The table above shows the rank order in which each of six candidates f

Question

Precinct  
  Benton  
  Carter  
  Hsieh  
  Maris  
  Okafor  
  Shah  
 
  ML-1 
 3 
 6 
 4 
 5 
 1 
 2 
 
  ML-2 
 3 
 4 
 1 
 6 
 2 
 5 
 
  ML-3 
 6 
 1 
 3 
 5 
 2 
 4 
 
  ML-4 
 6 
 3 
 2 
 5 
 4 
 1 
 
  ML-5 
 5 
 6 
 1 
 4 
 3 
 2 
 
  ML-6 
 6 
 2 
 5 
 4 
 1 
 3

The table above shows the rank order in which each of six candidates finished in each of six precincts in an election. 1 denotes the candidate who received the most votes in that district and 6 denotes the candidate who received the least votes in that district. A candidate (A) is said to completely outrank another candidate (B) if candidate A received more votes in every district than did candidate B.

For each of the following candidates, select Yes if that candidate completely outranked another, and No if that candidate did not completely outrank another.

Bunuel · Accepted Answer

Precinct	Benton	Carter	Hsieh	Maris	Okafor	Shah
ML-1	3	6	4	5	1	2
ML-2	3	4	1	6	2	5
ML-3	6	1	3	5	2	4
ML-4	6	3	2	5	4	1
ML-5	5	6	1	4	3	2
ML-6	6	2	5	4	1	3

The table above shows the rank order in which each of six candidates finished in each of six precincts in an election. 1 denotes the candidate who received the most votes in that district and 6 denotes the candidate who received the least votes in that district. A candidate (A) is said to completely outrank another candidate (B) if candidate A received more votes in every district than did candidate B.

For each of the following candidates, select Yes if that candidate completely outranked another, and No if that candidate did not completely outrank another.

A candidate completely outranks another candidate only if the candidate has a lower number in every one of the six precincts. Since 1 is best, a lower number means more votes.

So, we are looking to see whether each candidate has lower numbers than any one of the other candidates in all six precincts.

Hsieh: No. Hsieh does not have lower numbers than any one candidate in all six precincts, so Hsieh completely outranks no one.

Okafor: Yes. Okafor has lower numbers than Benton in all six precincts, so Okafor completely outranks Benton.

Shah: Yes. Shah has lower numbers than Maris in all six precincts, so Shah completely outranks Maris.

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Sajjad1994 · Answer

Official Explanation

This Table Analysis problem is a classic  "sort-and-scan"  style problem, one for which you'll want to sort the columns to group information to your liking and then scan for relevant information.

Here you can start by employing a little bit of up-front logic:

1)  If a person has a 6 in their column at any point, they were outranked by everyone in that precinct and therefore did not completely outrank anyone. (Alas, that isn't the case for any of the three candidates in question.)

2)  In any row that a candidate has a 1 they've outranked everyone for that precinct.

With that in mind, if you sort for each of the three candidates in question, you'll get all of their 1s up top and can start scanning on the lower rows.

If you start with Hsieh, notice that once the column is sorted the first two rows have 1s for Hsieh, so for two full precincts Hsieh outranked everyone. From there you can use process-of-elimination on the other rows: in any row, look at the numbers better than Hsieh's and rule them out as potential candidates that Hsieh outranked.

In the third row, Hsieh has a 2 and Shah has a 1, so eliminate Shah.

In the fourth row, Hsieh has a 3 and Carter and Okafor have 1 and 2, so now you're down to Benton and Maris as potential people that Hsieh completely outranked.

In the fifth row, Hsieh has a 4 and Benton has a 3, so Benton is out (Maris with a 5 remains a possibility).

And in the sixth row, Hsieh has a 5 and Maris has a 4, so you can eliminate Maris and conclude that Hsieh didn't outrank everyone.

For Okafor you have an advantage: Maris is in the directly adjacent column, and Maris doesn't have any 1s, 2s, or 3s (meaning that Maris performed very poorly while Okafor performed quite well). This one can give you a quick scan based on that proximity: you may still want to sort by Okafor to get the 1s and 2s at the top but then notice that Maris's best is a 4 and Okafor's worst is a 4. So all of Okafor's 1s, 2s, and 3s will outrank Maris, and when you see that Okafor's 4 corresponds with Maris's 5, you can quickly conclude that Okafor did completely outrank someone: Maris.

