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by Brent@GMATPrepNow » Wed Jul 28, 2010 8:06 am
t4nothing wrote:If (x-1).(x-1)=400 then x-5 = ?
A) 15 B) 14 C) -24 D) -25 E) -26

What is the rapid way to solve this problem?
Given: (x-1)(x-1)=400
If (something)(something) =400 then something = 20 or -20

So x-1 = 20 or x-1 = -20

case 1: x-1=20 --> x=21 --> x-5=16 (not one of the answer choices)
case 2: x-1=-20 --> x=-19 --> x-5=-24 --> choose C

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by aleph777 » Wed Jul 28, 2010 8:10 am
I thought I had a quick solution...

Since there's only one variable, x, that means it's a number times itself.

20^2 = 400.

x - 1 = 20
x = 21

So you plug that into the second equation:

21 - 5 = 16...

But that's not one of the answers. So now I'm at a loss, too!
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by selango » Wed Jul 28, 2010 8:55 am
aleph777 wrote:I thought I had a quick solution...

Since there's only one variable, x, that means it's a number times itself.

20^2 = 400.

x - 1 = 20
x = 21

So you plug that into the second equation:

21 - 5 = 16...

But that's not one of the answers. So now I'm at a loss, too!
It is 20 or -20.[Note whenever x is an perfect square,its roots are a or -a]

(-20)^2 = 400.

x - 1 = -20
x = -19

-19-5=-24

C
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