Five students - Akash, Chintan, Jignesh, Mukund and Venky -
appeared for an exam. There were total five questions - two
multiple choice (a, b or c) and three true/false questions.
They answered five questions each and answered as follow.
I II III IV V
--------------------------------------------------
Chintan c b True True False
Akash c c True True True
Jignesh a c False True True
Mukund b a True True False
Venky b b True False True
--------------------------------------------------
Also, no two students got the same number of correct answers.
Can you tell which are the correct answers? What are their
individual score?
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Answer Posted / guest
The correct answers are b, a, True, False and False. Also,
the scores are Jignesh (0), Akash (1), Chintan (2), Venky
(3) and Mukund (4).
As no two students got the same number of correct answers,
the total number of correct answers must be either 15
(1+2+3+4+5) or 10 (0+1+2+3+4).
Let's find out the maximum number of correct answers
possible from the answers given by them.
For Question I = 2 (b or c)
For Question II = 2 (b or c)
For Question III = 4 (True)
For Question IV = 4 (True)
For Question V = 3 (True)
Thus, the maximum number of correct answers possible are 15
(2+2+4+4+3) which means that Akash would have given all
correct answers as only he answered True for questions III,
IV and V. But then Chintan and Jignesh would have exactly 3
correct answers. And also, Mukund and Venky would have 2
correct answers. So no one got all five correct. One can
also arrive at this conclusion by trial-and-error, but that
would be bit lengthy.
Now, it is clear that total number of correct answers are 10
(0+1+2+3+4). Questions III and IV both can not be False. If
so, total number of correct answers would not be 10. So the
student who got all wrong can not be Chintan, Akash and Mukund.
If Venky got all wrong, then Chintan, Jignesh and Mukund
each would have atleast 2 correct answers. It means that
Akash would have to be the student with only one correct
answer and the correct answers for questions I and II would
be a and a respectively. But then the total number of
correct answers would be 1 (a) + 1 (a) + 1 (False) + 4
(True) + 2 (Flase) = 9.
Thus, Jignesh is the student with all wrong answers. The
correct answers are b, a, True, False and False. Also, the
scores are Jignesh (0), Akash (1), Chintan (2), Venky (3)
and Mukund (4).
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