30. 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 with the information given
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Whats the Mean
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scoobydooby
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B?
let the numbers be x,9,x+19
if mean: 10, sum of the 3 numbers: 30
or 28+2x=30,solving we get x=1 or the numbers are 1,9,20
all other choices give negative numbers for x, but it is given that all numbers are positive, only B works
let the numbers be x,9,x+19
if mean: 10, sum of the 3 numbers: 30
or 28+2x=30,solving we get x=1 or the numbers are 1,9,20
all other choices give negative numbers for x, but it is given that all numbers are positive, only B works
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rohangupta83
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I go with E as well
it could be anything from 9.3 - 15.3
when median is 9
range is 19
and all 3 integers are positive
(X+9+Y)/3 = Z
Y-X = 19
3 unknowns, 2 equations - info. not enough
it could be anything from 9.3 - 15.3
when median is 9
range is 19
and all 3 integers are positive
(X+9+Y)/3 = Z
Y-X = 19
3 unknowns, 2 equations - info. not enough
X,9,Ygmatrant wrote:30. 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 with the information given
Y-X =19
X+Y+9 = 3Z WHAT IS Z
Y-X = 19
X+Y = 3Z-9
2Y = 3Z+10
Y =3/2Z +5
USING ANSWER CHOICES THE MEAN HAS TO BE EVEN INTIGER
A OR B
PLUG IN
IF Z = 10 , X = 1, Y = 20
1,9,20...
IF Z = 22
19,9,38...........POSSIBLE 2
I DONT KNOW BUT LOOKS LIKE 22,10 CAN BE???????
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rohangupta83
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stop -stop@800 wrote:the question says "given a certain mean" largest range is 19
and we need to find this mean
It does not say that if range is 19
what is the largest mean.
Answer has to be B.
Nothing else
assuming that the range is 2
our numbers could be 8,9and 10
with mean being - 9
or if we're looking for the largest then 9,9,11
mean - 29/3
it's still less than 10 when range is 2.
Maybe I am misunderstanding the question....
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rohangupta83
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and how would i find the mean when the max range is 2 for example and median of three numbers is 9?
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KeyserSoze525
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You have the set B {x,9,y} where all elements are positive integers.30. 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 with the information given
We know x < 9 < y because if this were not true, 9 wouldn't be the median.
Now, the smallest possible value for x is 1, because 0 is not positive or negative. So the smallest possible value for y is then 1+19= 20.
The mean would then be:
(x+9+y)/3 =
(1+9+20)/3 =
30/3 = 10
10 is the minimum mean. So we can eliminate C and D because they are too low.
But wait, what's the largest possible value for x? That would be 9-1 = 8 and the largest possible value for y would then be 8+19 = 27.
Doing the math gives a mean of (8+9+27)/3 = 14 2/3. Since that is also the maximum mean, A (22) is eliminated because it's too high.
So we're left with B (10) and E (cannot be determined). The question contains the words "given a certain mean." The confusion is surrounding the word "certain" because people often think the word means unspecified. However, the word certain actually means:
i)definite but not specified or identified
or
ii)established beyond doubt or question; definitely known
Since the mean is definitely known, then it essentially translates into "the mean can be determined from the information in the question stem." E can be eliminated.
Finally, the correct answer is B.
KeyserSoze525 wrote:I disagree.We know x < 9 < y because if this were not true, 9 wouldn't be the median.
Now, the smallest possible value for x is 1, because 0 is not positive or negative. So the smallest possible value for y is then 1+19= 20.
The problem says that set B has 3 positive integers (it doesn't say they are 3 distinct positive integers; can be 9,9 and 9) and the largest possible range of the three numbers is 19 (it doesn't say the range is 19; the range can be minimum 0 and maximum 19).
Answer (B) can fit the bill.
But also (D) can do that.
8,9 and 10
the median is 9, the range is 2 and the mean is 9.
We have two choices that answer the question.
I go with (E) It cannot be determined with the information given.
