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Each of the 20 people working in a certain office contributed either

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Bunuel
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Each of the 20 people working in a certain office contributed either [#permalink] New post   03 Aug 2023, 05:00
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51% (01:35) correct 49% (02:08) wrong based on 220 sessions
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Each of the 20 people working in a certain office contributed either $9, $10, or $11 toward an office party. What was the average (arithmetic mean) amount contributed per person in the office?

(1) The number of people who contributed $9 was the same as the number of people who contributed $11.
(2) The number of people who contributed $9 was more than the number of people who contributed $10.
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Re: Each of the 20 people working in a certain office contributed either [#permalink] New post   03 Sep 2023, 16:41
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Bunuel wrote:
Each of the 20 people working in a certain office contributed either $9, $10, or $11 toward an office party. What was the average (arithmetic mean) amount contributed per person in the office?

(1) The number of people who contributed $9 was the same as the number of people who contributed $11.
(2) The number of people who contributed $9 was more than the number of people who contributed $10.


n = a + b + c = 20

We need to answer the question:

average = (9a + 10b + 11c)/(20) = ?

Statement One Alone:

=> The number of people who contributed $9 was the same as the number of people who contributed $11.

a = c
a + b + a = 20
b = 20 – 2a

average = (9a + 10(20 – 2a) + 11a)/20 = 200/20 = $10

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> The number of people who contributed $9 was more than the number of people who contributed $10.

If each person contributed $9, then the average was $9.

Whereas, if 19 people contributed $9 and 1 person contributed $10, then the average is greater than $9.

Statement two is not sufficient.

Answer: A
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Re: Each of the 20 people working in a certain office contributed either [#permalink] New post   03 Aug 2023, 05:15
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Bunuel wrote:
Each of the 20 people working in a certain office contributed either $9, $10, or $11 toward an office party. What was the average (arithmetic mean) amount contributed per person in the office?

(1) The number of people who contributed $9 was the same as the number of people who contributed $11.
(2) The number of people who contributed $9 was more than the number of people who contributed $10.


In a set, the positive difference w.r.t to the average (arithmetic mean) compensates for the negative difference w.r.t average (arithmetic mean).

Statement 1

(1) The number of people who contributed $9 was the same as the number of people who contributed $11.

  • Each person who contributed $9 contributed $1 less than $10.
  • Each person who contributed $11 contributed $1 more than $10.

We know that the number of people in the above two categories was the same. Hence, for each person who contributed $9, another person contributed $11, thereby keeping the average at $10. The statement is sufficient and we can eliminate B, C, and E.

Statement 2

(2) The number of people who contributed $9 was more than the number of people who contributed $10.

Knowing the fact that the number of people who contributed $9 was more than the number of people who contributed $10 doesn't help us find the average.

For example, if the number of people who contributed $11 was the same as the number of people who contributed $9, the average was $10. However, if the number of people between the two categories (people who contributed $9 and people who contributed $11) was not the same, the average was not $10.

Hence, the statement alone is not sufficient. We can eliminate D.

Option A
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Re: Each of the 20 people working in a certain office contributed either [#permalink] New post   06 Aug 2023, 06:55
let three set of people be
x,y,z ; x+y+z =20
our target
9x+10y+11z/ 20

#1
The number of people who contributed $9 was the same as the number of people who contributed $11.
x=z
20x+10y / 20 ;
(2x+y) / 2
pairs will be 2,18 ; 4,16, ; 6,14 so on
the avg will always be 10
sufficient
#2
The number of people who contributed $9 was more than the number of people who contributed $10

x>y
but no info about z
avg can be different as z is not known which is highest value

insufficient

OPTION A is correct
Bunuel wrote:
Each of the 20 people working in a certain office contributed either $9, $10, or $11 toward an office party. What was the average (arithmetic mean) amount contributed per person in the office?

(1) The number of people who contributed $9 was the same as the number of people who contributed $11.
(2) The number of people who contributed $9 was more than the number of people who contributed $10.
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Re: Each of the 20 people working in a certain office contributed either [#permalink]
06 Aug 2023, 06:55
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Bunuel
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