This Is Why I Don't Like To Discuss After Exams!

If you try each of the answers, the only one that could work is No.3 is A and No.4 is B. The other answers would give a contradiction since it forces someone to be wrong on both the answers they gave.

This isn't the only solution that's possible (I started by finding a solution that wasn't one of the choices), but it's the only one that works out of the choices given.

Its SO Easy!! That's the only one which fits the story. Even though you can try it theoretically. . Put a Table with columns as QUESTION NO. and rows as the STUDENTS. Fill up the table as per the dialogues and go..on..... then take one of Adam answer (C) correct, you'll find yourself in the wrong end... Go back and take Adam's other answer (A) correct you soon find its fits nicely... :)

Start by taking 1 is D as in the conversation given every question number has two or more possibilities except que 1..After taking 1 as D list out the possiblities.. 2->C/A/E 3->A/E 4->B/D 5->B/C

eliminate out one from each starting from calvin we will then have only one way to move to the solution getting all the answers.

ANS-1-D,2-E,3-A,4-B,5-C

Given information :-

1 - D (Calvin)

2 - C (Adam), E (Ben), A (Elvis)

3 - A (Adam), E (Dennis)

4 - D (Calvin), B (Dennis)

5 - B (Calvin), C (Elvis)

The question says that only one of the ans. given by each one is correct. Suppose Calvin's ans. D for question no.1 is correct. Then automatically, the ans. of question no. 5 is C given by Elvis. This means that Elvis's ans. A for ques. no. 2 is wrong. Since C is the ans. of ques. no. 5 , so, Adam's ans. C for ques. no. 2 is wrong giving the ans. for ques. no. 2 as E (given by Elvis). The ans. for ques. no. 3 will be A (Adam's answer) as E is the ans. of ques. no.2. As only one ans. of Ben can be correct, so it gives us the ans. of ques. no. 4 i.e. B (answer given by Dennis).

This gives us the following table :-

1 - D (Calvin's answer.)

2 - E (Ben's answer)

3 - A (Adam's answer)

4 - B (answer of Dennis)

5 - C (answer of Elvis)

Start with the First one "Adam"

Statement 1: Let No.3=A then this leads to Elvis who said No.2 is A Hence No.5 is C

Statement 2: Let No.2 is C then this goes to Elvis hence for Elvis It becomes NO.2 is A but both A & C cannot be No.2 Hence this Statement Is not Correct.

Hence Statement 1 is True, hence No.3=A & No.5=C

Now, We go to Ben

Statement 3: Let No.4=D then we go to Calvin & it becomes No.5=B then we go to Dennis & "No.3=E" But No.3 cannot be equal to E as this contradicts our fact that No.3=A

Statement 4: Let No.2=E Then we go to Dennis & it becomes No.4=B now we go to Calvin & No.1=D

Now, Statement $ doesn't contradicts any of our Assumption Hence No.2=E No.4=B & no.1=D

Hence, No.1=D No.2=E No.3=A No.4=B No.5=C

I solved it using this one: Adam A3 C2 BDE145 Ben D4 E2 ABC135 Calvin D1 B5 ACE234 Dennis B4 E3 ACD125 Elvins A2 C5 BDE134

A3 B4 C5 D1 E2

First of all, I compare what could be the possible answers. The rightmost part are those letters and numbers not chosen by an individual. So I look up at other answers. Suppose we compare Adam's answer w/c is A3 with Ben. You can see that Ben either choose A3 because it was not mentioned. On the other hand, Calvin could also answer A3. So if 3 guys get the answer correctly, then, A3 must be it. Moving from that on, I have deduced it given that only 1 of them had 1 correct answer.

Here's how I got the answer. I made a table with the names on the left and the No. Items on the top of the table. I then wrote the answers of Adam to Elvis, respectively, in the table. Basing on the table, no one answer item no. 1 but Calvin. So, D must be the answer to No. 1. With that, Calvin's answer to No. 5 must be wrong. In No. 5, only Elvin answered aside from Calvin. So, Elvin's answer in No.5 (C) must be correct and therefore his answer in No. 2 must be wrong. Making an assumption that no two No.s have the same letter answer, I concluded that: (1) No. 4 must be B (based on Dennis' answer) because Ben's answer is D (which was already answered in No. 1); (2) No. 2 must be E (based in Ben's answer) because the letter C was already answered in No. 5 and Ben's answer in No. 4 is wrong (since D has been answered in No.1); and finally (3) No. 3 must be A since all other letters has already been proven correct in other Nos.

Considering 1 is only mentioned once we can say the statement 1 is D is true. That makes 5 is B false. That means that the other statement in which 5 appears is true, so 5 is C. The other half of the affirmation is false, so 2 isn't A. The other times 2 appears say that 2 is C or 2 is E but 5 is already C so 2 is E. That makes 4 is D false which makes 4 is B true, which makes 3 is E false which makes 3 is A true. So: 1=D 2=E 3=A 4=B 5=C

I got it right and it was reasonably simple when using the statements as a basis. But originally I didn't use the statement and did it all in a chart, but then found out half couldn't be it due to them not being answers. It was a Fun question though.

D=1 therefore Calvin is wrong about his second guess, and B isn't 5 now we know that, Ben is wrong about 4, and Dennis is right about B=4. now we can assume that there other guesses are just the opposite. Ben was wrong about 4, so he has to be right about E=2, and Dennis was wrong about E completely. ( D=1. B=4. E=2. ) (false: 5=B, 3=E, 4=D.) we're down to A, C, 3, and 5; we can figure out this because there's only two options for No 3, and one of which has been proven wrong already. Also 2 has already been decided as E, giving even more evidence. Therefore Adam is correct about 3, but wrong about C; 3=A. And Elvis is quite simple to figure out now, he's obviously wrong about A, so his second question most be true; 5=C.

Sum: D=1, E=2, A=3, B=4, C=5.

Why start with D? You start with 1 being D; which can be figured out because it's the only question not being debated.

Process of elimination, if you try each answer out all the other choices would contradict themselves.

Only one person had an answer for number 1, meaning that it must be the only correct solution for number 1. From then on, it's a process of cross referencing the rest of the kids' solutions.

Probability that each one is correct = 1/2 , 1/2 , 1/2 , 1/2 , 1/2 But Probability that N0.3 is A correct is = 1 (100 %) from observation, Probability that No4 is B is also 1 (100 %) Hence Answer !!

All other probabilities are below this.

Solving this problem requires you to use the process of elimination. We choose one of the ten statements to be true(5 people with 2 answers each), and we solve accordingly. For example, if No.3 is A, then No. 2 CANNOT be C, because each person has only one correct answer. Also, Elvis' statement that No.2 is A is clearly incorrect, because we are assuming that No.3 is A. So, No. 5 must be C, and so on. You will not need to try all ten possibilities, because many of them can be tried in a single experiment. For example, if you try No.2 is A, and you are incorrect, you would already know that Elvis' other statement, No. 5 is C, is correct, and go from there. You would know if a statement was incorrect because there would be a contradiction somewhere. Here are the correct answers to each of the questions on the test: 1)D 2)E 3)A 4)B 5)C