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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: 41884

Kudos [?]: 128929 [0], given: 12183

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:

45% (medium)

Question Stats:

56% (01:07) correct 44% (01:07) wrong based on 36 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128929 [0], given: 12183

Senior Manager
Joined: 25 Feb 2013
Posts: 407

Kudos [?]: 176 [0], given: 31

Location: India
GPA: 3.82
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

Kudos [?]: 176 [0], given: 31

Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 173

Kudos [?]: 14 [0], given: 413

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

Kudos [?]: 14 [0], given: 413

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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