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(Gmat) Faster Method needed

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by logitech » Fri Nov 28, 2008 1:03 am
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?


-20
0
8
12
16

OA [spoiler]8[/spoiler]
LGTCH
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Re: (Gmat) Faster Method needed

by sudhir3127 » Fri Nov 28, 2008 4:46 am
logitech wrote: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?


-20
0
8
12
16

OA [spoiler]8[/spoiler]
correct me if i am wrong .. but i think the question shud read as
S^2- r^2-q^2...

i think plugging in would be the only approach .. though u can form a quadratic equation as well ..

first approach ..

with q=-2, r=0, and s=2. Plugging that in to the given equation gives us 0

q=2, r=4, s=6 gives us 16

q=-4, r=-2, s=0 gives us -20

i mean u can stop @ this because if see. we have gone from 0 to 12 and missed 8 . so it shud be 8.

second appraoch .

let the 3 numbers ve X, X+2 , X+4

(x+4)^2 - (x+2)^2 - x^2
= x^2 + 8x + 16 - x^2 - 4x - 4 - x^2
= -x^2 + 4x + 12

on C doesnt hold good..

hope that helps...
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by anayeri » Fri Nov 28, 2008 10:54 am
I don't get the equation method. I understand how you got as far as you did. I would even got a step further, and say that:

=-x^2+4x_12
=-(x-6)(x+2)

but so what? what do I do with that information?
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by logitech » Fri Nov 28, 2008 1:45 pm
anayeri wrote:I don't get the equation method. I understand how you got as far as you did. I would even got a step further, and say that:

=-x^2+4x-12
=-(x-6)(x+2)

but so what? what do I do with that information?
and you try the answer choices: -20,0,8,12,16

For example:

-x^2+4x-12 = 8
LGTCH
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