1. Calculate the total number of pitches made by Team Alpha: 5 members * 12 pitches/member = 60 pitches. 2. Calculate the total number of pitches made by all 8 team members combined: 8 members * 11 pitches/member = 88 pitches. 3. Determine the total number of pitches made by Team Beta by subtracting Team Alpha's total from the combined total: 88 pitches - 60 pitches = 28 pitches. 4. Calculate the average number of pitches per member for Team Beta: 28 pitches / 3 members = 9.333... pitches/member. 5. Round the average to two decimal places: 9.33. Why others are wrong: A — Correct answer. B — This option results from incorrectly assuming the overall average (11) is a simple arithmetic mean of Team Alpha's average (12) and Team Beta's average (X), i.e., (12 + X) / 2 = 11, which yields X = 10. This ignores the different number of members in each team. C — This option could be the result of rounding the correct answer down to the nearest whole number or a minor arithmetic error in calculating Team Beta's total pitches (e.g., if total was 27 instead of 28). D — This option incorrectly assumes that Team Beta's average must be the same as the overall combined average, failing to account for Team Alpha's above-average performance which pulls the overall average up.

To achieve an average of $1200 over five months, the total commission earned must be $1200 * 5 = $6000. The total commission earned in the first four months is $1100 + $1350 + $1050 + $1220 = $4720. To reach the target total, Agent X must earn $6000 - $4720 = $1280 in the fifth month. Why others are wrong: A — This is the average commission earned in the first four months, not what is needed in the fifth. B — This is the target average itself, not the amount needed to achieve it in the final month. D — This would be the amount needed if there was a calculation error in the sum of the first four months (e.g., if the sum was $4700 instead of $4720).

1. Calculate the number of clients acquired in January: 25 clients. 2. Calculate the number of clients acquired in February: 25 - 5 = 20 clients. 3. Calculate the number of clients acquired in March: 20 * 2 = 40 clients. 4. Sum the total clients for the quarter: 25 + 20 + 40 = 85 clients. 5. Determine the number of months in the first quarter: 3 months. 6. Calculate the mean (average): Total clients / Number of months = 85 / 3 = 28.333... 7. Rounding to two decimal places, the mean is 28.33 clients. Why others are wrong: A — This result would occur from incorrectly rounding the mean down to the nearest whole number. B — This result would occur from incorrectly rounding the mean up to the nearest whole number. C — This is the correct calculation. D — This result occurs if March's acquisition was mistakenly calculated as double January's clients (25 * 2 = 50), leading to a total of 25 + 20 + 50 = 95, and a mean of 95 / 3 = 31.67.

The initial total score for 15 students was 15 * 78 = 1170. The new total score for 16 students (including the new one) is 16 * 79 = 1264. The new student's score is the difference between the new total and the initial total. New student's score = 1264 - 1170 = 94. Why others are wrong: A — This is the new average score, not the individual score of the new student. B — This value is incorrect and would result from a miscalculation or misunderstanding of how the mean changes. D — This is the original average score, not the individual score of the new student.

The sum of scores for all 5 tests was 84 * 5 = 420. The sum of scores for the remaining 4 tests was 88 * 4 = 352. The lowest score removed is the difference between these two sums. Removed score = 420 - 352 = 68. Why others are wrong: A — Correct calculation. B — Incorrect calculation, possibly a small arithmetic error in sums or subtraction. C — Incorrect calculation, potentially subtracting a value other than the calculated difference from the initial average. For example, 84 - 8 = 76 (where 8 is twice the difference in averages). D — Incorrect calculation, potentially subtracting the difference in averages from the initial average (84 - (88 - 84) = 84 - 4 = 80).