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mean, mode and median

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by sana.noor » Fri Oct 25, 2013 9:43 am
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 is x

OA is C
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Source: — Data Sufficiency |

by theCodeToGMAT » Fri Oct 25, 2013 10:02 am
Sania, wrong section... You may flag to move to correct forum

Thanks!
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by theCodeToGMAT » Fri Oct 25, 2013 10:15 am
Mode = x

To find: Median - Mode

Statement 1:
Difference is less than "3"
Sets can be
x,x,x,x,x+1,x+1,x+1 ==> (x) - (x) = 0
Or,
x,x,x,x+1,x+1,x+2,x+2 ==> (x+1) - (x) = 1
INSUFFICIENT

Statement 2:
Average = x
x-1, x,x,x,x, x+1 ==> (x) - (x) = 0
x-4,x-3,x-2,x-1,x,x,x+10 ==> (x-1) - x = -1
INSUFFICIENT


Combining...

- - - - x - - - - -
The Left and Right side of "x" will have difference of max 2 and the average must be "x" .. that means LHS & RHS will be equal as "x" is integer.

So,
x-1,x,x,x,x+1 ==> (X) - (X) = 0

Answer {C}
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