Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most?

To determine whose mean test score will increase the most, we need to calculate the mean of their previous six test scores and compare it to their current mean score of 100%.

Theo:
Previous test scores: 90%, 85%, 88%, 92%, 95%, 87%
Mean of previous test scores: (90 + 85 + 88 + 92 + 95 + 87) / 6 = 89.5%
Increase in mean score: 100% - 89.5% = 10.5%

Ara:
Previous test scores: 85%, 88%, 90%, 92%, 86%, 89%
Mean of previous test scores: (85 + 88 + 90 + 92 + 86 + 89) / 6 = 88.3%
Increase in mean score: 100% - 88.3% = 11.7%

Jose:
Previous test scores: 85%, 90%, 89%, 92%, 87%, 84%
Mean of previous test scores: (85 + 90 + 89 + 92 + 87 + 84) / 6 = 87.8%
Increase in mean score: 100% - 87.8% = 12.2%

Dana:
Previous test scores: 86%, 84%, 87%, 91%, 88%, 85%
Mean of previous test scores: (86 + 84 + 87 + 91 + 88 + 85) / 6 = 86.8%
Increase in mean score: 100% - 86.8% = 13.2%

Therefore, Dana's mean test score will increase the most, with an increase of 13.2%.