Responding To Test of an Examiner

What was the test?

There are 2 possibilities of scores & that are either 0,1,2,3,4 or 1,2,3,4,5. First of all, let's arrange students' responses in order like below.

Table 1

What we notice here is that, there are few responses to same question by different student matching.

For the Question III, only Justin given different answers than other.

Case 1 : If we assume Justin's answer is correct then rest of all are wrong in response to Question III. That means either maximum score in test is 4 or Justin himself has scored 1 to 5.

Let's test that apart from Justin who can have score of 4. If any body other scores 4 then he must share at least 3 similar answers with other (excluding Answer III; refer image below). Only Adam has exact 3 matching responses with Justin.

Table 2

If Adam's score is 4 (Answers to I, II, IV, V are correct) then, Justin too would score 4 (Answers to II, III, IV,V are correct) since Adam & Justin have same responses to Questions II, IV,V).
  
If nobody scoring as 4 then Justin can have score of 4 or 5.

Case 1.1 : If his score is 4 then there has to be somebody has to be there scoring 0. Now Vince and Adam has at least 2 responses matching with the Justin. That means they can't score 0 since even 1 answer is wrong as Justin the other must be correct as Justin. Michael or Cabe can have 0 score in the case. If anybody of them has score 0 then answer as a TRUE to the Question IV is incorrect i.e. correct Answer IV is FALSE. So Justin is WRONG in Answer IV only. In short, a, c, FALSE, FALSE, TRUE is correct combination of answers. But thing is here in the case both Michael and Cabe would have score 0! Hence Justin's score can't be 4 too.

Case 1.2 : If Justin's score is 5, then a, c, FALSE, TRUE, TRUE are the right answers. No one would score 4 in that case with 3 as second highest by Adam.

Case 2 : In short, Justin's response to Question III is wrong & hence others' response is correct. So other 4 have non-zero score. Justin too can't score 5 but anybody from other 4 might have score of 5. But again no 2 from 4 students have 4 matching answers. Then who would score 4? 

Hence maximum score is 4, that's for sure. Since every body other except Justin have at least score 1 in form of response to Question III there must be only Justin whose score must be 0 (0 is minimum when 4 is maximum)!

From that we get, correct combination of Answers III, IV, V  as TRUE, FALSE, FALSE. Those who had given same answers as Justin to the Question I & II are wrong.  Now below is the table showing possible scores of each student.

Table - 3

If Adam has score 2 with his Answer I correct, then there is no body other who would have score 1. Hence, Adam's Answer I too is wrong. So the correct answer for Question I is b (a eliminated by Justin's wrong response). Only Michael and Vince have correct Answer I.

Till now we have score of Vince as 3,Justin as 0, Adam as 1.

Next if Michael's Answer II is wrong then he would be scoring 3 like Vince. Hence, his response a to Question II must be correct.

Eventually,we get correct possible combination of answers as b, a, True, False, False.

Now checking responses of students against these answers give us scores as - 

Michael - 4, Vince - 3, Cabe - 2, Adam - 1 and Justin - 0