We also could have approached this question by trial and error - certainly not as elegant a method as the one shown by netigen, but one that we need to be familiar with on test day for those questions for which we don't see the elegant solution.
If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?
It's a which of the following CANNOT question, so there's no way to predict an exact answer. However, let's look at the choices:
1. -20
2. 0
3. 8
4. 12
5. 16
None of the answers are very big. Therefore, we know that the values of q, r and s can't be too large. So, let's work with some small numbers and see which answers we can eliminate.
When we pick #s, we have to follow the rules. So, we need 3 consecutive even integers. The first 3 that likely come to mind are 2, 4 and 6.
S is the biggest of the 3, so when we plug in we get:
36 - 16 - 4 = 36-20 = 16.. eliminate (5).
At this point we notice that we just hit the biggest of the answer choices. If we pick bigger values for q, r and s the answer is just going to get bigger, so let's focus on smaller values.
Next up?: 0, 2 and 4
16 - 4 - 0 = 12... eliminate (4)
-2, 0 and 2
4 - 0 - 4 = 0... eliminate (2).
-4, -2 and 0
0 - 4 - 16 = -20... eliminate (1)
We've eliminated (1), (2), (4) and (5): pick (3)!
