If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c, and c^z = a, then xyz =
(A) 0
(B) 1
(C) 2
(D) a
(E) abc
This question is pretty challenging for me.please help me out here.
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a^x = b
b^y = c
c^z = a
Multiply both sides and we get the following :
(a^x)* (b^y)* (c^z) = abc
This equation can be true only if x,y and z are all 1.
Therefore xyz = 1.
b^y = c
c^z = a
Multiply both sides and we get the following :
(a^x)* (b^y)* (c^z) = abc
This equation can be true only if x,y and z are all 1.
Therefore xyz = 1.

 Master  Next Rank: 500 Posts
 Posts: 101
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a^x = b
b^y = c
c^z = a
Multiply both sides and we get the following :
(a^x)* (b^y)* (c^z) = abc
This equation can be true only if x,y and z are all 1.
Therefore xyz = 1.
b^y = c
c^z = a
Multiply both sides and we get the following :
(a^x)* (b^y)* (c^z) = abc
This equation can be true only if x,y and z are all 1.
Therefore xyz = 1.
 GMATGuruNY
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PLUG AND CHUG.shanice wrote:If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c, and c^z = a, then xyz =
(A) 0
(B) 1
(C) 2
(D) a
(E) abc
This question is pretty challenging for me.please help me out here.
Let c=2 and z=1.
Then a = c^z = 2Â¹ = 2.
Since b^y = c and c=2, we get:
b^y = 2.
Let b=2 and y=1.
Since a^x = b, a=2, and b=2, we get:
2^x=2.
Thus, x=1.
xyz = 1*1*1 = 1.
The correct answer is B.
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 vk_vinayak
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a^x = b, b^y = c, and c^z = ashanice wrote:If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c, and c^z = a, then xyz =
(A) 0
(B) 1
(C) 2
(D) a
(E) abc
This question is pretty challenging for me.please help me out here.
Start with a^x = b.  (1)
But it is given that a = c^z. Substitue the value of a in (1). We get (c^z)^x = b => (c)^zx = b  (2)
We are also given that c = b^y. Substitute this value of c in (2).
(c)^zx = b
(b^y)^zx = b
(b)^yzx = b
(b)^yzx = (b)^1. So, we get xyz=1.
 VK
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I will (Learn. Recognize. Apply)
B
If a^x = b then a = b^(1/x) similarly b= c^(1/y) and c=a^(1/z)
Put value of c in equation 2
b=[a^(1/z)]^(1/y)
Therefore b= a^(1/(ya))
But b= a^x then
A^x=a^(1/(ya))
Taking root x on both sides
A=a^(1/(xyz))
Since bases are same powers would have to be same
1/(xyz) = 1
Xyz=1
Hence B is the correct answer
If a^x = b then a = b^(1/x) similarly b= c^(1/y) and c=a^(1/z)
Put value of c in equation 2
b=[a^(1/z)]^(1/y)
Therefore b= a^(1/(ya))
But b= a^x then
A^x=a^(1/(ya))
Taking root x on both sides
A=a^(1/(xyz))
Since bases are same powers would have to be same
1/(xyz) = 1
Xyz=1
Hence B is the correct answer