varun289 wrote:333. A certain company's customer service department has five employees. The hourly wage for each employee ranges from $5 an hour to $20 an hour. Which of the following could be the average (arithmetic mean) hourly wage for the customer service employees?
1) $7.50 an hour
2) $9 an hour
3) $16.75 an hour

A. 1 only
B. 2 only
C. 3 only
D. 1 and 2 only
E. 2 and 3 only

Are you certain the question has been transcribed properly?
Consider these cases:
case a: The 5 employees each earn $7.50/hour. So, their average hourly wage is $7.50. Scenario I is possible.
case b: The 5 employees each earn $9/hour. So, their average hourly wage is $9. Scenario II is possible.
case c: The 5 employees each earn $16.75/hour. So, their average hourly wage is $16.75. Scenario III is possible.

So, the correct answer is F. all 3 are possible

Cheers,
Brent

aman88 wrote:Mr. Brent, can we figure out the answer to this by finding out the lower limit and the upper limit of hourly wages and then seeing which values out of three fit in that range?

Average: Lowest hourly wage of 5 employees per hour = $5
Average: Highest hourly wage of 5 employees per hour = $20.

All three options are between these values. So the right answer will be F as you said. Right?

Thanks.

Ah........ I see.
I read the question as suggesting that each employee earns between 5 and 20 dollars per hour.
However, it may be saying that the 5 hourly wages have a range of $15, and the lowest wage is $5/hour, and the highest wage is $20 hour.

If this is the case, here's my approach:

We'll use the following fact:
If n numbers have a mean of m, then the sum of the n numbers is nm

I. For the average wage to be $7.50/hour then the sum of the 5 wages must equal $37.50 (since 5 x 7.50 = $37.50)
If two of the wages are $5/hour and $20/hour, the remaining 3 wages must add to $12.50
This is impossible since each employee must earn at least $5/hour.

II. For the average wage to be $9/hour then the sum of the 5 wages must equal $45 (since 5 x 9 = $45)
If two of the wages are $5/hour and $20/hour, the remaining 3 wages must add to $25
This is possible. The 3 remaining could earn $10/hour, $10/hour and $5/hour.

III. For the average wage to be $16.75/hour then the sum of the 5 wages must equal $83.75
If two of the wages are $5/hour and $20/hour, the remaining 3 wages must add to $58.75
This is possible. The 3 remaining could earn $20/hour, $20/hour and $18.75/hour.

Since scenarios II and III are possible, the correct answer is E

Cheers,
Brent