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The mode of a set of integers is x. what is the difference b

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The mode of a set of integers is x. what is the difference b

by BTGmoderatorAT » Mon Dec 25, 2017 2:56 pm
The mode of a set of integers is x. what is the difference between the median of this set of integers and x?

(1) The difference between any two integers in the set is less than 3.
(2) The average of the set of integers s x.

What's the best way to determine whether statement 1 is sufficient? Can any experts help?
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Jan 15, 2018 10:08 pm
ardz24 wrote:The mode of a set of integers is x. what is the difference between the median of this set of integers and x?

(1) The difference between any two integers in the set is less than 3.
(2) The average of the set of integers s x.

What's the best way to determine whether statement 1 is sufficient? Can any experts help?
Statement 1 is not sufficient; pl. see the follwoing three cases.

Case 1: Say the set is {x, x, (x + 2)}; We have Mode = Median = x . The difference between the median of this set of integers and x = x - x = 0.

Case 2: Say the set is {x, x, (x + 1), (x + 2)}; We have Mode = x but Median = [x + (x + 1)]/2 = x + 0.5 . The difference between the median of this set of integers and x = x + 0.5 - x = 0.5. No unique answer. Insufficient.

Let's see another case for the sake of understanding.

Case 3: Say the set is {x - 1, x, x, (x + 1)}; We have Mode = Median = x . The difference between the median of this set of integers and x = x - x = 0.

Hope this helps!

-Jay
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