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# a^x=b^y=c^z

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Manager
Joined: 17 Aug 2019
Posts: 213
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Kudos [?]: 28 [0], given: 50

a^x=b^y=c^z [#permalink]  06 Nov 2019, 06:04
00:00

Question Stats:

48% (01:30) correct 51% (01:52) wrong based on 27 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.
Intern
Joined: 04 Nov 2019
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Kudos [?]: 3 [1] , given: 4

Re: a^x=b^y=c^z [#permalink]  06 Nov 2019, 09:19
1
KUDOS
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
Founder
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Kudos [?]: 2785 [1] , given: 10593

Re: a^x=b^y=c^z [#permalink]  07 Nov 2019, 14:03
1
KUDOS
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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Intern
Joined: 09 Dec 2018
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Kudos [?]: 18 [0], given: 20

Re: a^x=b^y=c^z [#permalink]  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.
GRE Instructor
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Kudos [?]: 3644 [2] , given: 61

Re: a^x=b^y=c^z [#permalink]  08 Nov 2019, 13:07
2
KUDOS
Expert's post
Asmakan 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
_________________

Brent Hanneson – Creator of greenlighttestprep.com

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