Why do we need the sign? they're asking if |x| = y - z ?
So if, x=y-z OR x=-y+z, this means that the above statement is true regardless of sign. If one of them is true, then above is true, NO? What's wrong in my thinking? Thanks
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Is |x| = y - z ?
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djiddish98
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We don't know that x = y - z.
Statement 1 tells us that x = z - y, once we isolate X. If we multiply all sides by negative 1, we get -x = y - z. So |x| will equal y-z only when x is a negative number, since |x| has to be positive.
It's a bit confusing because when we say -x, we're saying that x is a negative number, so -x is a positive number.
Plug in a few examples.
x = -1, y = 2, z = 1. This satisfies x+y = z and our original equation of |x| = y-z
x = 1, y = 2, z = 3. This satisfies x+y=z, but not our original equation.
Statement 1 tells us that x = z - y, once we isolate X. If we multiply all sides by negative 1, we get -x = y - z. So |x| will equal y-z only when x is a negative number, since |x| has to be positive.
It's a bit confusing because when we say -x, we're saying that x is a negative number, so -x is a positive number.
Plug in a few examples.
x = -1, y = 2, z = 1. This satisfies x+y = z and our original equation of |x| = y-z
x = 1, y = 2, z = 3. This satisfies x+y=z, but not our original equation.
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wingsoffire
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mehravikas wrote:Sorry for bumping into an old thread. I have a doubt...lets make the question simpler
Is |x| = 3?
1. x = -3
2. x < 0
from the question we get if x > 0 then x = 3 or if x < 0 then x = -3
Statement 1 - tells us that x = -3, why do we have to consider different values of x i.e. +ve or -ve. Isnt this statement sufficient to answer that x would be equal to -3 when x < 0
Statement 2 - if x < 0, then x will be equal to -3
please make note that your taking the question as a truth. X is any value less than 3.
Am I missing something, please explain.
maihuna wrote:I have a simple logic it seems:
Given : |X| = y-z
if x<0, -x = y-z
if x>0 x = y-z
From 1: -x = y-z we dont know abt sign of x
From 2: We know x<0 so combine will give me Yes
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prashant misra
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i am not able to understand this question.i tried to simplify this question is |x| = y - z ? statement 1 says x+y=z i put y=z-x in the question and simplifying got |x|=-x i tried picking numbers but like 1 and -1 so it was both sufficient and insufficient but statement 2 says x is less than zero then the |x| will always give positive value so i chose option B.anyone please explain it to me in a more concise way by picking numbers
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kumadil2011
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much simpler way..
We know |x|>= 0
Simplify the question is y-z>=0?
st1- y-z=-x (Insuff, as we do not know whether x is +ve or -ve)
st2- x < 0 (Insuff, as no info on y and z)
Now i leave it up to you to decide what u choose C or E.. knowing that -x is +ve and hence y-z is +ve C
We know |x|>= 0
Simplify the question is y-z>=0?
st1- y-z=-x (Insuff, as we do not know whether x is +ve or -ve)
st2- x < 0 (Insuff, as no info on y and z)
Now i leave it up to you to decide what u choose C or E.. knowing that -x is +ve and hence y-z is +ve C
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immaculatesahai
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C is it... taking both together. You have to consider both positive and negative cases of the modulus to arrive at the answer.
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ronnie1985
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S1. x = z-y, does not give any light on the sign of x and hence not sufficient
S2. Not sufficient as it does not tell us anything about y and z
S1 and S2 both are sufficient.
(C) is answer.
S2. Not sufficient as it does not tell us anything about y and z
S1 and S2 both are sufficient.
(C) is answer.
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jayoptimist
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Q. |x|= y-z? x= y-z or -(y-z)/(z-y)
Stmt 1) x+y = z
x = z-y
but we dont know z-y is +ive or -ive
Stmt 2) x<0 ; so x is -ive.
but nothing is mentioned about y or z.
however when we combine 1 and 2, we have z-y is -ive.hence y-z = positive x.
|x| = x = y-z.Ans to the question is YES.
