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If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 58428
If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

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New post Updated on: 23 Jul 2019, 10:18
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:40) correct 22% (01:31) wrong based on 50 sessions

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Originally posted by Bunuel on 07 Apr 2019, 21:39.
Last edited by SajjadAhmad on 23 Jul 2019, 10:18, edited 1 time in total.
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Intern
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Joined: 09 Apr 2018
Posts: 32
Re: If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

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New post 07 Apr 2019, 21:56
Since a,b and c can't be 0 or 1, x, y and z have to be 1.
Hence xyz=1

Answer: B

Alternately,

Since we have a^x=b & b^y=c, (a^x)^y=c
a^xy=c
Again,
c^z=a And hence (a^xy)^z=a
a^xyz=a
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B
Joined: 24 Jun 2018
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Re: If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

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New post 08 Apr 2019, 11:42
Simple substitution can give us the answer:

Given:
a^x = b
b^y=c
c^z=a

Now,
b^y=c
=> (a^x)^y=c
=> a^xy=c ------> (1)

Now,
c^z=a
From 1
(a^xy)^z=a
Hence, a^xyz=a

Since a is not equal to 0 or 1, for both sides to be equal

xyz must be equal to 1
hence xyz = 1
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Re: If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

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New post 09 Apr 2019, 18:01
1
I did it this way, just keep adding the exponents, given:

\(a^x = b\)
\(b^y = c\)
\(c^z = a\)

Take the first one and add ^y to both sides.

\(a^x^y = b^y = c\) Now add the ^z so the whole term can be equal to a.

\(a^x^y^z = b^y^z = c^y^z = a\)

so

\(a^x^y^z = a^1\)

\(xyz = 1\)

B
GMAT Club Bot
Re: If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z   [#permalink] 09 Apr 2019, 18:01
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