Corey is reviewing a practice test but has lost the answer key to the ten true/false questions. He knows that: * there are the same number of true answers as false answers; * the first and last answers are the same * there are at least three false answers in a row * the answers to questions 5 and 9 are false while question 8 is true; * there are more true answers than false answers in the first five questions. How many possible answer keys meet these criteria?

Question Opt 1

1 v

2 v

3 v

4 f

5 f

6 f

7 f

8 v

9 f

10 v

Step-by-step explanation:

We are certain that the answers to the questions 5 and 9 are false and the answer to the question 8 is true. For the first answer and last answer, we know both questions must be true or both questions must be false.

Then we have two possibilities

Question Opt 1 Opt 2

1 v f

2

3

4

5 f f

6

7

8 v v

9 f f

10 v f

How there are at least three false answers in a row and there are more true answers than false answers in the first five questions and there are the same number of true answers as false answers. We have:

Question Opt 1 Opt 2

1 v f

2 v v

3 v v

4 f v

5 f f

6 f f

7 f f

8 v v

9 f f

10 v f

The option two is not possible because we would need six question with answer false to satisfy the criterion: there are at least three false answers in a row.

Then the only possible option is

Question Opt 1

1 v

2 v

3 v

4 f

5 f

6 f

7 f

8 v

9 f

10 v