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

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.

Explanation:

The median being zero gives \[\frac{b+c}{2}=0\], hence \[b=-c\].

The mean being zero gives \[a+b+c+d=0\].

Since \[b+c=0\], this becomes \[a+d=0\], so \[a=-d\].