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Set B has three positive integers with a median of 9. If the [#permalink]
05 Sep 2004, 22:36
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Set B has three positive integers with a
median of 9. If the largest possible range of the
three numbers is 19, given a certain mean, what is
(E) It cannot be determined from the information given
We're told the range is 19, so y-x = 19
To find the mean, we need to find x+9+y
But we do not have any other information, nor are we told x and y are evenly seperated from 9.
So (E), the mean cannot be determined from the information given.
Sorry guys, this time you lost
Paul got it. I didn't understand why he considered it inconclusive...
In this problem, you have to plug in your answers.
Start with (B) because 10 is usually an easy number to deal with.
If the mean is 10 and the median is 9, what would the largest possible range of the three integers be?
Our three integers must fit into the equation :
(a+b+c)/3 = 10
The median, b, equals 9, so 21 = a+c . The range is defined as c-a , to make c-a as large as possible, given that a+c =21 , we can set a=1 and c=20 .
That does give us a range of 19, so (B) is the correct answer.
Help me, people. I would consider that we know a few things:
1. set of three integers, all positive
So, we know one integer =9. And that the range=19. Theoretically, the first integer can also=9. So a set of (9,9, and 9+19 or 28) is possible. Perhaps I am knitpicking, but I don't see that the question (while a good math question) has the clarity needed for a real GMAT question.
Basically, how is everyone reading the question so as not to fall into the trap I did?
(1), Subtitute M = 22, 2A = 38, A = 19, Wrong since A should be lesser than 9
(2), Subtitute M = 10, 2A = 2, A = 1, A correct solution, Numbers are 1, 9 and 20.
(3), Subtitute M = 9.6, 2A = 38, A = .8, Wrong since A has to be integer
(4), Subtitute M = 9, 2A = -1, A = -.5, Wrong since A has to be positive integer
Just for the record, as paul said, three numbers 8-9-27 satisfies the conditions and gives a mean of 14.67.
The fact that we basksolve is to save time and that is not expected out of a ETS method of problem solving. So, I still stay with E.
Again what if the answer choice (3) was 14.67 instead of 9.6.
The ans is (B) to the actual question if the stem is "Which of the following is a possible value for mean?" instead of "what is that mean?"
I totally agree with you anuramm, I had the same feeling because I coudn't get the answer and even with the OA I found the answer kind of weird....I just wanted to know your ideas and your explantions so that maybe I can understand the OA better, but it doesn't seem it's going to happen
Daytest I would have answered E without any doubts.