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11 May 2023, 06:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
62% (00:51) correct
38%
(00:43)
wrong
based on 53
sessions
History
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Not Attempted Yet
Is \(x>0\)?
(1) \(x = |x|\)
(2) \(x^2 - x = 0\)
(1) \(x = |x|\)
(2) \(x^2 - x = 0\)
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
11 May 2023, 09:16
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We need to find if x > 0?
STAT 1: x = |x|
Now, this can be true for any non-negative value of x
=> x ≥ 0
Ex: x = -3, |x| = |-3| = 3 ≠ -3 ≠ x
Ex: x = 3, |x| = |3| = 3 = x
So, Statement 1 alone is NOT SUFFICIENT as x can = 0 or x can be > 0
STAT 2: \(x^2 - x = 0\)
=> x * (x - 1) = 0
=> x = 0 or x = 1
So, Statement 2 alone is NOT SUFFICIENT as x can = 0 or x can be > 0 (i.e 1)
Combining both of them we get
x ≥ 0 and x = 0 or x = 1
=> x = 0 or x = 1
Same as Statement 2
=> NOT SUFFICIENT
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
STAT 1: x = |x|
Now, this can be true for any non-negative value of x
=> x ≥ 0
Ex: x = -3, |x| = |-3| = 3 ≠ -3 ≠ x
Ex: x = 3, |x| = |3| = 3 = x
So, Statement 1 alone is NOT SUFFICIENT as x can = 0 or x can be > 0
STAT 2: \(x^2 - x = 0\)
=> x * (x - 1) = 0
=> x = 0 or x = 1
So, Statement 2 alone is NOT SUFFICIENT as x can = 0 or x can be > 0 (i.e 1)
Combining both of them we get
x ≥ 0 and x = 0 or x = 1
=> x = 0 or x = 1
Same as Statement 2
=> NOT SUFFICIENT
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
11 May 2023, 13:11
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Bunuel
Statement 1
(1) \(x = |x|\)
Inference: x is non-negative.
If x = 0, the answer to the target question Is \(x>0\)? No
If x > 0, the answer to the target question Is \(x>0\)? Yes
As we have contradicting answers to the target question, the statement alone is not sufficient. Eliminate A and D.
Statement 2
(2) \(x^2 - x = 0\)
\(x^2 = x\)
If x = 0, the answer to the target question Is \(x>0\)? No
If x = 1, the answer to the target question Is \(x>0\)? Yes
As we have contradicting answers to the target question, the statement alone is not sufficient. Eliminate B.
Combined
Both the cases in Statement 1 and Statement 2 are still applicable when the statements are combined. Hence, the statements combined do not help either.
Option E
