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07 Aug 2018, 10:22
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Difficulty:
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Question Stats:
47% (02:33) correct
53%
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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
1) The range of K is 4
2) The elements of K are distinct positive integers
07 Aug 2018, 21:04
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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.
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.
07 Aug 2018, 21:40
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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.
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
