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A certain company's profit is comprised of the profits of the 3 divisi

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A certain company's profit is comprised of the profits of the 3 divisi  [#permalink]

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New post 21 Feb 2017, 16:49
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  95% (hard)

Question Stats:

33% (01:51) correct 67% (02:12) wrong based on 77 sessions

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A certain company's profit is comprised of the profits of the 3 divisions in the company. Is the total profit greater than $4.3 million?

1) The range of the 3 divisions' profits is $2.9 million, and the average (arithmetic mean) of the profit is equal to its median..

2) The minimum value of the 3 divisions' profit is $1.5 million.

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Re: A certain company's profit is comprised of the profits of the 3 divisi  [#permalink]

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New post 24 Feb 2017, 00:33
(1) Let x be a profit for division with least profit. Then the most profitable division has x+2.9mio. Because there are only three divisions and median equals average, the profit for the third division is exactly between the other divisions' profit which is (x + x + 2.9)/2 = x + 1.45. Sum of the profits is x + x + 2.9 + x + 1.43 = 3x + 4.45. Because the profit is a positive number, the combined profit is greater than 4.3. This statement is sufficent.
(2) if a minimum value is 1.5, sum of three must at least greater than or equal to 1.5*3 = 4.5. This statement is sufficient.
Answer is D.
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Re: A certain company's profit is comprised of the profits of the 3 divisi  [#permalink]

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New post 09 Jun 2018, 22:31
1
Is the total profit greater than $4.3 million?
Let profit of divisions be a, b and c. a < b < c

Statement 1:
c - a = $2.9M. (range of the 3 divisions' profits is $2.9 million)
a + b + c = 3b (the average (arithmetic mean) of the profit is equal to its median)
a + c = 2b.
Suppose if a = 0 ( As he says it is profit, the least value a can take is 0$ ).
Then, c = $2.9M and b = $1.45M
So, a + b + c = $4.35M which is greater than $4.3M.
So, Statement 1 is sufficient.

Statement 2:
a = $1.5M (The minimum value of the 3 divisions' profit is $1.5 million)
b > $1.5M and c >$1.5M
3a = $4.5M. So we can for sure say that, a + b + c > $4.5M.
So, Statement 2 is sufficient.

Correct choice is option D.
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Re: A certain company's profit is comprised of the profits of the 3 divisi &nbs [#permalink] 09 Jun 2018, 22:31
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