It is currently 21 Jan 2018, 01:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 310

Kudos [?]: 625 [0], given: 193

Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

28 Sep 2011, 09:12
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:20) correct 41% (01:14) wrong based on 73 sessions

### HideShow timer Statistics

Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2} greater than the median?

(1) The highest number in the set is 6

(2) The lowest number in the set is 2

[Reveal] Spoiler:
is my understanding correct ? 1) possibilities of sets with 6 highest number are [1,2,3,4,6], [1,2,4,5,6], [2,3,4,5,6] ... Thus sufficient.... 2) 2 being the lowest element in set, the possibility of the sets are numerous but Avg will be always greater than Mean. e.g [2,3,4,6,100] or [2,4,5,6,1000] in all cases Avg will greater than Mean, thus sufficient. So answer is D.....

M05-37
[Reveal] Spoiler: OA

_________________

I'm the Dumbest of All !!

Kudos [?]: 625 [0], given: 193

Manager
Joined: 14 Mar 2011
Posts: 196

Kudos [?]: 139 [1], given: 21

Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

28 Sep 2011, 09:34
1
KUDOS
shrive555 wrote:
Is the average of a set of 5 distinct positive integers { a , b , 4, 6, 2} greater than the median?
1. the highest number in the set is 6
2. the lowest number in the set is 2

statement 1 -the highest number in the set is 6

1 possible set can be (1,2,3,4,6) Then avg =3.2 and median 3 , so avg > median .
Another set can be (2,3,4,5,6) then avg =4 and median 4, so avg =median
so statement 1 insufficient.

statement 2 -the lowest number in the set is 2
1possible set can be (2,3,4,5,6) then avg =4 and median 4, so avg =median
Another possible set can be (2,3,4,6,10) avg =6 and median 4 , so avg > median
so statement 2 insufficient.

combining 2 statements, only set possible is (2,3,4,5,6). avg = median. we get a definite answer 'No' average is not greater than median. Answer C.

Kudos [?]: 139 [1], given: 21

Intern
Joined: 05 Sep 2011
Posts: 2

Kudos [?]: 9 [1], given: 0

Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

28 Sep 2011, 09:55
1
KUDOS
Hey, here's how I would answer this question. I'm going to try and write it out as clearly as I can. Minus the explanation this can be solved well within 2 minutes.

1. Highest number in the set is 6

Since they're all integers and distinct, the mean will be highest when a and b equal 3 & 5 (or vice versa, doesn't matter).

=> {2,3,4,5,6}
Mean = 4
Median = 4

Mean will be at its lowest when a & b equal 1 & 3.

=> {1,2,3,4,6}
Mean = 3.2
Median = 3

This is all we need to know to conclude that the first statement is INSUFFICIENT. In the first case the mean is not greater than the median, but in the second case it is.

2. The lowest number in the set is 2

Since the numbers are positive and there is now no upper limit on the integers, it is important to first find the lowest possible value of the mean since adding 300 or any huge number will ensure that the mean is greater than the median.

a & b equal 3 & 5

=> {2,3,4,5,6}
Mean = 4, Median = 4.

Again we have a case where the mean is not greater and one where it is (i.e. adding a huge number to the set). INSUFFICIENT.

Combining the two we know that 2 is the lowest number and 6 is the highest, and from our calculations it is clear that while the mean can equal the median, it CAN NOT be greater.

Kudos [?]: 9 [1], given: 0

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 310

Kudos [?]: 625 [0], given: 193

Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

29 Sep 2011, 09:01
Thanks Guys, i know what i was missing ...
_________________

I'm the Dumbest of All !!

Kudos [?]: 625 [0], given: 193

Current Student
Joined: 28 Nov 2014
Posts: 918

Kudos [?]: 231 [0], given: 79

Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

13 Sep 2016, 03:12
I have a question w.r.t Statement 2. Can we get a 'Yes' case. The cases that I can see in the official solution and the ones that are posted here produce a 'No' in case of Statement 2 (precisely Mean is not greater than Median, and Mean=Median) I cannot locate a case where Mean > Median and I believe that probably can make Statement 2 sufficient.

Bunuel - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

Kudos [?]: 231 [0], given: 79

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139638 [1], given: 12794

Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

13 Sep 2016, 03:59
1
KUDOS
Expert's post
Keats wrote:
I have a question w.r.t Statement 2. Can we get a 'Yes' case. The cases that I can see in the official solution and the ones that are posted here produce a 'No' in case of Statement 2 (precisely Mean is not greater than Median, and Mean=Median) I cannot locate a case where Mean > Median and I believe that probably can make Statement 2 sufficient.

Bunuel - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

The average of {2, 4, 6, 100, 200}, which is ~62, is greater than the median of {2, 4, 6, 100, 200}, which is 6.
_________________

Kudos [?]: 139638 [1], given: 12794

Current Student
Joined: 28 Nov 2014
Posts: 918

Kudos [?]: 231 [0], given: 79

Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]

### Show Tags

13 Sep 2016, 04:56
Thanks Bunuel

Kudos [?]: 231 [0], given: 79

Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2   [#permalink] 13 Sep 2016, 04:56
Display posts from previous: Sort by