Average problem

[phoenix9801]

3-
What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217


4-
A sales force brings in $351,000 in sales this quarter. The top 33 % of the sales force brings in an average (arithmetic mean) of $201,000 in sales per person while the rest of the sales force averages $150,000 per person. What is the average (arithmetic mean) sales per member of the sales force?

a) $ 167,00
b) $ 160,000
c) $ 175,500
d) $ 186,000
e) $ 217,000

[aneesh.kg]

3-
What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217

Let there be 'x' number of heaviest people.
Average weight
= Total weight/Number of people
= (Sum of the weight of heaviest people + Sum of others' weight)/Number of people
= [201*x + 150*(p - x)]/p
= [150p + 51x]/p
= 150 + 51(x/p)

We atleast need the ratio of number of heaviest people (x) to the total number of people (p) to be able to solve this. The overall average will be between 150 and 201, but its exact value will depend on (x/p).

Insufficient Data.

[aneesh.kg]

4-
A sales force brings in $351,000 in sales this quarter. The top 33 % of the sales force brings in an average (arithmetic mean) of $201,000 in sales per person while the rest of the sales force averages $150,000 per person. What is the average (arithmetic mean) sales per member of the sales force?

a) $ 167,000
b) $ 160,000
c) $ 175,500
d) $ 186,000
e) $ 217,000

This is similar to the previous problem, except that the required ratio is given in this case.

Average sales = Total Sales/Number of people
Ignoring the '000' temporarily,
= [201x + 150y]/N
= 201(x/N) + 150(y/N)
It is given that x/N = 1/3, y/N = 2/3, therefore
= 201(1/3) + 150(2/3)
= (201 + 300)/3
= 167

Average = $ 167,000
(Assuming that you've missed out a '0' in (A), I've corrected it (in red).)
[spoiler](A)[/spoiler] is correct.

P.S.: 'A sales force brings in $351,000 in sales this quarter.': How is this data required? This is superfluous. Also, $351,000 = $200,000 + $151,000. It is not possible for the Total sales to be $351,000 because for every salesperson that brings in $200,000, there are two salespeople who bring in $151,000.

The language of the problem is also ambiguous. The problem starts with saying that the total sales are for a quarter, but does not specify if the average is to calculated for a quarter, or a year, or two years, etc. This is far from a GMAT problem.

What is the source?

[phoenix9801]

My apologies there was a typo in the problem I thought it was fixed it supposed to be P/3 next to the word heaviest.

What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the p/3 heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217

3-
What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217

Let there be 'x' number of heaviest people.
Average weight
= Total weight/Number of people
= (Sum of the weight of heaviest people + Sum of others' weight)/Number of people
= [201*x + 150*(p - x)]/p
= [150p + 51x]/p
= 150 + 51(x/p)

We atleast need the ratio of number of heaviest people (x) to the total number of people (p) to be able to solve this. The overall average will be between 150 and 201, but its exact value will depend on (x/p).

Insufficient Data.

[aneesh.kg]

My apologies there was a typo in the problem I thought it was fixed it supposed to be P/3 next to the word heaviest.

What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the p/3 heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217

Average = 150 + 51(x/p)
Since x = p/3,
Average = 150 + 51(1/3) = 167

[spoiler](A)[/spoiler] is correct.

By the way in GMAT the options are always arranged in a descending order, unlike the options here.