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Is |x| = y - z ? 1) x + y = z 2) x < 0
[#permalink]
30 Oct 2011, 11:34
30 Oct 2011, 11:34
Show timer
00:00
A
B
C
D
E
Difficulty:
55%
(hard)
Question Stats:
54% (01:00) correct
46%
(02:18)
wrong
based on 13
sessions
Tried searching but couldnt find ...
Is |x| = y - z ?
1) x + y = z
2) x < 0
OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-y-z-1-x-y-z-2-x-84821.html
Is |x| = y - z ?
1) x + y = z
2) x < 0
Show SpoilerPlease comment on my solution and say if its right or wrong
1) x = z-y
|x| = x or |x| = -x
Dont know if x is positive or negative .... Hence insufficient
2)X< 0
no info about x and y .... hence insufficient
taking 1 and 2 together
x< 0 thus |x| = -x
-x = -(z-y)
thus |x| = y-z
hence c ---- sufficient
|x| = x or |x| = -x
Dont know if x is positive or negative .... Hence insufficient
2)X< 0
no info about x and y .... hence insufficient
taking 1 and 2 together
x< 0 thus |x| = -x
-x = -(z-y)
thus |x| = y-z
hence c ---- sufficient
OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-y-z-1-x-y-z-2-x-84821.html
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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0
[#permalink]
Updated on: 30 Oct 2011, 12:17
Updated on: 30 Oct 2011, 12:17
What is the source of the problem ?
imho OA should be C too. Here's my explanation :
Given,
Is |x| = y-z ?
Rephrase the Question :
x = y-z or -x = y-z ( => x = z-y ),
so the question could be re-phrased as : x = y-z or z-y . Is this True ?
Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient
Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). It does not give info about y or z . Hence insufficient.
Taken Together :
From statement 1 , x = z - y
From statement 2, x < 0 => |x| = -x. But from above we have -x = - (z-y) = (y-z). Hence x can be both z-y or y-z. Sufficient
Hence Ans is C !
imho OA should be C too. Here's my explanation :
Given,
Is |x| = y-z ?
Rephrase the Question :
x = y-z or -x = y-z ( => x = z-y ),
so the question could be re-phrased as : x = y-z or z-y . Is this True ?
Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient
Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). It does not give info about y or z . Hence insufficient.
Taken Together :
From statement 1 , x = z - y
From statement 2, x < 0 => |x| = -x. But from above we have -x = - (z-y) = (y-z). Hence x can be both z-y or y-z. Sufficient
Hence Ans is C !
Re: Is |x| = y - z ? 1) x + y = z 2) x < 0
[#permalink]
30 Oct 2011, 12:12
30 Oct 2011, 12:12
hoogly wrote:
What is the source of the problem ?
imho OA should be E. Here's my explanation :
Given,
Is |x| = y-z ?
Rephrase the Question :
x = y-z or -x = y-z ( => x = z-y ),
so the question could be re-phrased as : x = y-z or z-y . Is this True ?
Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient
Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). This statement says, -x = y-z or x = z-y . Hence insufficient.
Taken Together :
X < 0 and |x| = -x. Both mean the same and imply -x = y-z or x = z-y . Hence insufficient.
Hence Ans is E !
Infact if statement 2 is x > 0 , Then C could be the answer.
imho OA should be E. Here's my explanation :
Given,
Is |x| = y-z ?
Rephrase the Question :
x = y-z or -x = y-z ( => x = z-y ),
so the question could be re-phrased as : x = y-z or z-y . Is this True ?
Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient
Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). This statement says, -x = y-z or x = z-y . Hence insufficient.
Taken Together :
X < 0 and |x| = -x. Both mean the same and imply -x = y-z or x = z-y . Hence insufficient.
Hence Ans is E !
Infact if statement 2 is x > 0 , Then C could be the answer.
First of all statement 2 doesnt tell us anything about y and z's relationship... I think you brought the equation from statement 1 ... when thinking about statement 2 you should leave statement 1 behind...
Now, getting back to your solution
1 gives x = z- y
2 gives x< 0 thus |x| = - x
1 and 2 combined
from 1 we know x = z-y
substitute this in 2 , we get
-x = -(z-y)
but -x = |x|
thus |x| = y-z or |x| = z-y (from 1)
hence c
