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Old 23rd October 2012, 08:48 PM   #1 (permalink)
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[PUZZLE] How much did Cody scored?

In a pop-quiz, there are 10 questions, each with a choice of either True(T) or False(F). There is only one correct choice for each question. 1 mark is awarded for each question and no penalty for getting a question wrong.
Anna answered the paper as follows:
1. T 2. T 3. F 4. F 5. T 6. T 7. T 8. F 9. T 10. F
Brad answered as follows:
1. T 2. T 3. T 4. F 5. F 6. T 7. T 8. T 9. F 10. T
Cody answer as follows:
1. F 2. F 3. F 4. T 5. T 6. F 7. F 8. F 9. T 10. F

Anna scored 7/10 and Brad scored 4/10. How much did Cody scored?

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Old 24th October 2012, 06:45 PM   #2 (permalink)
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A well set puzzle question. Though I wouldn't call it Mathematics, rather I call it logic.

Cody got 6 marks for the quiz.

Sent from my GT-P6200 using Tapatalk 2

EDIT:
SOLUTION:

According to the question

Q: 1 2 3 4 5 6 7 8 9 10
A: T T F F T T T F T F
B: T T T F F T T T F T
C: F F F T T F F F T F

A got 7/10
B got 4/10

By observation, for Question 3,5,8,9,10, A & B have different answers. For Question 1,2,4,6,7, A & B have same answers.
For questions which A and B answered differently, either one must be correct.
For questions which A and B answered the same, either is both right or both wrong.

Thus, if we add the marks together for A and B (which is 7+4=11). The summation of marks obtained from questions answered differently is 5.
It could be concluded that the number of marks that A & B get from same answer is 6.

With the above result, in the questions of the same answer, they got 3 correct, 2 questions wrong.
Since in all of C's answer, he answered differently from A & B, C got 3 incorrect, 2 correct.

Now with this information, we can find A and B individual marks in the questions they answered differently.
A got 7 correct, 3 correct from the same answers, thus 4 correct from the different answers.
B got 4 correct, 3 correct from the same answers, thus 1 correct from the different answers.

Observing C's answer, C answered the same as A in the questions answered differently. Thus the number of marks he obtained in the different answers is 4.

Summing it up, C got 6/10

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Last edited by Tetrahedron; 24th October 2012 at 07:42 PM.
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Old 26th November 2012, 11:48 PM   #3 (permalink)
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Re: [PUZZLE] How much did Cody scored?

Ignore all the lengthy and redundant reasoning....

For people who can't understand this question, let me try rephrasing:

B :4 out of 10 questions right
C : Exact opposite options for the T/F questions

Therefore, it is obvious that the answer that what B have gotten correct C would have gotten it wrongly and what B have gotten incorrect C would have gotten it correct....

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