Hence C.
(Pls. correct if the logic is flawed)
Stmt 1) x+y = z
x = z-y
but we dont know z-y is +ive or -ive
Stmt 2) x<0 ; so x is -ive.
but nothing is mentioned about y or z.
however when we combine 1 and 2, we have z-y is -ive.hence y-z = positive x.
|x| = x = y-z.Ans to the question is YES.
Hence C.
(Pls. correct if the logic is flawed)
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ArunangsuSahu
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Simpler way of doing
Statement 1:
x+y=z
or, x=z-y
|x|=|z-y|=|y-z|...But x not known..So INSUFFICIENT
means |x| can be either z-y or y-z depending on x
Statement 2:
x < 0..x is negative..INSUFFICIENT
Combining(1) and (2)..Sufficient
Yes or No Question
Statement 1:
x+y=z
or, x=z-y
|x|=|z-y|=|y-z|...But x not known..So INSUFFICIENT
means |x| can be either z-y or y-z depending on x
Statement 2:
x < 0..x is negative..INSUFFICIENT
Combining(1) and (2)..Sufficient
Yes or No Question
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ronnie1985
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Lifetron
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1. x+y=z gives us y-z=(-x). This is equal to the question when x=0 or x= -ve number. When x= +ve number, it fails. INSUFFICIENT
2. x= -ve number. No info about z and y. INSUFFICIENT
1&2. We have a common case. x= -ve number. Taking the equ from 1. SUFFICIENT
Answer is C
2. x= -ve number. No info about z and y. INSUFFICIENT
1&2. We have a common case. x= -ve number. Taking the equ from 1. SUFFICIENT
Answer is C
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Ganesh hatwar
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Jayanth2689
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I searched for this question on BTG as you had cited this as an example in the absolute value study hall! This makes sense now.lunarpower wrote:statement 1:
we can rephrase this to x = z - y.
there are thus 3 possibilities for the absolute value |x| :
(a) if z - y is positive, then |x| = z - y, and will NOT equal y - z (which is a negative quantity).
(b) if z - y is negative, then |x| = y - z (the opposite of z - y).
(c) if z - y = 0, then |x| equals both y - z and z - y, since each is equal to 0.
TAKEAWAY: when you consider absolute value equations, you'll often do well by considering the different CASES that result from different combinations of signs.
notice that (a) and (b), or (a) and (c), taken together prove that statement 1 is insufficient.
--
statement 2:
we don't know anything about y or z, so this statement is insufficient.**
if you must, find cases: say y = 2 and z = 1. if x = -1, then the answer is YES; if x is any negative number other than -1, then the answer is NO.
--
together:
if x < 0, then this is case (b) listed above under statement 1.
therefore, the answer to the prompt question is YES.
sufficient.
--
**note that, if i were particularly evil, i could craft a statement that doesn't mention all three of x, y, z and yet IS STILL SUFFICIENT.
here's one way i could do that:
(2) y < z
in this case, y - z is negative and therefore CAN'T equal |x| -- no matter what x is -- since |x| must be nonnegative.
so, this statement is a definitive NO, and is thus sufficient even though it doesn't mention x at all.
this is evil, but i see no reason why it wouldn't be on the test.
But Ron, if statement 2 said " x > 0 " Would both the statements still be sufficient?
1) given: x+y = z
=> -x = y-z
but, the question does not mention whether |x| is -x or +x. so we need something more. this alone is insufficient!
2) x<0
No other parameters given. Hence, insufficient!
combining (1) and (2)
if x<0, it clearly indicates that |x| = -x. Hence proved yes!
Ans: [C]
=> -x = y-z
but, the question does not mention whether |x| is -x or +x. so we need something more. this alone is insufficient!
2) x<0
No other parameters given. Hence, insufficient!
combining (1) and (2)
if x<0, it clearly indicates that |x| = -x. Hence proved yes!
Ans: [C]
