If set S consists of even number of integers, is the median of set S negative?
(1) Exactly half of all elements of set S are positive
(2) The largest negative element of set S is -1
please elaborate the answer ..
OA C
tough statistics question
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Sat Feb 23, 2013 12:12 pm
- Thanked: 5 times
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
Statement 1: Exactly half of all the elements of set S are positive.gmatquant25 wrote:If set S consists of even number of integers, is the median of set S negative?
(1) Exactly half of all elements of set S are positive
(2) The largest negative element of set S is -1
Hence, the rest of all the elements are either all negative or some negative and some zeroes or all zeroes. Consider the following cases,
- {-2, -2, 1, 2} --> Median = (-2 + 1)/2 = -0.5 --> Negative
{-2, -1, 1, 2} --> Median = (-1 + 1)/2 = 0 --> Not negative
Statement 2: This means -1 is a element of the S. But from this we cannot determine whether the median is negative or not.
Not sufficient
1 & 2 Together: As we know that exactly half of the elements of S are positive and S has even number of elements, the median of S will be (smallest positive element + the integer just smaller than the smallest positive element)/2.
Now, smallest positive integer that can be in S is 1.
And, the integer just smaller than the smallest positive element of S is either 0 or -1.
Hence, the smallest value of the median is (1 - 1)/2 = 0
So, the median is always non-negative.
Sufficient
The correct answer is C.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
-
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Tue Apr 16, 2013 10:57 am
- Location: New York
- Thanked: 2 times
- GMAT Score:770
First, we know we have an even number of integers, so the median wil be the AVERAGE of the two middle terms.
Looking at 1) we know that half are positive, so half must be negative or 0. To know if the median is negative, we need to know which integer that goes into the median "weighs more", or is further from 0. Whichever term is furthest from 0 will "pull" the sign of the median in that direction.
Since we don't know anything about either of the two middle terms, 1) is therefore not sufficient.
Examining 2) we are provided a single element of the set with no context, so we can't know if -1 is in the middle, or on one of the ends of the set. Again, insufficient.
Putting them together, we know that the median is the average of -1 (the highest negative) and some x (the lowest positive). Referring back, we still need the distance from 0 of the positive term in order to figure out the sign. So our answer is E.
Ben
[email protected]
Looking at 1) we know that half are positive, so half must be negative or 0. To know if the median is negative, we need to know which integer that goes into the median "weighs more", or is further from 0. Whichever term is furthest from 0 will "pull" the sign of the median in that direction.
Since we don't know anything about either of the two middle terms, 1) is therefore not sufficient.
Examining 2) we are provided a single element of the set with no context, so we can't know if -1 is in the middle, or on one of the ends of the set. Again, insufficient.
Putting them together, we know that the median is the average of -1 (the highest negative) and some x (the lowest positive). Referring back, we still need the distance from 0 of the positive term in order to figure out the sign. So our answer is E.
Ben
[email protected]
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
Hi Ben,BenMiller wrote:Putting them together, we know that the median is the average of -1 (the highest negative) and some x (the lowest positive). Referring back, we still need the distance from 0 of the positive term in order to figure out the sign. So our answer is E.
First of all, the median need not be average of -1 and the lowest positive integer. It can very well be average of 0 and the lowest positive integer. But for the minimum possible median, it will average of -1 and the lowest positive integer.
And we do not need to know the lowest positive.
Even if we make the lowest positive element as small as possible, it'll be 1 (as all the elements are integers), and the smallest median in that case will be (-1 + 1)/2 = 0, which is a non-negative.
Hence, we can conclude that median will be always non-negative.
However, your solution would have been perfect if it was not mentioned that all the elements are integers.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
- mariofelixpasku
- Senior | Next Rank: 100 Posts
- Posts: 41
- Joined: Sun Sep 23, 2012 4:26 am
- Thanked: 2 times
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
Experts please suggest
If 0 is positive int ( As shoown in ans (-1 + 1)/2 = 0 +ve) then median could be -ve
of series -2,-1,0,1
-1 + 0 / 2 = -1/2
If 0 is positive int ( As shoown in ans (-1 + 1)/2 = 0 +ve) then median could be -ve
of series -2,-1,0,1
-1 + 0 / 2 = -1/2
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
0 is neither positive nor negative.vipulgoyal wrote:If 0 is positive int ( As shoown in ans (-1 + 1)/2 = 0 +ve) then median could be -ve
of series -2,-1,0,1
-1 + 0 / 2 = -1/2
I've written : '{-2, -1, 1, 2} --> Median = (-1 + 1)/2 = 0 --> Not negative'
That doesn't mean it is positive.
Hope that helps.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §