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10 Oct 2017, 01:06
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B
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Fresh GMAT Club Tests' Challenge Question:
If x is a non-zero integer, what is the value of x?
(1) \((\frac{x}{2})^x = 1\)
(2) \((|x|)^x = 4\)
M36-57
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08 Nov 2021, 08:13
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Bunuel
Official Solution:
If \(x\) non-zero integer, what is the value of \(x\)?
(1) \((\frac{x}{2})^x = 1\)
Since \(x \neq 0\), then \((\frac{x}{2})^x = 1\) to be true, the base, (\(\frac{x}{2}\)), should be 1 and the exponent (\(x\)) could be any number (\(1^{anything}=1\)) or the base, (\(\frac{x}{2}\)), should be -1 and the exponent (\(x\)) should be even (\((-1)^{even}=1\)).
If \(\frac{x}{2}=1\), then \(x=2\).
If \(\frac{x}{2}=-1\), then \(x=-2=even\).
\(x\) could be 2 or -2. Not sufficient.
(2) \((|x|)^x = 4\)
If \(x < 0\), then we'd have \((-x)^x = 4\). No negative integer satisfies this equation because \((-x)^x = (positive \ integer)^{(negative \ integer)}\) is less than or equal to 1 (\((-x)^x = (positive \ integer)^{(negative \ integer)}\) would be \(1, \ \frac{1}{4}, \ \frac{1}{27}, \ ...\)).
If \(x > 0\), then we'd have \(x^x = 4\). This gives \(x=2\).
\(x\) could be only 2. Sufficient.
Answer: B
General Discussion
10 Oct 2017, 02:37
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(1) (x/2)^x=1
Testing differenet cases we get that x=2 or -2 so we cannot define concrete value.
x=2
(2/2)^2=1
x=-2
(-2/2)^-2= (-1)^-2=1/(-1)^2=1
Insufficient
(2) After testing cases I got that only x=2 satisfies the equation (|x|)^x=4
P.S. maybe there is something more.
Answer B.
Testing differenet cases we get that x=2 or -2 so we cannot define concrete value.
x=2
(2/2)^2=1
x=-2
(-2/2)^-2= (-1)^-2=1/(-1)^2=1
Insufficient
(2) After testing cases I got that only x=2 satisfies the equation (|x|)^x=4
P.S. maybe there is something more.
Answer B.
