**When the mean, median and mode of the list 10,2,4,2,5,2,and x are arranged in increasing order, they form a non-constant arithmetic progression. FInd the sum of all such real x?**

**A) 3 B) 6 C) 9 D) 17 E) 20**

**Source : AMC 12**

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Nice one.

Now the mode is 2 is quite evident.

Median depends on the value of x that is if 2<x4 then 4 is the median.

Mean = (25+x)/7

So now consider 2<x4, then 4 is the median so the mean should be 6. So x=17

So the sum of values is 17+3=20

Celebrating LifeOctober 2, 2008 at 4:20 pm

Typo

Median is x if 2<x4

Celebrating LifeOctober 2, 2008 at 4:21 pm

hmm I thought its a typo but it’s not getting typed at all..regarding median,

If x lies b/w 2 and 4, then median is x and if x is greater than 4 the median is 4.

Celebrating LifeOctober 2, 2008 at 4:22 pm

Option E

17 +3 = 20

mode=2

If x is the median

2,2,2,x,4,5,10

value of x comes to be three

When x considered to be greater than 4 , its value 17. As mode , median ,mean are in A.p. x cannot be placed in first 4 places as that would make mode and median equal.

tyroOctober 2, 2008 at 5:03 pm

x cannot be placed before 2 in the first 4 places when arranged in an increasing order and cannot be equal to 2.

tyroOctober 2, 2008 at 5:05 pm