Each member of a team consisting of 6 researchers and 4 assistants

Question

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.

Bunuel · Answer

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.

prepapr · Answer

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

MartyMurray · Answer

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.

Average = Sum/Number

From the passage, we have the sum of the researchers' bonuses and the number of researchers.

So, using the information from the passage and from this statement, we could calculate the average of the researchers' bonuses, subtract 300 to get the average of the assistants' bonuses, and multiply by the number of assistants to get the sum of the assistants' bonuses.

Sufficient.

(2) The sum of the bonuses of 3 of the researchers and 2 of the assistants was $4,500.

If all of the researchers got the same bonus and all of the assistants got the same bonus, this statement would be sufficient.

At the same time, we don't have information indicating that the bonuses were the same for all people in each of the two groups. So, we can't assume that.

Thus, this statement provides information on only some of the bonuses, meaning that the others could be of various sizes.

Insufficient.

Correct answer:   A

kaustubhkohli12 · Answer

i thought of second statement in the way 3R+ 2A = 4500 . So multiply by 2 , which makes 6R+4A = 9000 . I know i am assuming that for remaining 3 it would be same number and that's why it is wrong or something else i missed ?

Bunuel · Answer

Yes, that is the issue. Statement (2) does not say that the bonuses are equal within each group, so we cannot simply double the given amount.

findingmyself · Answer

Need clarity:

By using statement 2: We know that 3 of the researchers and 2 assistants bonus equals 4500.
3R+2A=4500, Multiplies by 2 we will have 6R+4A=9000, We are told in stem that 6 Researchers bonus total to $7200. So 4A= 1800, Sum of assistants bonus is $1800.

What is wrong here.

Bunuel · Answer

Have you checked this  post ?

You cannot double 3R + 2A = 4500 because  R and A do not represent equal individual bonuses .

The other 3 researchers and 2 assistants could have received different amounts.

MrMaxMan · Answer

We cannot assume that the bonuses are equal. Knowing the sum of some bonuses does not mean that multiplying the number of people by 2 gets us to the same total as in the prompt.
Statement 1 explicitly tells us the average which lets us safely determine the total, but statement 2 only focuses on a few people and does not say average, so we cannot use it's information to determine the answer for the whole.

Each member of a team consisting of 6 researchers and 4 assistants

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Each member of a team consisting of 6 researchers and 4 assistants

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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