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a^x=b^y=c^z

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a^x=b^y=c^z [#permalink] New post 06 Nov 2019, 06:04
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Question Stats:

66% (01:11) correct 33% (01:33) wrong based on 9 sessions
If \(a^x=b^y=c^z\), \(\frac{b}{a}=\frac{c}{b}\), and a, b and c have different values.

Quantity A
Quantity B
\(\frac{2z}{x+z}\)
\(\frac{y}{x}\)


A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

ID: Q02-86
[Reveal] Spoiler: OA

Last edited by Asmakan on 08 Nov 2019, 11:20, edited 1 time in total.
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Re: a^x=b^y=c^z [#permalink] New post 06 Nov 2019, 09:19
The answer is C, because x, y and z can only be zero. Zero divided by zero is an undefined expression, so you get two undefined expressions 2*0/(0+0) and 0/0
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Re: a^x=b^y=c^z [#permalink] New post 07 Nov 2019, 14:03
Expert's post
@Asmakan

I told you always to provide the ID of the question. Otherwise, I have to go through 10 tests and 200 questions to find it.

Many thanks
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Re: a^x=b^y=c^z [#permalink] New post 08 Nov 2019, 11:22
Where am I going wrong?

Let a=2, b=4, c=8; x=3, y=3/2, z=1.

Then 2z/(x+z) =2/4=1/2, and y/z = 3/2. NOT the same.
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Re: a^x=b^y=c^z [#permalink] New post 08 Nov 2019, 13:07
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Expert's post
Asmakan Array[WROTE]:
If \(a^x=b^y=c^z\), \(\frac{b}{a}=\frac{c}{b}\), and a, b and c have different values.

Quantity A
Quantity B
\(\frac{2z}{x+z}\)
\(\frac{y}{x}\)


A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

ID: Q02-86


Let's build on Chakolate's solution....

If \(a^x=b^y=c^z\), \(\frac{b}{a}=\frac{c}{b}\), then it COULD be the case that a=2, b=4, c=8, x=3, y=3/2, z=1.
In this case, we get:
QUANTITY A: 2z/(x+z) = (2)(1)(3 + 1) = 2/4 = 1/2
QUANTITY B: y/x = (3/2)/3 = 1/2


It COULD be the case that a=2, b=4, c=8, x=0, y=0, z=0.
In this case, we get:
QUANTITY A: 2z/(x+z) = 0/0
QUANTITY B: y/x = 0/0
Can we say that 0/0 = 0/0?
No.
0/0 is undefined. In other words, it's not an actual number.
It's like asking "Which is greater, lemon or lemon?"
Since we can only compare numbers in a Quantitative Comparison question, this is a faulty question.

If this were an official GRE question, there would be some proviso that says the denominator cannot be zero.

Cheers,
Brent
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Re: a^x=b^y=c^z   [#permalink] 08 Nov 2019, 13:07
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