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10 Sep 2017, 05:10
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A
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:
67% (01:03) correct
33%
(00:54)
wrong
based on 105
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If 0 < x < 1, which of the following is the greatest?
A. \(x^{(-\frac{1}{2})}\)
B. \(x^0\)
C. \(x^{(\frac{1}{2})}\)
D. \(x^1\)
E. \(x^2\)
A. \(x^{(-\frac{1}{2})}\)
B. \(x^0\)
C. \(x^{(\frac{1}{2})}\)
D. \(x^1\)
E. \(x^2\)
10 Sep 2017, 09:58
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0 < x < 1
lets assume x=0.16
A)x^(-1/2)
=1/{x^(1/2)}
=1/(0.16)^1/2
=1/0.4
=2.5
B)x^0=1
c)x^1/2
=0.16^1/2
=0.4
D)x^1
=0.16^1
=0.16
E)x^2
=0.16^2
=0.0256
Hence Answer is option A
Kudos if it helps.
lets assume x=0.16
A)x^(-1/2)
=1/{x^(1/2)}
=1/(0.16)^1/2
=1/0.4
=2.5
B)x^0=1
c)x^1/2
=0.16^1/2
=0.4
D)x^1
=0.16^1
=0.16
E)x^2
=0.16^2
=0.0256
Hence Answer is option A
Kudos if it helps.
10 Sep 2017, 14:09
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Bunuel
If 0 < x < 1, which of the following is the greatest?
A. \(x^{(-\frac{1}{2})}\)
B. \(x^0\)
C. \(x^{(\frac{1}{2})}\)
D. \(x^1\)
E. \(x^2\)
If 0 < x < 1, it is a proper fraction, (e.g., \(\frac{1}{2}\)). A. \(x^{(-\frac{1}{2})}\)
B. \(x^0\)
C. \(x^{(\frac{1}{2})}\)
D. \(x^1\)
E. \(x^2\)
Number properties
If very fluent in properties of these fractions, finding the answer is quick and no calculations are needed:
The negative exponent with the smallest value will yield the greatest answer. Only choice A has a negative exponent.
Given their equal absolute values, you could compare Answer A and Answer C (see below for calculation) to be sure.
After that or at a glance, the greatest result is
Answer A
Test a value
Because the answer choices contain square roots, and to keep things simple, choose a unit fraction whose denominator is a perfect square, e.g. \(\frac{1}{9}\)
A. \((\frac{1}{9})^{(-\frac{1}{2})}\) =\(9^{(\frac{1}{2})}\) = \(\sqrt{9} =\\
3\)
B. \((\frac{1}{9})^0\) = 1
C.\((\frac{1}{9})^{(\frac{1}{2})}\) =\(\sqrt{\frac{1}{9}}\) = \(\frac{1}{3}\)
D. \((\frac{1}{9})^1\) = \(\frac{1}{9}\)
E. \((\frac{1}{9})^2\) = \(\frac{1}{81}\)
Greatest of these results?
ANSWER A
