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09 Jun 2022, 13:00
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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:
45%
(medium)
Question Stats:
59% (01:28) correct
41%
(01:40)
wrong
based on 86
sessions
History
Date
Time
Result
Not Attempted Yet
If m is an integer and \(x^m = \frac{1}{x^m}\), what is the value of x?
(1) x is an integer.
(2) m in a non-zero integer
Are You Up For the Challenge: 700 Level Questions
(1) x is an integer.
(2) m in a non-zero integer
Are You Up For the Challenge: 700 Level Questions
13 Jun 2022, 10:09
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Bunuel
Target question: What is the value of x?
Given: m is an integer and \(x^m = \frac{1}{x^m}\)
When we see the equation \(x^m = \frac{1}{x^m}\), we should ask ourselves "Under what circumstances can \(x^m\) equal \(\frac{1}{x^m}\)?"
A few of circumstances include:
I. \(x =\) any non-zero integer, and \(m = 0\), in which case the given equation of satisfied.
II. \(x = 1\), and \(m =\) any integer, in which case the given equation of satisfied.
III. \(x = -1\), and \(m =\) any even integer, in which case the given equation of satisfied.
Once we see the two statements, we can eliminate case I, but cases II and III remain, which means we can jump straight to . . .
Statements 1 and 2 combined
There are several values of m and x that satisfy BOTH statements. Here are two:
Case a: \(x = 1\) and \(m = 1\). In this case, the answer to the target question is \(x = 1\)
Case b: \(x = -1\) and \(m = 2\). In this case, the answer to the target question is \(x = -1\)
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
09 Oct 2023, 22:44
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Bunuel
\(x^m = \frac{1}{x^m}\)
\(x^{2m}=1\)
This will happen
a) when the power 2m=0 or m=0.
b) when x is 1 or -1
(1) x is an integer.
If x is 1 or -1, yes
If any other value, would depend on value of m.
Insufficient
(2) m in a non-zero integer
If x is 1 or -1, yes, otherwise no.
Insufficient
Combined
Still depends on value of x.
If x is 1 or -1, yes, otherwise no.
Insufficient
E
