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28 May 2026, 12:38
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Each member of a team consisting of 6 researchers and 4 assistants received a bonus. If the sum of the researchers’ bonuses was $7,200, what was the sum of the assistants’ bonuses?
(1) The average (arithmetic mean) of the researchers’ bonuses was $300 greater than the average of the assistants’ bonuses.
(2) The sum of the bonuses of 3 of the researchers and 2 of the assistants was $4,500.
(1) The average (arithmetic mean) of the researchers’ bonuses was $300 greater than the average of the assistants’ bonuses.
(2) The sum of the bonuses of 3 of the researchers and 2 of the assistants was $4,500.
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28 May 2026, 12:39
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Each member of a team consisting of 6 researchers and 4 assistants received a bonus. If the sum of the researchers’ bonuses was $7,200, what was the sum of the assistants’ bonuses?
The researchers’ average bonus was 7200/6 = 1200.
(1) The average of the researchers’ bonuses was $300 greater than the average of the assistants’ bonuses.
So the assistants’ average bonus was 1200 - 300 = 900.
Since there are 4 assistants, the sum of the assistants’ bonuses was 4 * 900 = 3600. Sufficient.
(2) The sum of the bonuses of 3 of the researchers and 2 of the assistants was $4,500.
This gives only a combined sum for some researchers and some assistants. Since the individual researcher bonuses are not known, the assistants’ total cannot be determined. Not sufficient.
Answer: A.
The researchers’ average bonus was 7200/6 = 1200.
(1) The average of the researchers’ bonuses was $300 greater than the average of the assistants’ bonuses.
So the assistants’ average bonus was 1200 - 300 = 900.
Since there are 4 assistants, the sum of the assistants’ bonuses was 4 * 900 = 3600. Sufficient.
(2) The sum of the bonuses of 3 of the researchers and 2 of the assistants was $4,500.
This gives only a combined sum for some researchers and some assistants. Since the individual researcher bonuses are not known, the assistants’ total cannot be determined. Not sufficient.
Answer: A.
29 May 2026, 00:15
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We know total bonuses of 6 researchers = $7,200
Need to find total bonuses of 4 assistants.
Analyzing Statement (1)
Average researcher bonus:
7200/6=1200
Researchers’ average is $300 greater than assistants’ average, so:
1200−300=900
Average assistant bonus = $900.
Since there are 4 assistants:
4×900=3600
Statement (1) is sufficient.
Analyzing Statement (2)
We only know that 3 researchers and 2 assistants together received $4,500.
We do not know how the bonuses were distributed among researchers or assistants, so the total assistants’ bonuses cannot be determined.
Statement (2) is insufficient.
Correct Answer: A
Need to find total bonuses of 4 assistants.
Analyzing Statement (1)
Average researcher bonus:
7200/6=1200
Researchers’ average is $300 greater than assistants’ average, so:
1200−300=900
Average assistant bonus = $900.
Since there are 4 assistants:
4×900=3600
Statement (1) is sufficient.
Analyzing Statement (2)
We only know that 3 researchers and 2 assistants together received $4,500.
We do not know how the bonuses were distributed among researchers or assistants, so the total assistants’ bonuses cannot be determined.
Statement (2) is insufficient.
Correct Answer: A
Bunuel
