Five students each answered five questions on an quiz consisting of two multiple-choice questions (A, B or C) and three True-False questions. They answered the questions as follows:
Student Q1 Q2 Q3 Q4 Q5
Alex A A T T T
Bert B B T F T
Carl A B T T F
Dave B C T T F
Eddy C A F T T
No two students got the same number of correct answers. Who got the most correct answers?
As the results range from 0 to 5, you've either someone which has all wrong or someone which has al true.
We have to check both cases separately and to try to find if there is a possible solution...
If someone has all good answers, we have the following :
If Alex has all good, it also means that the 4 other have exactly TWO good answer in Q3-5.
This means that the 4 other have scores from 2 to 4... Only 3 results for 4 people so 2 must have same result which is false.
So Alex DON'T have all good.
This exclude AA from the good answers for Q1-2
As Carl and Dave have same result for Q3-5, their result for Q1-2 must
differ, which excludes BB (1 point), CA (0 points) and AC (1 point) for
the possibles answers for Q1-2
so, neither Bert nor Eddy have all good.
So Carl or Dave has to be all good...
Anwsers would be ABTTF or BCTTF
results :
3 2
2 2
5 3
3 5
1 1
Both sets have the same number appearing twice and so, are wrong. So nobody has all good answers.
Someone has to have all wrong answers
If it is Alex, it means that Q3-5 is "FFF" and the 4 other would
have from 1 to 3 correct answers so two would have same result. So,
alex don't has all wrong.
as FFF don't appear, we know that it can't be the all incorrect and that there is at least 1 "T" present.
If there was 2 or 3 "T", they would all have at least 1/2 points on
Q3-5. But we know that someone has all incorrect... Correct answer has
to have exactly ONE "T"
So, Alex will have 1 point on Q3-5, the one with all incorrect will have 0 and the other will have 2 points.
As Carl and Dave have same answers on Q3-5, we can exclude BB, AC and
CA from the good answers because it'd give them the same result.
We can also reject AA. alex would have 3 points (2+1) and Carl or Eddy would also have 3 points (1+2).
remains AB, BA, BC, CC as possible good answers.
Alex can have 1 or 2 points.
Someone has 0 points
the 3 other must have 3,4 and 2 or 1 depending on Alex' result.
which means that someone has to have the good answers on Q1-2 and that
he has to have 2 points in Q3-5. Which also means that BA and CC can't
be the good answers (noone have these).
Good answer is AB or BC... So Carl and Dave have 2 and 4 points.
If correct answer is AB, Alex would have 2 points which is impossible. so correct answer should be BC
Dave : 4
Carl : 2
Alex : 1
Bert : 3
Eddy : 0
Maybe an hint towards answer
