Let's get started by first understanding what we're dealing with in terms of definitions.
Definition 1 states that the percentile rank of a score is calculated by dividing the number of scores below it by the total number of scores.
Definition 2, on the other hand, states that the percentile rank of a score is calculated by dividing the sum of the number of scores below it and half the number of scores equal to it, by the total number of scores.
Then, we multiply the quotient by 100 in both definitions to convert it into a percentage. This is the percentile rank of the score.
Let's now check the validity of the statements:
Beginning with the score 83, using definition 1, we calculate the percentile rank by counting the number of scores below 83. There are 3 scores of 83, which make up 15% of the total scores according to our calculation. Statement a) claims that the percentile rank of the score 83 is the 67th percentile, which contradicts our calculated percentile rank of 15%. Hence, statement a) is false.
Next, for the score 87, using definition 2, we count the number of scores below it and half the number of scores equal to it. There are 14 scores below 87, and 1 score equal to it, hence our calculated percentile rank is 72.5%. Statement b) claims that the percentile rank of the score 87 is the 50th percentile, which contradicts our calculated percentile rank of 72.5%. Hence, statement b) is false.
Now, if we apply both definitions to the score 87, we would see that the calculated percentile ranks differ. So, statement c), which claims that definitions 1 and 2 would yield a similar percentile rank for the score 87, is false.
Since statements a), b), and c) are all false, statement d) which indicates that a), b), and c) are the right answer choices, is definitely false.
In conclusion, the correct answer is e) none of the answers is the right answer choice for this question.