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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]  21 Jul 2013, 07:14
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Question Stats:

64% (02:22) correct 36% (01:53) wrong based on 122 sessions
If x, y and z are integers, what is y – z?

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

(2) $$10^y = 20^x5^{z+1}$$
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Kudos [?]: 62507 [2] , given: 9457

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

Hope it's clear.
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Kudos [?]: 1613 [1] , given: 219

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