Consecutive QRS

[PFWinkler]

PS: If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s2 – r2 – q2?

Instead of setting up the following:

s2– (s –2)2 – (s – 4)2 =
s2– (s2 – 4s + 4) – (s2 – 8s + 16) =
s2– s2 + 4s – 4 – s2 + 8s – 16 =
-s2 + 12s – 20

And then testing out the various answer choices to see what factors and what doesn't, why can't we just pick smart numbers here:

S = 8, R = 6, Q = 4.

s2 - r2 - q2 = 2, which is the even integer spread - thus we know the that 8 would be incorrect...?

Source: Question Bank - Algebra - MGMAT (First Problem)

[PFWinkler]

Ummm....then again....

doesn't s2– s2 + 4s – 4 – s2 + 8s – 16 = simplify to just: -s2 + 4s -12??! Answer key might be wrong? what am I missing?

[RonPurewal]

Ummm....then again....

doesn't s2– s2 + 4s – 4 – s2 + 8s – 16 = simplify to just: -s2 + 4s -12??! Answer key might be wrong? what am I missing?

no.

4 + 8 = 12, so 4s + 8s = 12s.
and, –4 – 16 = –20.
so, the expression simplifies to s^2 + 12s – 20.

[RonPurewal]

And then testing out the various answer choices to see what factors and what doesn't, why can't we just pick smart numbers here:

S = 8, R = 6, Q = 4.

the question is "which CANNOT work?"
think about that question with ordinary common sense-- you can't solve it by testing only one thing. if you're going to use "smart numbers" here, you need to keep testing different numbers until you've found 4 answer choices that CAN work, thus eliminating those 4 choices.

s2 - r2 - q2 = 2, which is the even integer spread - thus we know the that 8 would be incorrect...?

^^ sorry, i'm not following this.