If all the employees of a company fall into one and only one of 3 groups, X, Y, or Z, with 250, 100, and 20 members in

BTGmoderatorDC wrote: ↑
Sat Dec 31, 2022 11:19 pm
If all the employees of a company fall into one and only one of 3 groups, X, Y, or Z, with 250, 100, and 20 members in each group, respectively, what is the average (arithmetic mean) weekly salary of all the employees of this company, if all employees are paid every week of the year?

(1) The average (arithmetic mean) annual salary of the employees in Group X is $10,000, in Group Y $15,000 and in Group Z $20,000.
(2) The total annual payroll is $4,400,000.

OA D

Source: GMAT Prep

Given: All the employees of a company fall into one and only one of 3 groups, X, Y, or Z, with 250, 100, and 20 members in each group, respectively.
So, the total number of employees = 250 + 100 + 20 = 370

Target question: What is the average (arithmetic mean) weekly salary of all the employees of this company, if all employees are paid every week of the year?

Statement 1: The average (arithmetic mean) annual salary of the employees in Group X is $10,000, in Group Y $15,000 and in Group Z $20,000.
The weighted averages formula says: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
So, the average ANNUAL salary of all employees = (250/370)($10,000) + (100/370)($15,000) + (20/370)($20,000)
Since we COULD calculate the average ANNUAL salary, we could also calculate the average WEEKLY salary (of course we wouldn't waste valuable time on test day doing so).
Since we could answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The total annual payroll is $4,400,000.
So, the average ANNUAL salary of all employees = $4,400,000/370
This also means we could calculate the average WEEKLY salary.
Statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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