Question

Given that a, b, c, d are non-zero integers such that a < b < c < d. If the mean and median of a, b, c, d are equal to zero, then a = ________ and b = ________.

Answer 1

Mean of a, b, c, d $=\frac{a+b+c+d}{4}$
$$\begin{gathered} \therefore \frac{a+b+c+d}{4}=0\left(\mathrm{Given}\right) \\ \Rightarrow a+b+c+d=0.....\left(1\right) \end{gathered}$$

Now,

Median of a, b, c, d = Mean of 2nd observation and 3rd observation $=\frac{b+c}{2}$
$$\begin{gathered} \therefore \frac{b+c}{2}=0\left(\mathrm{Given}\right) \\ \Rightarrow b+c=0.....\left(2\right) \end{gathered}$$

From (1) and (2), we get

$a+d=0\Rightarrow a=-d$

Also, $b+c=0\Rightarrow b=-c$

Given that a, b, c, d are non-zero integers such that a < b < c < d. If the mean and median of a, b, c, d are equal to zero, then a = ___−d___ and b = ___−c___.