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Difficulty:
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Question Stats:
71% (02:34) correct
29%
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wrong
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Of the people who donated money to a certain local theater last year, 1/4 donated $20 or less and 2/3 donated more than $20 but less than $1,000. If the average (arithmetic mean) amount donated by the people who donated more than $20 but less than $1,000 was $180, what was the average amount donated by the people who donated $1,000 or more?
(1) The average amount donated by the people who donated less than $1,000 was $132.
(2) The average amount donated by the people who donated more than $20 was $360.
2023-08-15_11-00-18.png [ 134.86 KiB | Viewed 27699 times ]
(1) The average amount donated by the people who donated less than $1,000 was $132.
(2) The average amount donated by the people who donated more than $20 was $360.
Attachment:
2023-08-15_11-00-18.png [ 134.86 KiB | Viewed 27699 times ]
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29 Aug 2023, 09:39
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Bunuel
Each person who donated is a member of exactly one of the following subgroups.
Subgroup 1: $20 or less
fraction of the whole = 1/4 = 3/12
average = a₁
Subgroup 2: between $20 and $1,000
fraction of the whole = 2/3 = 8/12
average = $180
Subgroup 3: $1,000 or more
fraction of the whole = 1 – 3/12 – 8/12 = 1/12
average = a₃
We need to answer the question:
a₃ = ?
Statement One Alone:
=> The average amount donated by the people who donated less than $1,000 was $132.
Using the weighted arithmetic average formula, we could determine a₁:
[(3/12)a₁ + (8/12)180]/(3/12 + 8/12) = 132
However, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
=> The average amount donated by the people who donated more than $20 was $360.
Using the weighted arithmetic average formula, we could determine a₃:
[(8/12)180 + (1/12)a₃]/(8/12 + 1/12) = 360
We could answer the question. Statement two is sufficient.
Answer: B
18 Mar 2024, 19:59
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Hi all,
I found a simpler way to solve the question than the ways shared in this post.
Imagine just drawing a BAR Graph with the 3 Groups
1) people who donated 20 or less --> 1/4 or 3/12 of the total donors
2) people who donated more than 20 and less than $1000 --> 2/3 or 8/12 of the total donors - AVG MEAN of this donatios $180
3) people who donated more than $1000 --> 1/12 of the total donors (1 - the previous values)
Notice that for this excersie we can set a proportion of 3 : 8 : 1 respectively for the donors groups.
Statement #1
They give us just information about Group 1 and Group 2. There is no possible way to estimate how much Group 3 donated.
So discarded, but note that we could get the average of group 1 if needed.
Eliminate answers: A & D
Statement #2
They give us information about the Group 2 and Group 3! Bingo!
So $360 is the average for 9 donors -> Total donations: $3240 form Group 2 & 3.
If we estimate the total Donations for just group 2 (it would be $180 x 8 --> $1440)
So Group 3 is the difference of this values, beign $1800 for just 1 donor.
So statement 2 is correct
Answer B
I found a simpler way to solve the question than the ways shared in this post.
Imagine just drawing a BAR Graph with the 3 Groups
1) people who donated 20 or less --> 1/4 or 3/12 of the total donors
2) people who donated more than 20 and less than $1000 --> 2/3 or 8/12 of the total donors - AVG MEAN of this donatios $180
3) people who donated more than $1000 --> 1/12 of the total donors (1 - the previous values)
Notice that for this excersie we can set a proportion of 3 : 8 : 1 respectively for the donors groups.
Statement #1
They give us just information about Group 1 and Group 2. There is no possible way to estimate how much Group 3 donated.
So discarded, but note that we could get the average of group 1 if needed.
Eliminate answers: A & D
Statement #2
They give us information about the Group 2 and Group 3! Bingo!
So $360 is the average for 9 donors -> Total donations: $3240 form Group 2 & 3.
If we estimate the total Donations for just group 2 (it would be $180 x 8 --> $1440)
So Group 3 is the difference of this values, beign $1800 for just 1 donor.
So statement 2 is correct
Answer B
