top five suppliers show a much lower performance metrics than the supplier - Forge. Hence, we can select 5 suppliers.

Hence,  YES .

pappal · Answer

I approached reverse, since higher the no. lower is the value 
3.exactly 05 selected means exactly 01 excluded-->if we take F as excluded then all the 05 others have values in each of the metrics higher than its-  YES  
2.exactly 03 selected means exactly 03 others excluded-->if we take D,E & F excluded then all the 03 others(A,B,C) doesn't have values in each of the metrics higher than theirs :here C in the metric 06 seems to violate-  NO 
1.exactly 02 selected means exactly 04 others excluded-->if we take C,D,E & F excluded then all the 02 others(A,B) have values in each of the metrics higher than theirs-  YES

tomloveless · Answer

I read this carefully acknowledging the "lower is better portion" then while formulating my answer I forgot about it and got all the opposite answers. Bummer.

A manufacturer evaluated 6 suppliers - Apex, Beacon, Cascade, DeltaCo,

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Supplier	Metric 1	Metric 2	Metric 3	Metric 4	Metric 5	Metric 6
	Risk score (lower is better)
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

Yes	No
		Exactly 2 suppliers
		Exactly 3 suppliers
		Exactly 5 suppliers

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A manufacturer evaluated 6 suppliers - Apex, Beacon, Cascade, DeltaCo,

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