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29 Nov 2018, 01:42
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A
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Difficulty:
35%
(medium)
Question Stats:
67% (01:31) correct
33%
(01:38)
wrong
based on 542
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If x ≠ 0, what is the value of x?
(1) |x + 2| = |x|
(2) |x^x| = 1
M36-34
(1) |x + 2| = |x|
(2) |x^x| = 1
M36-34
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18 Oct 2021, 04:39
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Bunuel
Official Solution:
If \(x ≠ 0\), what is the value of \(x\)?
(1) \(|x + 2| = |x|\)
Square to get rid of the absolute value (note here that we can safely do that since both sides of the equation are non-negative):
\(x^2+4x+4=x^2\);
\(x=-1\). Sufficient.
(2) \(|x^x| = 1\)
If \(x^x > 0\), then we'd get \(x^x = 1\), which gives \(x = 1\);
If \(x^x < 0\), then we'd get \(x^x = -1\), which gives \(x = -1\).
Not sufficient.
Answer: A
General Discussion
29 Nov 2018, 01:51
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From statement 1:
|x+2| = |x|
Squaring on both sides
\(x^2+4+4x\) =\(x^2\)
4+4x = 0
4(1+x) = 0
4 cannot be equal to 0. Hence x+1 = 0 or x = -1.
Sufficient.
From statement 2:
|x^x| = 1
x^x = +1 or -1
Either x = 1 or -1, Since \(1^1\) = 1 or \(-1^{-1}\) = -1
Insufficient.
A is the answer.
|x+2| = |x|
Squaring on both sides
\(x^2+4+4x\) =\(x^2\)
4+4x = 0
4(1+x) = 0
4 cannot be equal to 0. Hence x+1 = 0 or x = -1.
Sufficient.
From statement 2:
|x^x| = 1
x^x = +1 or -1
Either x = 1 or -1, Since \(1^1\) = 1 or \(-1^{-1}\) = -1
Insufficient.
A is the answer.
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