SAT Mathematics Practice Test 5

If the mean score of 8 players is $14.5,$ then the total of all 8 scores is $14.5\times 8=116.$ If the mean of $7$ scores is $12,$ then the total of all 7 scores is $12\times 7=84$. Since the set of 7 scores was made by removing the highest score of the set of 8 scores, then the difference between the total of all 8 scores and the total of all 7 scores is equal to the removed score: $116-84=32.$
Choice A is incorrect because if 20 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $\frac{\left(14.5\cdot 8\right)-20}{7}\approx 13.71,$, not 12. Choice B is incorrect because if 24 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $\frac{\left(14.5\cdot 8\right)-24}{7}\approx 13.14$ , not 12. Choice D is incorrect because if 36 is removed from the group of 8 scores, then the mean score of the remaining 7 players is $\frac{\left(14.5\cdot 8\right)-36}{7}\approx 11.43$ is not 12