Question

If p, q, r, and s are consecutive even integers such that p < q < r < s, then how much greater is s - p than r - q ?

Answer 1

Answer:

Whenever you assume values, try and make them as accurate as possible i.e. I am looking for consecutive even numbers so I will assume the values to be (2n - 2), 2n and (2n + 2)

s2−r2−q2=(2n+2)2−(2n)2−(2n−2)2s2−r2−q2=(2n+2)2−(2n)2−(2n−2)2

You get: 4n (4 - n)

So the solution must have 4 as a factor, which we see all options do.

To get -20, n(4-n) must be (-5). It will happen when n = 5.

To get 0, n = 0

To get 12, n(4-n) must be 3. It will happen when n = 3

To get 16, n(4-n) must be 4. It will happen when n = 2

There is no way n(4-n) could be 2 if n is an integer so 8 is not possible.Step-by-step explanation: