A certain company conducted phone interviews with each of 6 candidates

Question

A certain company conducted phone interviews with each of 6 candidates—Candidates U through Z—for the purpose of determining who should be invited for an on-site interview. The candidates were rated according to 5 criteria (Criteria A through E). If not all of the phone interview candidates are invited for the on-site interview, then, by company policy, each candidate in the group invited for the on-site interview must have had greater ratings for each of the 5 criteria than each of the candidates that are not invited. For each of the 6 candidates, the table shows the ratings assigned to the candidate for each criterion.

Assuming the on-site interview candidates are selected in a manner consistent with the company policy, for each of the following numbers, select Yes if a group with exactly that number of candidates could be invited for the on-site interview from among these 6 candidates. Otherwise, select No.

Candidate	A	B	C	D	E
	Rating
Z	4.8	4.4	4.8	4.2	5.0
U	4.6	4.8	4.4	4.2	4.2
Y	4.6	4.6	4.4	4.2	5.0
W	4.4	4.0	4.2	3.8	4.0
X	3.6	3.8	3.4	3.6	4.0
V	2.0	2.8	3.6	4.0	2.8

(Sort ↕ the table by clicking on the headers)

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Attachment:

DS 1.png

tdew · Accepted Answer

I came up with this.

First, I sorted A, Z had the highest rating. However, sorting B showed U had the highest rating, meaning Z doesn’t dominate all criteria. 
So,   Q1 = No .

For two candidates, because Y and U had same ratings in A. we couldn't invite only Z and Y or Z and U. 
Thus,   Q2 = No .

For three candidates, sorted all criterion and found that Y, U, and Z together meet the requirement, with no other candidate having a higher rating. 
So,   Q3 = Yes .

Hope this helps!

Rucha.Shukla · Answer

The way I solved this question was to re-create the table with ascending values per criteria.

From the table (attaching here), it is clear that:

a) From the options given, only a group of 3 (U, Y & Z) could be selected since they were the only ones with ratings higher than others for each criteria

b) The group of U, Y & Z cannot be further reduced since each had at least 1 criteria where they scored lowest amongst them

chetan2u · Answer

The table gives the ratings that six candidates, U through Z, get in 5 different categories. If a person is selected, then every other person having a rating higher in each of the categories is also selected.

The question asks us to find how many candidates could have been called for on site interview. 
 Any one called should have the ratings in each category higher than who are not called. For example, someone, say T, with the highest rating in one criteria but lowest in another would ensure that he is selected if any one is selected ( T has highest rating in one criteria) and that everyone is selected if he is selected ( T is the lowest in one criteria).

(a) If we look at the candidates and ratings in criteria, V is lowest in 4 of them and not the highest in any. So, he is surely left out if all six were not called.

(b) However, in D criteria, X and W have got lesser lesser rating than V. So, if V is left out, X and W are also surely left out.
 From the above two, we can say all six can be called but not four or five as X, V and W have higher ratings than eac other in some criteria.

Thus, remaining three (3) can be called for interview as their ratings are higher in all categories than the threes who are not called.

(c) Next, U out of the remaining three has the highest rating in B, so cannot be left out else all will have to be rejected,
(d) But U out of the three also has the lowest rating in E amongst the three, so cannot be selected unless other two are selected.

Thus, there is no one amongst three who has the highest rating in all the categories.  Thus we can have three selected, but not one or two.

1: No
2: No
3: Yes

Shivang29 · Answer

if you forget the table for a second essentially the question is asking you what is the minimum number of people you need in a group to meet the policy. The policy being that at least one of the members of the group should have the highest rating in each category. If you frame it like this you can quickly see by sorting each category that Candidate Y, U and Z each have at least one category in which they have the highest rating.

bumpbot · Answer

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A certain company conducted phone interviews with each of 6 candidates

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