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by arjunshn » Fri Apr 22, 2011 12:53 am
A List of positive integers is arranged in ascending order such that the 19th number in the series represents the median of the series. If the sum of all the numbers in the series is 222, what is the average of the given list?
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by force5 » Fri Apr 22, 2011 1:25 am
if 19th number is the median then total numbers are 37

hence average is sum of the numbers/total numbers

= 222/37 = 6

answer should be 6
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by Brent@GMATPrepNow » Fri Apr 22, 2011 5:11 am
arjunshn wrote:A List of positive integers is arranged in ascending order such that the 19th number in the series represents the median of the series. If the sum of all the numbers in the series is 222, what is the average of the given list?
As it stands, this question is missing an important piece of information.
I think we need to state that all of the numbers are different, or state that the 19th number is unique.
Here's why:
Given the information, there could 21 numbers altogether. Let's say the first 20 numbers are 1 and the last number is 202 (e.g., 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,202)
Here the 19th number is 1 and this is the median. For this set, the mean (average) is 222/21

Conversely, there could 23 numbers altogether. The first 22 numbers can be 1, and the last number can be 200 (e.g., 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,200)
Here the 19th number is 1 and this is the median. For this set, the mean (average) is 222/23
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by force5 » Fri Apr 22, 2011 5:31 am
actually the question was falling apart if i didnt consider that 19th value was unique since the poster has not given answer choices nor any other information was given.
You are correct Brent.
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by Ian Stewart » Fri Apr 22, 2011 10:34 am
Brent@GMATPrepNow wrote:
arjunshn wrote:A List of positive integers is arranged in ascending order such that the 19th number in the series represents the median of the series. If the sum of all the numbers in the series is 222, what is the average of the given list?
As it stands, this question is missing an important piece of information.
I think we need to state that all of the numbers are different, or state that the 19th number is unique.
Yes, not only does the question need to make clear that the numbers are distinct, it also misuses terminology. A 'series' in mathematics is a sum; it is not the same thing as a 'list' or a 'sequence', and it doesn't have a median. I'd be concerned about studying other questions from the same source if the author is that careless about language - where is the question from?
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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