Skientist wrote:
John owns stock in nine different companies, for a total of 21,000 of stock. If the number of shares he has in any company is not equal to the number of shares he has in any other company, does he own at least 3,000 shares of Command C stock?
1) John has more shares of Company C stock than any other company's stock, except for Company A and Company B.
2) The number of shares of company C stock that John owns is less than 20% greater than the number of shares of any other company's stock that John owns.
This is a hard question. I am happy to help with this.
So, John owns share from nine companies, for a total of 21000 shares. Number of shares from each company unequal to all the others.
Statement #1:
John has more shares of Company C stock than any other company's stock, except for Company A and Company B.We could construct scenarios in which the answer to the prompt is true or false
For example
A = 20000 shares, B = 979 shares, C = 7, D = 6, E = 5, F = 4, G = 3, H = 2, I = 1
This extreme scenario gives an answer of no.
A = 5500, B = 4500, C = 4000, D= 3000, E = 2500, F = 2000, G = 1500, H = 1000, I = 500
This scenario give an answer of yes.
Because we can construct scenarios which answer the prompt question either way, we have no way to give a definitive answer based on this sentence. Therefore, this sentence, by itself, is
insufficient.
Statement #2:
The number of shares of company C stock that John owns is less than 20% greater than the number of shares of any other company's stock that John ownsClearly, in an extreme case, John could own 1 share of C, and more than 1 share of everything else, and the answer would be no. The question, then, remains, would it be possible to construct a scenario consistent with this statement that give a "yes' answer to the prompt?
In order for C to be as big as possible, we would need the minimum to be as large as possible, which implies that the values on the list are all close together.
If C = 3000, that leaves 18000 for the other eight companies, which is an average of 18000/8 = 9000/4 = 2250 shares each. Of course, they couldn't all equal that value, so some would have to be slightly above that, and others, including the minimum, would have to be slightly below that.
What is 20% more than 2250? 1.20*2250 = 2700, far less than 3000.
Thus, it turns out, given the constraint of this statement, it's absolutely impossible for C to be as large as 3000. It absolutely must be smaller than 3000. This statement is
sufficient.
Answer =
BDoes all this make sense?
Mike