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# The expression x^(-1)/5^x is greatest for which of the following value

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Math Expert
Joined: 02 Sep 2009
Posts: 46216
The expression x^(-1)/5^x is greatest for which of the following value [#permalink]

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10 Sep 2017, 05:05
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Difficulty:

35% (medium)

Question Stats:

71% (01:07) correct 29% (01:16) wrong based on 72 sessions

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The expression $$\frac{x^{(-1)}}{5^x}$$ is greatest for which of the following values of x?

A. 2
B. 1
C. 1/2
D. –1
E. –2

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The expression x^(-1)/5^x is greatest for which of the following value [#permalink]

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10 Sep 2017, 12:25
Bunuel wrote:
The expression $$\frac{x^{(-1)}}{5^x}$$ is greatest for which of the following values of x?

A. 2
B. 1
C. 1/2
D. –1
E. –2

The question can be written as $$\frac{1}{x5^{x}}$$. For this expression to have the greatest value $$x$$ has to be positive.
Hence Option D & E can be ommitted
Also as numerator is $$1$$, so any integer value of $$x$$ will make the denominator an integer, hence the value of the expression will be farther away from $$1$$. So we can remove option A & B. Hence Correct option C

We can test this by substituting the values for $$x$$

A. $$\frac{1}{(2*5^{2})}$$ $$= \frac{1}{50}$$

B. $$\frac{1}{(1*5^{1})}$$ $$= \frac{1}{5} > option A$$

C. $$1/(1/2*5^{1/2})$$ $$= \frac{2}{\sqrt{5}}$$. Multiplying numerator and denominator by $$\sqrt{5}$$, we get
$$(2*\sqrt{5})/5 > Option B$$

Hence Option C
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Re: The expression x^(-1)/5^x is greatest for which of the following value [#permalink]

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29 Sep 2017, 09:37
Bunuel wrote:
The expression $$\frac{x^{(-1)}}{5^x}$$ is greatest for which of the following values of x?

A. 2
B. 1
C. 1/2
D. –1
E. –2

hi

lets think this way ..

to maximize any fraction, we need to maximize the numerator
and we know, any proper fraction with negative exponent will have the greatest value
here, in this question "x" is raised to a negative exponent, so lets substitute the "x" with a proper fraction

only C fits

no math here, guys

cheers through the kudos button if this helps
Re: The expression x^(-1)/5^x is greatest for which of the following value   [#permalink] 29 Sep 2017, 09:37
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