Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 03:18

### 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

# K is a data set containing five real numbers. If A is the arithmetic

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Feb 2017
Posts: 164
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

### Show Tags

07 Aug 2018, 10:22
3
00:00

Difficulty:

(N/A)

Question Stats:

43% (02:13) correct 57% (02:26) wrong based on 65 sessions

### HideShow timer Statistics

K is a data set containing five real numbers. If A is the arithmetic mean of K, and B is the median of K, is |A − B| ≤ 2?
1) The range of K is 4
2) The elements of K are distinct positive integers

_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than \$)
Manager
Joined: 29 Sep 2017
Posts: 117
Location: United States
Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

### Show Tags

07 Aug 2018, 21:04
1
Plug and play. Try random digits:

1, 2, 3, 4, 5. Mean = median = 3.
1, 1, 1. 4. 5. Mean = 12/5. Median = 1.

In both cases, the magnitude between A and B is ≤ 2. A is sufficient.

Can reject B as it says distinct and second example above proves it is not necessary.
_________________
If this helped, please give kudos!
Manager
Joined: 10 May 2018
Posts: 123
Concentration: Finance, Sustainability
Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

### Show Tags

07 Aug 2018, 21:40
1
Here is my take on this question:

By asking this |A − B| ≤ 2? the question is actually asking whether the mean and the median differ by at most 2?

Statement 1
If the set K is spread across just 4 numbers the values of mean and median would lie between these four numbers. Hence the difference between the two would never be more than 2 or -2 (depending on which one of them is greater, this is why the question had a modulus in it, I think). Sufficient to answer the question.

Statement 2
If the elements are distinct and positive the median and mean may not necesarily be close to each other. Not everytime at least. Not sufficient.

Raksat wrote:
K is a data set containing five real numbers. If A is the arithmetic mean of K, and B is the median of K, is |A − B| ≤ 2?
1) The range of K is 4
2) The elements of K are distinct positive integers

_________________
Stuck in the 600-700 score bracket? I welcome you to read my four-step course of action to a modest score.
I also invite you to critique and help me find flaws in my modus operandi. Thanks!
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

### Show Tags

07 Aug 2018, 22:27
1
Raksat wrote:
K is a data set containing five real numbers. If A is the arithmetic mean of K, and B is the median of K, is |A − B| ≤ 2?
1) The range of K is 4
2) The elements of K are distinct positive integers

|A − B| ≤ 2 means the difference between the mean and median is NOT greater than 2.

1) The range of K is 4
what can be the max difference between the two when median is least possible
so let the least number and also the median be x, so numbers will be x,x,x,x+5,x+5.
the two largest are x+5 so that the SUM and thus the average is largest
so
a) Median = x
b) average = $$\frac{x+x+x+x+5+x+5}{5}=\frac{5x+10}{5}=x+2$$
difference = (x+2)-(x)=2
thus ans is YEs
sufficient

2) The elements of K are distinct positive integers
1,2,3,100,101..... ans NO
1,2,3,4,5........ ans YES
Insuff

A
_________________
Intern
Joined: 04 Jun 2010
Posts: 40
Location: India
GPA: 3.22
Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

### Show Tags

10 Jul 2019, 03:16
chetan2u wrote:
Raksat wrote:
K is a data set containing five real numbers. If A is the arithmetic mean of K, and B is the median of K, is |A − B| ≤ 2?
1) The range of K is 4
2) The elements of K are distinct positive integers

|A − B| ≤ 2 means the difference between the mean and median is NOT greater than 2.

1) The range of K is 4
what can be the max difference between the two when median is least possible
so let the least number and also the median be x, so numbers will be x,x,x,x+5,x+5.
the two largest are x+5 so that the SUM and thus the average is largest
so
a) Median = x
b) average = $$\frac{x+x+x+x+5+x+5}{5}=\frac{5x+10}{5}=x+2$$
difference = (x+2)-(x)=2
thus ans is YEs
sufficient

2) The elements of K are distinct positive integers
1,2,3,100,101..... ans NO
1,2,3,4,5........ ans YES
Insuff

A

but sir range of K is 4...............how can the largest numbers be x+5?? it should be x+4
Re: K is a data set containing five real numbers. If A is the arithmetic   [#permalink] 10 Jul 2019, 03:16
Display posts from previous: Sort by