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

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07 Jan 2005, 13:41

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B

C

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E

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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 that mean?

(A) 22

(B) 10

(C) 9.6

(D) 9

(E) It can not be determined from the information given.

Banerjeea, I agree with your calculation which is exactly why I said I would have picked B. However, there are other sets of numbers that will satisfy the condition too but with a different mean.

1) {1,9,20} => Mean = 10 (choice B), Range = 19
2) {4,9,23} => Mean = 12, Range = 19
3) {7,9,26} => Mean = 14, Range = 19

Given that there are other sets why do you pick B as opposed to E?
Or Am I thinking like I would for a Data Sufficiency problem, i.e, if there are more than one solution, it is insufficient?

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 can not be determined from the information given.

The range of mean is 10 to 44/3. the value of the mean in the answer choices in between the range is only 10. therefore the OA is 10. However, E underestimates the acceptability of B as OA.

Plug in your answers here. Don't start with C, because 9.6 is an annoying number to calculate with. Start with (B) instead. If the mean is 10 and the median is 9, what would the largest possible range of the three integers be? To find that, our three integers must fit into the equation (a+b+c)/3 = 10. The median, b, equals 9, so a+c=21. 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.

Plug in your answers here. Don't start with C, because 9.6 is an annoying number to calculate with. Start with (B) instead. If the mean is 10 and the median is 9, what would the largest possible range of the three integers be? To find that, our three integers must fit into the equation (a+b+c)/3 = 10. The median, b, equals 9, so a+c=21. 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.

but there are other sets which satisfies the requirement. why B then?

From the info given, we know mean=(x+9+x+19)/3=(2x+28)/3, where x is the smallest of the three integers.
It's easy to see that when x takes different values mean would be different. So E would definitely be the answer.

However, if the question stem changes to "what could be the mean", then B would be the answer. To solve this we would have to plug in the smallest possible x (x=1) and the biggest x (x=8) to see what the mean is. We then know that the range of the mean is from 10 to 44/3, so only B fits the bill.
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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 that mean?

(A) 22 (B) 10 (C) 9.6 (D) 9 (E) It can not be determined from the information given.