Question

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

Answer 1

The statement is always true

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.