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Value of n in the list

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by force5 » Fri Apr 29, 2011 5:03 am
welcome

please hide your answers while posting.

here is my solution

from statement 1 if median is 9 then the value of n has to be 9 (hence suffcient)

the list will become 3,8,9,15,17

statement 2- since the range is 14 largest number can be 22

list will become 3,8,15,17,22 ( hence n = 22)
or 3,3,8,15,17 (n=3)
or 3,n,8,15,17 ( where n can have any value between 3 and 17) range will still be 14
hence insufficient.

therefore choose A

hope it helps
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Apr 29, 2011 5:05 am
goodyear wrote:Hi,

This is my first post. It would be great if anyone can give an explanation to the answer.

Question is

n, 8, 3, 15, 17

What is the value of n in the list above?

(1) The median in the numbers in the list above is 9.
(2) The difference between the greatest number in the list and the least number in the list is 14.

The answer is
Statement(1) ALONE is sufficient, but Statement(2) ALONE is not sufficient.

Thanks!
Statement 1: median = 9.
To determine the median, list the numbers in ascending order: 3,8,15,17 -- and n.
When n is included, there will an odd number of numbers in the list.
Thus, the median will be the middle value.
Since 9 is not already in the list, in order for the median to be 9, n=9 must be the median:
3, 8, n=9, 15, 17.
Sufficient.

Statement 2: Range (the difference between the biggest and the smallest numbers) = 14.
Without n, the biggest value is 17, the smallest 3. Range = 17-3 = 14.
Thus, the range will remain 14 if n is any value between 3 and 17, inclusive.
If n=3, the values will be:
n=3, 3, 8, 15, 17. Biggest-smallest = 17-3 = 14.
If n=10, the values will be:
3, 8, n=10, 15, 17. Biggest-smallest = 17-3 = 14.
Since n can be different values, insufficient.

The correct answer is A.
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