Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46305

What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
13 Mar 2016, 09:24
Question Stats:
41% (01:51) correct 59% (01:12) wrong based on 69 sessions
HideShow timer Statistics



Intern
Joined: 29 Mar 2015
Posts: 15
Location: India
GPA: 3.23
WE: Information Technology (Computer Software)

Re: What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
13 Mar 2016, 16:10
From the questions part, all I could conclude is that : Irrespective of the value of 'a', the median of this list will be one value among 22, 23, 24, 25 and 26. (1) The mean of the 5 integers is equal to the median of the 5 integers. The mean and median of the list are : 98 +a/5. Since a is an integer, 98+a should be divisible by 5. Only 22 satisfies that condition. Hence 98+a/5 = 22. This gives us the value of a as 12. Hence 1 is SUFFICIENT, as my list comes out to be 12, 20, 22, 26 and 30 and 22 is my median and mean. (2) The range of the 5 integers is greater than a. a can not be between 20 and 30 and greater than 30, because then the range will be less than a, hence it has to be less than 20, infact it has to be less than 15, irrespective of that the median will be 22. SUFFICIENT. As both 1) and 2) are SUFFICIENT, the answer should be D. I am sure it will sound complicated and I might have made a mistake somewhere. Please correct me, if I am wrong !
_________________
Thanks,
Akki



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
13 Mar 2016, 16:23
akxshay wrote: From the questions part, all I could conclude is that :
Irrespective of the value of 'a', the median of this list will be one value among 22, 23, 24, 25 and 26.
(1) The mean of the 5 integers is equal to the median of the 5 integers.
The mean and median of the list are : 98 +a/5. Since a is an integer, 98+a should be divisible by 5. Only 22 satisfies that condition. Hence 98+a/5 = 22. This gives us the value of a as 12.
Hence 1 is SUFFICIENT, as my list comes out to be 12, 20, 22, 26 and 30 and 22 is my median and mean. (2) The range of the 5 integers is greater than a.
a can not be between 20 and 30 and greater than 30, because then the range will be less than a, hence it has to be less than 20, infact it has to be less than 15, irrespective of that the median will be 22.
SUFFICIENT.
As both 1) and 2) are SUFFICIENT, the answer should be D.
I am sure it will sound complicated and I might have made a mistake somewhere. Please correct me, if I am wrong ! Your analysis of statement 1 is not correct. The median of 5 terms is NOT = average in general but only in particular cases. What if the values are 20,a,22,26,30 in this case, median = 22 and mean = (98+5)/a but if the values are 20,22,26,30, a , the median = 26 and mean = (98+a)/5. Thus you get 2 different medians for the same statement and hence this statement is NOT sufficient. Additionally, since a is an integer, it is NOT necessary that (98+a)/5 must be an integer. The main question stem only mentions that 'a' is an integer and nothing about the nature of the mean. You are assuming something that the question wants you to prove. This is a dangerous way of tackling DS questions. Hope this helps.



Intern
Joined: 29 Mar 2015
Posts: 15
Location: India
GPA: 3.23
WE: Information Technology (Computer Software)

Re: What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
13 Mar 2016, 16:34
Engr2012 wrote: What if the values are 20,a,22,26,30 in this case, median = 22 and mean = (98+5)/a but if the values are 20,22,26,30, a , the median = 26 and mean = (98+a)/5. Thus you get 2 different medians for the same statement and hence this statement is NOT sufficient. True ! Got my mistake. Thanks !
_________________
Thanks,
Akki



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
15 Mar 2016, 00:24
Bunuel wrote: What is the median of five integers 20, 22, 26, 30 and a?
(1) The mean of the 5 integers is equal to the median of the 5 integers. (2) The range of the 5 integers is greater than a. Good Question! Let's place the numbers on the number line: _______________________20 __ 22 ____ 26 ____ 30 ______________ and a The median of 5 numbers will be the middle number. So median could be 22 or 26 or a, depending on the value of a. (1) The mean of the 5 integers is equal to the median of the 5 integers. The mean and median could be 22 such that a = 12 The mean and median could be 26 such that a = 32 So we see that already we do not have a unique median. Not Sufficient (2) The range of the 5 integers is greater than a. The range of the given four integers is 30  20 = 10. If range is greater than a, a must be less than 10. But in that case, the range will increase to 30  a. Hence the range will not be 10. a is either less than 20 or more than 30 (to get a greater range). But if a > 30, Range = a  20. Range cannot be more than 'a' since it is 20 less than a. So a must be less than 20 and median must be 22. This is possible as we saw in the analysis of statement 1. Sufficient. Answer (B)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



NonHuman User
Joined: 09 Sep 2013
Posts: 7053

Re: What is the median of five integers 20, 22, 26, 30 and a? [#permalink]
Show Tags
19 Sep 2017, 23:56
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the median of five integers 20, 22, 26, 30 and a?
[#permalink]
19 Sep 2017, 23:56






