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If x, y and z are integers, what is y – z?

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If x, y and z are integers, what is y – z? [#permalink] New post 21 Jul 2013, 07:14
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If x, y and z are integers, what is y – z?

(1) 100^x = 2^y5^z

(2) 10^y = 20^x5^{z+1}
[Reveal] Spoiler: OA
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Re: If x, y and z are integers, what is y – z? [#permalink] New post 21 Jul 2013, 07:41
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If x, y and z are integers, what is y – z?

(1) 100^x = 2^y5^z
2^{2x}5^{2x}=2^y5^z so y-z=2x-2x=0.
Sufficient

(2) 10^y = 20^x5^{z+1}
2^y5^y=2^{2x}5^x5^{z+1} so y=2x and y=x+z+1. We cannot determine y-z.
Consider y=4,x=2 and z=1 so y-z=3; or y=8,x=4 and y=3 so y-z=5.
Not sufficient

A
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Re: If x, y and z are integers, what is y – z? [#permalink] New post 29 Aug 2013, 22:09
I could not get the explanation here, can anybody explain this, please ?
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Re: If x, y and z are integers, what is y – z? [#permalink] New post 30 Aug 2013, 03:46
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vishalrastogi wrote:
I could not get the explanation here, can anybody explain this, please ?


If x, y and z are integers, what is y – z?

(1) 100^x = 2^y5^z --> 2^{2x}5^{2x}=2^y5^z --> equate the exponents: 2x=y and 2x=z --> thus 2x-2x=y-z=0. Sufficient.

(2) 10^y = 20^x5^{z+1} --> 2^y5^y=2^{2x}*5^{x+z+1} --> y=2x and y=x+z+1. We cannot get the value of y-z from this. Not sufficient,

Answer: A.

Hope it's clear.
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Re: If x, y and z are integers, what is y – z?   [#permalink] 30 Aug 2013, 03:46
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