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19 Dec 2019, 02:03
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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:
55%
(hard)
Question Stats:
62% (02:34) correct
38%
(03:02)
wrong
based on 128
sessions
History
Date
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Not Attempted Yet
If x and y are non zero integers and a is a positive integer, is \(|x| = |y|\)?
(1) \(|x - y| = 2|x - a|\)
(2) \(|y - a| = |y|\)
Are You Up For the Challenge: 700 Level Questions
(1) \(|x - y| = 2|x - a|\)
(2) \(|y - a| = |y|\)
Are You Up For the Challenge: 700 Level Questions
19 Dec 2019, 10:01
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Statement 1
Distance of x from y is twice as that of x from a. There are 2 cases possible.
Case 1- x=a/2 and y= -a/2; |x|=|y|
Case 2- x=3a/2 and y=a/2; |x|≠|y|
Statement 2-
Distance of y from a is same as that of y from origin.
y=a/2
Combining 2 statements
x=3a/2 and y=a/2; |x|≠|y| {only this case is possible}
Sufficient
Distance of x from y is twice as that of x from a. There are 2 cases possible.
Case 1- x=a/2 and y= -a/2; |x|=|y|
Case 2- x=3a/2 and y=a/2; |x|≠|y|
Statement 2-
Distance of y from a is same as that of y from origin.
y=a/2
Combining 2 statements
x=3a/2 and y=a/2; |x|≠|y| {only this case is possible}
Sufficient
Bunuel
19 Dec 2019, 11:39
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#1
\(|x - y| = 2|x - a|\)
x=8 & y = 4 we get NO
and
x=2 and y = -2 ; we get yes
insufficient
#2
\(|y - a| = |y|\)
solve
we get a = 2y ; y = a/2
x not know insufficient
from1 &2
lx-a/2l = 2*lx-al
we get x= 3a/2 which is not = y ; a/2
sufficient to say that \(|x|= |y|\)
IMO C
\(|x - y| = 2|x - a|\)
x=8 & y = 4 we get NO
and
x=2 and y = -2 ; we get yes
insufficient
#2
\(|y - a| = |y|\)
solve
we get a = 2y ; y = a/2
x not know insufficient
from1 &2
lx-a/2l = 2*lx-al
we get x= 3a/2 which is not = y ; a/2
sufficient to say that \(|x|
IMO C
Bunuel
