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Five students - Adam, Cabe, Justin, Michael and Vince appeared for a
competitive exam. There were total five questions asked from them from
which were two multiple choice questions (a, b or c) and three were
true/false questions. Their answers are given as follows:
Name I II III IV V
Cabe c b True True False
Adam c c True True True
Justin a c False True True
Michael b a True True False
Vince b c True False True
Also, no two students got the same number of correct answers. Can you
tell the correct answer? Also, what are their individual score?
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.
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| 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.
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| 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.
