In a list of seven
integers, one integer denoted as x is unknown. The other six integers are 20,4,10,4,8
and 4. If the mean, median and mode of these 7 integers are arranged in increasing
order, they form an arithmetic progression. The sum of all possible values of x
is:

(1)26 (2) 32
(3) 34 (4) 38 (5) 40

For Answer Click on
"Read more" below:

**Solution:**
Arranging the given six
integers in increasing order:

4,4,4,8,10,20

Irrespective of the value
of x, the number of occurrences being three, 4 is the mode.

**Mode = 4**;

**Mean**= (4+4+4+8+10+20+x)/7 =

**(50+x)/7**

Here three cases arise:

**Case-I**If x≤4, median = 4

**Case-II**If 4

**Case-III**If x>8, median = 8

__Case-I:__
x≤4; Median = 4;

Given that mean, median
and mode arranged in ascending are in AP

Since mode=median=4,
ascending order is not possible here and hence this case is excluded.

**Case-II:**

4

4 possible values
for x are 5,6,7 and 8

But, Mean which is (50+x)/7
is integer only for x=6

=>

**x = 6**

__Case-III:__
x>8; Median = 8;

x>8 => (50+x)/7 >
8

Hence 4, 8, (50+x)/7 are in AP
=> 8 - 4 = (50+x)/7 - 8 => 4 = (50+x-56)/7

=> 28 = x-6 =>

**x = 34**
In all the cases, the
possible values of x are 6 and 34

Sum of possible values of
x = 6+34 =

**40****Answer (5)**
## No comments:

## Post a Comment