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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:
35%
(medium)
Question Stats:
65% (01:22) correct
35%
(01:25)
wrong
based on 4940
sessions
History
Date
Time
Result
Not Attempted Yet
Is |x| = y - z ?
(1) x + y = z
(2) x < 0
(1) x + y = z
(2) x < 0
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
05 Oct 2009, 05:31
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Is |x| = y - z[/m]?
For a start, take into account that for the equation |x| = y - z to hold true, y - z must be greater than or equal to 0. This is due to the fact that it's equated to the absolute value of a number, |x|, which cannot be negative. In essence, the question is asking whether y - z is non-negative and if their difference equals |x|.
(1) -x = y - z.
If x > 0, -x would be negative, which would imply that y - z is also negative. This doesn't meet our initial criteria. For instance, if x = 1 and y - z = -1, then (|x| = 1) is not equal to (y - z = -1).
If x ≤ 0, -x would be non-negative, which would imply y - z is also non-negative, a valid scenario. For instance, if x = -1 and y - z = 1, then (|x| = 1) is equal to (y - z = 1).
This gives us two possible outcomes and does not definitively answer our question. Not sufficient.
(2) \(x<0\).
This condition alone is not sufficient because it only gives information about x. We still need to know whether the value of y - z equals |x|.
(1) + (2) Given that x < 0, |x| = -x, and so our original question becomes: is -x = y - z? The second statement gives a direct YES answer to this question. Sufficient.
Answer: C.
For a start, take into account that for the equation |x| = y - z to hold true, y - z must be greater than or equal to 0. This is due to the fact that it's equated to the absolute value of a number, |x|, which cannot be negative. In essence, the question is asking whether y - z is non-negative and if their difference equals |x|.
(1) -x = y - z.
If x > 0, -x would be negative, which would imply that y - z is also negative. This doesn't meet our initial criteria. For instance, if x = 1 and y - z = -1, then (|x| = 1) is not equal to (y - z = -1).
If x ≤ 0, -x would be non-negative, which would imply y - z is also non-negative, a valid scenario. For instance, if x = -1 and y - z = 1, then (|x| = 1) is equal to (y - z = 1).
This gives us two possible outcomes and does not definitively answer our question. Not sufficient.
(2) \(x<0\).
This condition alone is not sufficient because it only gives information about x. We still need to know whether the value of y - z equals |x|.
(1) + (2) Given that x < 0, |x| = -x, and so our original question becomes: is -x = y - z? The second statement gives a direct YES answer to this question. Sufficient.
Answer: C.
01 Aug 2010, 14:15
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is |x|=y-z?
given:
(1) x+y=z
(2) x<0
solving (1) first:
y=z-x
|x|=(z-x)-z
|x|=-x
take x=1, z=2, y=1
1=1-2 (no)
take x=-1, z=2, y=3
|x|=y-z?
|-1|=3-2=1 YES
so what solving for |x|=-x meant was that x MUST be negative for the equation to be true, if it is positive then it is not true (since in that case, |x| would not equal -x).
hence the answer is C.
given:
(1) x+y=z
(2) x<0
solving (1) first:
y=z-x
|x|=(z-x)-z
|x|=-x
take x=1, z=2, y=1
1=1-2 (no)
take x=-1, z=2, y=3
|x|=y-z?
|-1|=3-2=1 YES
so what solving for |x|=-x meant was that x MUST be negative for the equation to be true, if it is positive then it is not true (since in that case, |x| would not equal -x).
hence the answer is C.
