Which is correct regarding the statement: "fx is an odd Integer, then the median of x, X + 2, X + 6, and x + 10 is an odd number"

the statement is always true

there is not enough information provided to answer the question

the statement is always false

the statement is sometimes true

The statement is always true

Step-by-step explanation:

We have,

x, x+2, x+6, x+10

There are even number of terms. So for the median we add the two middle terms and divide it by 2.

Median = (x+2+x+6) / 2

= (2x+8) / 2

= 2 (x+4) / 2

= x+4

As we know that an odd number is always odd number if we add some even number to it.

In the question, x is an odd integer so, if we add 4 then it would be again an odd integer. Therefore, the median is also an odd integer.

The statement is always true.