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

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

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New post 07 Aug 2018, 09:22
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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

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Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

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New post 07 Aug 2018, 20:04
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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.
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Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

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New post 07 Aug 2018, 20:40
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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.

Hence Answer should be A.
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

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Re: K is a data set containing five real numbers. If A is the arithmetic  [#permalink]

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New post 07 Aug 2018, 21:27
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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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: K is a data set containing five real numbers. If A is the arithmetic &nbs [#permalink] 07 Aug 2018, 21:27
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