With Shah, again sort by the relevant column for Shah. And here either of the above two strategies will work: you have quick column proximity between Shah and Maris (and you know that Maris's best is a 4 so that's an easy target). Or you can go full process of elimination. Shah's first row is a 1 so there Shah outranks everyone. From there:

The second and third rows are 2s, with Okafor and Hsieh having the 1s so eliminate those two,.

The fourth row is a 3 with Okafor and Carter as the 1 and 2, so eliminate Carter.

The fifth row is a 4, with Maris and Benton at 5 and 6 so Maris and Benton are still possibilities.

And the sixth row is a 5...but Maris has the 6 so Shah completely outranks Maris.

Therefore Shah and Okafor did completely outrank someone, but Hsieh did not.

arunbhati · Answer

Bunuel ,

Please explain this question. i am not able to understand the meaning of this question

egmat · Answer

Hi arunbhati,

The wording here is what's tripping you up, so let's decode the setup first, then the rule.

What the table shows

Each number is a  finishing position  in that precinct, not a vote count. Reading down a precinct row (say ML-1: Benton 3, Carter 6, Hsieh 4, Maris 5, Okafor 1, Shah 2): the candidate with  1  finished first (most votes), and  6  finished last (fewest votes). So a  smaller number is a better result.

What "completely outrank" means

Candidate A completely outranks candidate B only if A beat B in  every single precinct  - all  six . Since a better finish is a smaller number, this means:

A's number must be  smaller than B's number in all six precincts (ML-1 through ML-6).

If B beats A in even one precinct, then A does  not  completely outrank B.

Seeing it work - Okafor vs. Maris

Compare their two columns precinct by precinct:

- Okafor:  1, 2, 2, 4, 3, 1 
- Maris:  5, 6, 5, 5, 4, 4

Okafor's number is smaller in  every  row, so Okafor  completely outranks Maris  - Yes. You only need to find  one  such person to earn a Yes; that's why Okafor and Shah are Yes.

For Hsieh, no matter which other candidate you line up against, someone always beats Hsieh in at least one precinct - so Hsieh is  No .

Quick rehearsal to lock the rule

Tiny  2 -precinct example - is the claim "A completely outranks B" true?

- A:  2, 3 
- B:  4, 1

A beats B in precinct  1  ( 2  <  4 ), but B beats A in precinct  2  ( 1  <  3 ). Because it must hold in  every  precinct, the answer is  No . That's the exact test to run for each candidate.

Answer: Hsieh: No, Okafor: Yes, Shah: Yes

Lasagna · Answer

Is it Just me or is the question very misleading as another would suggest whether they outrank any of them in the 3 names provided whereas "any other" would mean the entire list.

Bunuel · Answer

“Another” here means another candidate in the election, not just another candidate among the three listed in the question. So each of Hsieh, Okafor, and Shah must be compared against all five other candidates.

“Any other candidate” would be slightly more explicit, but I think the intended meaning of “another” is still clear from the context.

egmat · Answer

Hi Lasagna,

Good instinct to slow down on the wording, but here "another" is broader than you're reading it. It means  any one of the other five candidates in the whole table  - not just the other two names from the list of three you're asked about.

Think of the three names (Hsieh, Okafor, Shah) as the candidates you're being  asked about , not the pool you're comparing  within . For each of them, the question is: "Did this candidate completely outrank  anyone at all  in the table?" So your comparison set is all  five  other columns: Benton, Carter, Hsieh, Maris, Okafor, Shah (minus whichever one you're testing).

The clearest proof that the scope is the full table is in the answers themselves:

-  Okafor  earns a Yes because Okafor completely outranks  Benton  - smaller number in all  six  precincts. Benton isn't one of the three names on the list.
-  Shah  earns a Yes because Shah completely outranks  Maris  - again, someone not on the three-name list.

If "another" were limited to the three named candidates, neither of those Yes answers would work, since the candidate each one beats sits outside that group.  Therefore , the question only makes sense - and only matches the official answers - if "another" spans the entire field of  six .

Rule to carry forward:  when a stem asks whether a candidate outranked "another," test that candidate against  every other column  in the table, then stop the moment you find one it beats in all  six  rows. One success anywhere = Yes.

That's why Hsieh is No: check Hsieh against  all five  others, and in every single matchup someone beats Hsieh in at least one precinct - so there's no one Hsieh completely dominates.

Answer: Hsieh: No, Okafor: Yes, Shah: Yes

The table above shows the rank order in which each of six candidates f

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The table above shows the rank order in which each of six candidates f

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