If (v+w)/4, (w+x)/4, (x+y)/4 and (y+z)/4 are consecutive positive integers such that v
There are few options:
x^2
x^2-1
x^2-2
x^2+2
x^2-4
When I do it, I get a difference of 50 between (w*y) and (x^2), which doesn't correspond to any of the answer choices. Help?!
There are few options:
x^2
x^2-1
x^2-2
x^2+2
x^2-4
When I do it, I get a difference of 50 between (w*y) and (x^2), which doesn't correspond to any of the answer choices. Help?!
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My apologies if this is a bit hand-wavy, but I'm not too sure about my answer (x^2 - 4).
Since I know that (v + w)/4 and so on are consecutive integers, I can find some relationships between the variables as follows:
(v + w)/4 + 1 = (w + x)/4
v + w + 4 = w + x
v + 4 = x
Thus, I found that v + 4 = x, w + 4 = y, and x + 4 = z.
The difficult part is trying to find the relationships between variables 'adjacent' to each other (v and w, for example).
What I did was I assumed that v + 2 = w, w + 2 = x, and so on. To check to see if it made sense, I substituted v into every expression given, and found that they looked like:
(1/2)v + 1/2
(1/2)v + 3/2
(1/2)v + 5/2
(1/2)v + 7/2
As you can see, they all differ by 1. With this in mind, I just did some substitution as follows:
w * y = (x - 2) * (x + 2) = x^2 - 4
Since I know that (v + w)/4 and so on are consecutive integers, I can find some relationships between the variables as follows:
(v + w)/4 + 1 = (w + x)/4
v + w + 4 = w + x
v + 4 = x
Thus, I found that v + 4 = x, w + 4 = y, and x + 4 = z.
The difficult part is trying to find the relationships between variables 'adjacent' to each other (v and w, for example).
What I did was I assumed that v + 2 = w, w + 2 = x, and so on. To check to see if it made sense, I substituted v into every expression given, and found that they looked like:
(1/2)v + 1/2
(1/2)v + 3/2
(1/2)v + 5/2
(1/2)v + 7/2
As you can see, they all differ by 1. With this in mind, I just did some substitution as follows:
w * y = (x - 2) * (x + 2) = x^2 - 4