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# Set B has three positive integers with a median of 9. If the

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VP
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Set B has three positive integers with a median of 9. If the [#permalink]

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05 Sep 2004, 22:36
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
that mean?
(A) 22
(B) 10
(C) 9.6
(D) 9
(E) It cannot be determined from the information given
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05 Sep 2004, 23:20
E should be it
1) 8-9-27 --> range 19 mean 14.67
2) 1-9-20 --> range 19 but mean is 10
inconclusive
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Paul

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05 Sep 2004, 23:24
The three integers will be x,9,y

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.
VP
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06 Sep 2004, 02:17
Sorry guys, this time you lost
Paul got it. I didn't understand why he considered it inconclusive...

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.
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:? I'm missing something here [#permalink]

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06 Sep 2004, 06:42
Help me, people. I would consider that we know a few things:
1. set of three integers, all positive
2. median=9
3. range=19

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?
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06 Sep 2004, 07:14
I feel that the answer should be E.
This is because , we just know that
1. there are three positive integers.
2. the median is 9.
3. the largest possible range for a given mean is 19.

This means that we can have multiple values of mean, 10 being one of them.
If the question read like this- what could be the mean , then probably E is right.

But when the question says - what is that mean , it sounds like there is only one mean.
Please correct me if i am worng.

I was about to post this question since i felt that the OA was wrong. Glad to see it already posted. It saves me some time.
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06 Sep 2004, 11:25
Veru good sum. My explanation:

Let the three numbers be A, B and C.
Given: B = 9, C-A = 19
To Find: Mean, M = A+B+C/3

M = [A+B+C]/3
= [(A+C) + 9]/3
= [(19+2A) + 9]/3
= [2A + 28]/3

3M = 2A+28 ----(1)

(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?"
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06 Sep 2004, 17:50
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.
06 Sep 2004, 17:50
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