31) C

Since Jill is so sure that she will finish third, she must be at lest 7 points ahead of the player who is last. She must also be 7 points behind 2nd place.

Karen and Gemma must have equal number of points as no matter what positions they finish in after the 10th round, there would be no ties.
We need to take into consideration the highest number of points that the person in 4th could possibly have. Therefore, we need to assume that they win the 10th round and get 6 points.

Also, total number of points gained in each round = 6 + 3 + 1 = 10 points.
After the 10th round, total number of points should add up to 100. After 9th round, 90 etc.

Let us go through the options:

A – Wrong
If 4th place had ended the competition with a total score of 13, they would have 7 points at the end of the 9th round. Jill would have 14 points (7 points ahead of 4th place) and Karen and Gemma would both have a score of 21 each (7 ahead of Jill). This adds up to 63. This is much smaller than 90.

B – Wrong 
If 4th place had ended the competition with a total score of 15, they would have 9 points at the end of the 9th round. Jill would have 16 points (7 points ahead of 4th place) and Karen and Gemma would both have a score of 23 each (7 ahead of Jill). This adds up to 71. This is smaller than 90.

C – Correct
If 4th place had ended the competition with a total score of 19, they would have 13 points at the end of the 9th round. Jill would have 20 points (7 points ahead of 4th place) and Karen and Gemma would both have a score of 27 each (7 ahead of Jill). This adds up to 87. This is rather close to 90

D – Wrong 
If 4th place had ended the competition with a total score of 21, they would have 15 points at the end of the 9th round. Jill would have 22 points (7 points ahead of 4th place) and Karen and Gemma would both have a score of 29 each (7 ahead of Jill). This adds up to 95. Even though this is close to 90, you must remember that the score cannot be higher than 90.

E – Wrong 
If 4th place had ended the competition with a total score of 23, they would have 17 points at the end of the 9th round. Jill would have 24 points (7 points ahead of 4th place) and Karen and Gemma would both have a score of 31 each (7 ahead of Jill). This adds up to 103. This is much higher than 90.

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