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31 May 2024, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
9% (02:59) correct
91%
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wrong
based on 70
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A certain company has 500 employees split among three divisions, such that there are at least 100 employees in each division. An $8,000,000 benefits budget is to be distributed among the three divisions, and a division will be considered underfunded if it receives no more than $10,000 per employee, and overfunded if it receives at least $40,000 per employee. How many divisions of the company are overfunded?
(1) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded.
(2) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded.
(1) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded.
(2) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded.
arkaja11
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Schools: ISB '27 (A) INSEAD '26 Tuck '27
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Posts: 42
31 May 2024, 07:01
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Looks scary to be honest, but probably it's a tricky question. In my opinion, its option D (Both are alone sufficient)
Let us first put all the parameters:
The total number of employees is 500, split among three divisions (A,B,C) with each division having at least 100 employees. The total benefits budget is $8,000,000.
We denote the number of employees in division A,B and C as a,b and c with a+b+c = 500 and a,b,c ≥100
We denote the budget to divisions in division A,B and C as x,y and z with x+y+z = $ 8000k
We need to check how many of these divisions receive at least $40,000 per employee:
How many of (x/a , y/b , z/c ) ≥ $ 40k
Lets look at Statement 1 :
"If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded"
This implies : x/a > $ 10k and y/b > $ 10k and z/c > $ 10k
Supposing one division to be just overfunded -
Let's say division A has least number of employees = 100 and receives benefits of $ 40k/employee. Hence, x = $ 4000k
This will imply --> y+z = $ 4000k and b+c = 400 (from above constraints)
For any combination, it's not possible for both B and C to not stay underfunded.
(Let's take y/b = $ 11k and b = 200, then c = 200 and z/c = $ 9k (underfunded))
Hence, if 1 division is overfunded, atleast 1 division will be underfunded.
So, we can conclude that for any arrangement where "there is no possible rearrangement in which any division is underfunded", number of overfunded divisions = 0
Hence statement 1 is sufficient.
Lets look at Statement 2 :
"If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded."
x/a < $ 40k, y/b < $ 40k or z/c < $ 40k
Since this ensures that no division is overfunded in any rearrangement, it implies no division is overfunded with the original budget distribution.
Hence statement 2 is also sufficient.
We can conclude that both the statements are sufficient alone. Hence Option D.
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Let us first put all the parameters:
The total number of employees is 500, split among three divisions (A,B,C) with each division having at least 100 employees. The total benefits budget is $8,000,000.
We denote the number of employees in division A,B and C as a,b and c with a+b+c = 500 and a,b,c ≥100
We denote the budget to divisions in division A,B and C as x,y and z with x+y+z = $ 8000k
We need to check how many of these divisions receive at least $40,000 per employee:
How many of (x/a , y/b , z/c ) ≥ $ 40k
Lets look at Statement 1 :
"If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded"
This implies : x/a > $ 10k and y/b > $ 10k and z/c > $ 10k
Supposing one division to be just overfunded -
Let's say division A has least number of employees = 100 and receives benefits of $ 40k/employee. Hence, x = $ 4000k
This will imply --> y+z = $ 4000k and b+c = 400 (from above constraints)
For any combination, it's not possible for both B and C to not stay underfunded.
(Let's take y/b = $ 11k and b = 200, then c = 200 and z/c = $ 9k (underfunded))
Hence, if 1 division is overfunded, atleast 1 division will be underfunded.
So, we can conclude that for any arrangement where "there is no possible rearrangement in which any division is underfunded", number of overfunded divisions = 0
Hence statement 1 is sufficient.
Lets look at Statement 2 :
"If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded."
x/a < $ 40k, y/b < $ 40k or z/c < $ 40k
Since this ensures that no division is overfunded in any rearrangement, it implies no division is overfunded with the original budget distribution.
Hence statement 2 is also sufficient.
We can conclude that both the statements are sufficient alone. Hence Option D.
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03 Jun 2024, 05:50
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Let amount distributed to each division be x, y, z and no of employees in each division be a, b, c
x+y+z=4000k and a+b+c=500
Min no of employees = 100, no maximum provided
Statement 1: "If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded"
Let's assume that one division is overfunded in original arrangement. With min no of employees 100
x/a ≥ 40k i.e x/100 ≥40k. So x will be 4000k
This brings y+z=4000k and b+c=400
With this condition, another division can not be over funded i.e 4000k/100 where 3rd division will be left without any funds. At this point no of divisions overcrowded ≤1
Let's assume, 2nd division is underfunded. Now the distribution will become:
4000k/100 + 1000k/100 + 3000k/200
Rearranging this in another two possibilities will leave a division in one of them. Even if we distribute the remaining funds and employees equally to 2nd & 3rd division we will end up in a similar scenario.
Possible rearrangements:
1000k/100 + 3000k/100 + 4000k/200 - Fair distribution
3000k/100 + 4000k/100 + 1000k/200 - Fair / overfunded / underfunded
Therefore, there can not be a division which is overfunded or no of divisions overfunded is 0
Hence, Statement 1 alone is sufficient.
Statement 2: "If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded."
Applying the same analysis as for statement 1 will give one overfunded possibility
So, in this case we should start with underfunded division, for which we don't have maximum no of employees per division.
Hence, Statement 2 alone is not sufficient.
Answer: A
x+y+z=4000k and a+b+c=500
Min no of employees = 100, no maximum provided
Statement 1: "If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded"
Let's assume that one division is overfunded in original arrangement. With min no of employees 100
x/a ≥ 40k i.e x/100 ≥40k. So x will be 4000k
This brings y+z=4000k and b+c=400
With this condition, another division can not be over funded i.e 4000k/100 where 3rd division will be left without any funds. At this point no of divisions overcrowded ≤1
Let's assume, 2nd division is underfunded. Now the distribution will become:
4000k/100 + 1000k/100 + 3000k/200
Rearranging this in another two possibilities will leave a division in one of them. Even if we distribute the remaining funds and employees equally to 2nd & 3rd division we will end up in a similar scenario.
Possible rearrangements:
1000k/100 + 3000k/100 + 4000k/200 - Fair distribution
3000k/100 + 4000k/100 + 1000k/200 - Fair / overfunded / underfunded
Therefore, there can not be a division which is overfunded or no of divisions overfunded is 0
Hence, Statement 1 alone is sufficient.
Statement 2: "If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded."
Applying the same analysis as for statement 1 will give one overfunded possibility
So, in this case we should start with underfunded division, for which we don't have maximum no of employees per division.
Hence, Statement 2 alone is not sufficient.
Answer: A
