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The expression (x - a)^a/a^(x - a) = 1 is true for which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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10 Sep 2017, 05:07
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Question Stats:

68% (00:47) correct 32% (00:36) wrong based on 25 sessions

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The expression $$\frac{(x - a)^a}{a^{(x - a)}}=1$$ is true for which of the following values for x and a?

A. x = 1 and a = 0
B. x = 0 and a = 1
C. x = 1 and a = 1
D. x = 2 and a = 1
E. x = 1 and a = 2
[Reveal] Spoiler: OA

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Kudos [?]: 132619 [0], given: 12326

Director
Joined: 25 Feb 2013
Posts: 542

Kudos [?]: 246 [0], given: 33

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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10 Sep 2017, 12:36
Bunuel wrote:
The expression $$\frac{(x - a)^a}{a^{(x - a)}}=1$$ is true for which of the following values for x and a?

A. x = 1 and a = 0
B. x = 0 and a = 1
C. x = 1 and a = 1
D. x = 2 and a = 1
E. x = 1 and a = 2

As per the question $$(x-a)^a = a^{x-a}$$. In an equation this can only be true when Base of RHS = Base of LHS and Exponent of RHS = Exponent of LHS
this implies $$x-a = a$$ or $$x = 2a$$

Only Option D satisfies the relation between $$x$$ & $$a$$

We can also substitute the values of $$x$$ & $$a$$ from the options to test the equation

Option $$D$$

Kudos [?]: 246 [0], given: 33

Intern
Joined: 07 Dec 2016
Posts: 41

Kudos [?]: 9 [0], given: 74

Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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11 Sep 2017, 13:25
Option D

Substituted the values given in options and checked the equality

Kudos [?]: 9 [0], given: 74

Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the   [#permalink] 11 Sep 2017, 13:25
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