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10 Sep 2017, 05:13
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Difficulty:
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69% (01:36) correct
31%
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If 0 < a < 1, which of the following is the greatest?
A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
10 Sep 2017, 12:55
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Bunuel
If 0 < a < 1, which of the following is the greatest?
A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
as \(a\) is positive and \(a<1\), so \(\frac{1}{a}>1\). Hence a fraction where \(a\) is in the denominator and numerator is \(1\) will have a value greater than \(1\). Hence we can straight away eliminate options B, C & E as \(a\) is in the numerator (essentially option B, C & E are same \(= a^2\) and as it is given \(a<1\), so squaring both sides will yield \(a^2<1\))
Option A: can be written as \(\frac{1}{(2a)^{2}}\) \(= \frac{1}{4a^2}\)
Option D: can be written as \(\frac{1}{a^2}\). Multiply the numerator and the denominator by \(4\). we get
\(\frac{4}{4a^2} > \frac{1}{4a^2}\)
Hence Option D
14 Sep 2017, 11:09
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Bunuel
If 0 < a < 1, which of the following is the greatest?
A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
Let a = \(\frac{1}{4}\), and evaluate each answer choice. Straight algebra -- reciprocals, fractions, and squares -- became too tangled. A. \((-2a)^{(-2)}\)
B. \(\frac{1}{a^{(-2)}}\)
C. \((\frac{1}{a})^{(-2)}\)
D. \(a^{(-2)}\)
E. \(a^2\)
A. \((-2a)^{(-2)}\) --> \(\frac{1}{(-2*a)^2}\)
\(\frac{1}{(-2*\frac{1}{4})^2}\) =
\(\frac{1}{(-\frac{1}{2})^2}\) = \(\frac{1}{(\frac{1}{4})}\) = 4
B. \(\frac{1}{a^{(-2)}}\) --> \(\frac{a^2}{1^2}\)
\(a^2\) = \((\frac{1}{4})^2\) =\(\frac{1}{16}\)
C.\((\frac{1}{a})^{(-2)}\) --> \(\frac{a^2}{1^2}\)=
\(a^2\). Same as Answer B =\(\frac{1}{16}\)
D. \(a^{(-2)}\)--> \(\frac{1}{a^2}\)
\(\frac{1}{(\frac{1}{4})^2}\) = \(\frac{1}{\frac{1}{16}}\) = 16
E. \(a^2\) = same as Answer B = \(\frac{1}{16}\)
ANSWER D
