Question

If 12, 16, 18, x + 2, x + 4, 45, 48, 52 are arranged in ascending order and their median is 31, find the value of x.

Answer 1

Given: 12, 16, 18, x + 2, x + 4, 45, 48, 52 are in ascending order and median = 31.

Step-wise calculation:

1. There are 8 numbers, so the median is the average of the 4th and 5th terms `n/2`th and `(n/2 + 1)`th.

2. 4th term = x + 2 and 5th term = x + 4. 

So median = `[(x + 2) + (x + 4)]/2`

= `(2x + 6)/2`

= x + 3

3. Set x + 3 = 31

x = 28

4. Check order: x + 2 = 30 and x + 4 = 32, which lie between 18 and 45, so the given ascending order is valid.