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11 Feb 2013, 01:09
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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:
64% (01:17) correct
36%
(01:25)
wrong
based on 503
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x ?
(1) x^4 = |x|
(2) x^2 > x
M22-03
(1) x^4 = |x|
(2) x^2 > x
M22-03
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11 Feb 2013, 01:18
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What is the value of \(x\) ?
(1) \(x^4 = |x|\).
This statement implies that \(x = -1\), \(x = 0\), or \(x = 1\). Not sufficient.
(2) \(x^2 \gt x\).
Rearrange and factor out \(x\) to get \(x(x - 1) > 0\). The roots are \(x = 0\) and \(x = 1\). The "\(>\)" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root; therefore, the given inequality holds true for: \(x < 0\) and \(x > 1\). Not sufficient.
(1) + (2) The only value of \(x\) from (1) that is within the range from (2) is \(x = -1\). Sufficient.
Answer: C
(1) \(x^4 = |x|\).
This statement implies that \(x = -1\), \(x = 0\), or \(x = 1\). Not sufficient.
(2) \(x^2 \gt x\).
Rearrange and factor out \(x\) to get \(x(x - 1) > 0\). The roots are \(x = 0\) and \(x = 1\). The "\(>\)" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root; therefore, the given inequality holds true for: \(x < 0\) and \(x > 1\). Not sufficient.
(1) + (2) The only value of \(x\) from (1) that is within the range from (2) is \(x = -1\). Sufficient.
Answer: C
General Discussion
09 Jan 2015, 17:53
Kudos
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Hi All,
This DS question can be solved with a variety of Number Properties and TESTing VALUES:
We're asked for the value of X.
Fact 1: X^4 = |X|
While this certainly looks "scary", there can't be that many values that will "fit" this equation.
X = 0 is fairly obvious. Since we have a "fourth power" and an absolute value, I'd be looking for other solutions that are fairly close to 0 and possibly negative.
X = 1 and X = -1 also fit.
Fact 1 is INSUFFICIENT
Fact 2: X^2 > X
Here we can use a Number Property to our advantage - EVERY negative number, when squared, becomes positive.
So, X = ANY negative.
This is enough to prove that Fact 2 is INSUFFICIENT on its own, but I want to add a bit more detail to what X^2 > X means.
X CANNOT be 1, since 1^2 is NOT > 1.
X CANNOT be 0, since 0^2 is NOT > 0
X CANNOT be between 0 and 1 either (because of another Number Property - positive fractions, when squared, get SMALLER).
C CANNOT be 1/2, since (1/2)^2 is NOT > 1/2.
X CAN be > 1 though (choose any value greater than 1 and you can prove it).
Fact 2 is INSUFFICIENT
Combined, we know...
X = -1, 0 or 1
X CANNOT BE 0 OR 1
Thus, X can ONLY be -1
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved with a variety of Number Properties and TESTing VALUES:
We're asked for the value of X.
Fact 1: X^4 = |X|
While this certainly looks "scary", there can't be that many values that will "fit" this equation.
X = 0 is fairly obvious. Since we have a "fourth power" and an absolute value, I'd be looking for other solutions that are fairly close to 0 and possibly negative.
X = 1 and X = -1 also fit.
Fact 1 is INSUFFICIENT
Fact 2: X^2 > X
Here we can use a Number Property to our advantage - EVERY negative number, when squared, becomes positive.
So, X = ANY negative.
This is enough to prove that Fact 2 is INSUFFICIENT on its own, but I want to add a bit more detail to what X^2 > X means.
X CANNOT be 1, since 1^2 is NOT > 1.
X CANNOT be 0, since 0^2 is NOT > 0
X CANNOT be between 0 and 1 either (because of another Number Property - positive fractions, when squared, get SMALLER).
C CANNOT be 1/2, since (1/2)^2 is NOT > 1/2.
X CAN be > 1 though (choose any value greater than 1 and you can prove it).
Fact 2 is INSUFFICIENT
Combined, we know...
X = -1, 0 or 1
X CANNOT BE 0 OR 1
Thus, X can ONLY be -1
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
