Is |X| = Y-Z ?
1. X+Z is not equal Y
2. X<0
Number Theory
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- vineeshp
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I'd go with E here.
Y X Z
3 4 7
3 4 8
3 -1 2
3 -1 3
In all these cases, Y is not equal to X + Z.
But in 1st and 3rd, |X| = Y-Z.
So N.S
Adding stmt 2 to Stmt 1 takes away 1st and 2nd set of values. But other 2 still remain.
So E.
Y X Z
3 4 7
3 4 8
3 -1 2
3 -1 3
In all these cases, Y is not equal to X + Z.
But in 1st and 3rd, |X| = Y-Z.
So N.S
Adding stmt 2 to Stmt 1 takes away 1st and 2nd set of values. But other 2 still remain.
So E.
Vineesh,
Just telling you what I know and think. I am not the expert.
Just telling you what I know and think. I am not the expert.
I initially thought the answer would be A, but maybe I am falling into a trap here.
Vineeshp, you note the example y=3 and z=7, and x=4. And you state Y is not equal to X + Z and |X| = Y-Z. However wouldn't Y-Z = 3-4 = -4. If x = 4, |X| = 4. 4 does not equal -4. I point this out because I think we can say that given statement one, the stimulus can't be true.
Since statement 1 says X+Z is not equal Y, it tells us X is definitely negative, (or simply any arbitrary number.) I would say it tells us sufficiently that the answer to the stimulus is no. I don't see how statement 1 can tell us in any way that the stimulus holds true.
Thoughts?
Vineeshp, you note the example y=3 and z=7, and x=4. And you state Y is not equal to X + Z and |X| = Y-Z. However wouldn't Y-Z = 3-4 = -4. If x = 4, |X| = 4. 4 does not equal -4. I point this out because I think we can say that given statement one, the stimulus can't be true.
Since statement 1 says X+Z is not equal Y, it tells us X is definitely negative, (or simply any arbitrary number.) I would say it tells us sufficiently that the answer to the stimulus is no. I don't see how statement 1 can tell us in any way that the stimulus holds true.
Thoughts?
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I also like A.
If |X| = Y - Z, then y > z, since the answer has to be positive (or y = z and x = 0)
x = y - z when x is positive
-x = z - y when x is negative
both cases let us know that x + z = y when we rearrange terms. Since statement 1 tells us that x + z != y, then we know that |X| != Y - Z, which is sufficient.
If |X| = Y - Z, then y > z, since the answer has to be positive (or y = z and x = 0)
x = y - z when x is positive
-x = z - y when x is negative
both cases let us know that x + z = y when we rearrange terms. Since statement 1 tells us that x + z != y, then we know that |X| != Y - Z, which is sufficient.
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- Ian Stewart
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I received a PM asking for comment.
Your line of reasoning here wasn't entirely clear to me, but Statement 1 does not guarantee that X is negative - X+Z can be different from Y when X is positive as well. It is, however, true that we always get a 'no' answer to the question when X is positive (I go into more detail below), so if we want to get a 'yes' answer to the question, we'll need to look at negative values of x.uslalas22 wrote: Since statement 1 says X+Z is not equal Y, it tells us X is definitely negative, (or simply any arbitrary number.)
There's a problem with your math here, which I've highlighted in red. If you are considering the case when X is negative, and you have the equation |X| = Y-X, then since X is negative you can replace |X| with -X. But you certainly should not replace Y-Z with Z-Y; Y-Z is still equal to Y-Z. That is, you should not apply a negative sign to both sides of the equation, as you did above; those will always just cancel each other out no matter what equation you look at. You want only to replace |X| with -X, nothing more. If it's not clear why that's the case, imagine a simpler equation: |x| = 3. When you want to find the negative solution for x, when you are getting rid of the absolute value brackets you don't put a negative sign on both sides of the equation - you only put a negative on the left side.djiddish98 wrote:
If |X| = Y - Z, then y > z, since the answer has to be positive (or y = z and x = 0)
x = y - z when x is positive
-x = z - y when x is negative
both cases let us know that x + z = y when we rearrange terms. Since statement 1 tells us that x + z != y, then we know that |X| != Y - Z, which is sufficient.
If, from Statement 1, X+Z is not equal to Y, then certainly X is not equal to Y-Z. If X is not equal to Y-Z, and if X is positive, then |X| will also not equal Y-Z, so if X is positive, the answer to the question is 'no'. But we need to consider the possibility that X is negative as well - this is how we might get a 'yes' answer to the question. If, say, X = -1, Y = 2 and Z = 1, then Statement 1 is true (X+Z is not equal to Y) and |X| = Y-Z is also true - we can get a 'yes' answer to the question as well. The answer is E here, since it's also possible to get a 'no' answer when X is negative (just use the same numbers as before but let X be -10, say).sourabh33 wrote:Is |X| = Y-Z ?
1. X+Z is not equal Y
2. X<0
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