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01 Jul 2014, 04:06
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
42% (01:47) correct
58%
(02:03)
wrong
based on 101
sessions
History
Date
Time
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Not Attempted Yet
If x and y are non-zero integers, is x = y ?
(1) (x-25)^2 = (y-25)^2
(2) x/y = y/x
I have been told that \((x-25)^2\) = \((y-25)^2\) is the same as (x-25) = (y-25)
In my defence, if I think \(x^2\) = \(y^2\) is the same as x=y , isn't thinking \(9^2\) = \(5^2\) the same thing?
(1) (x-25)^2 = (y-25)^2
(2) x/y = y/x
I have been told that \((x-25)^2\) = \((y-25)^2\) is the same as (x-25) = (y-25)
In my defence, if I think \(x^2\) = \(y^2\) is the same as x=y , isn't thinking \(9^2\) = \(5^2\) the same thing?
01 Jul 2014, 04:42
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iaratul
No, that's not correct. \(x^2=y^2\) means that \(|x|=|y|\), so \(x=y\) or \(x=-y\). For example, \((5)^2 = (5)^2\) as well as \((5)^2 = (-5)^2\).
If x and y are non-zero integers, is x = y ?
(1) (x-25)^2 = (y-25)^2 --> \(|x-25|=|y-25|\) --> \(x-25=y-25\) or \(x-25=-(y-25)\) --> \(x=y\) or \(x+y=50\) (for example x=20 and y=30). Not sufficient.
(2) x/y = y/x --> \(x^2=y^2\) --> \(x=y\) or \(x=-y\) (x+y=0). Not sufficient.
(1)+(2) From above it must be true that \(x=y\). Sufficient.
Answer: C.
Hope it's clear.
01 Jul 2014, 05:54
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Bunuel
Since I'm still learning the basics, I just want to clarify this part. Are you deriving the conclusion: \(|x|=|y|\), so \(x=y\) or \(x=-y\) from this (breaking it down):
|x| = |y| can have four solutions ==>
1. x = y
2. -x = -y
3. -x = y
4. x = -y
1 and 2 are the same, 3 and 4 are also the same - is that how you derived to the above-mentioned conclusion?
