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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]

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21 Jul 2013, 08:14
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63% (02:27) correct 37% (01:56) wrong based on 152 sessions

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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]

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21 Jul 2013, 08:41
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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

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Re: If x, y and z are integers, what is y – z? [#permalink]

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29 Aug 2013, 23:09
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]

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30 Aug 2013, 04:46
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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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Re: If x, y and z are integers, what is y – z? [#permalink]

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01 May 2016, 10:32
WHaaaaTT!???

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Re: If x, y and z are integers, what is y – z? [#permalink]

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01 May 2016, 10:54
Bunuel wrote:
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.

How can 1 be sufficient??? In the given statement, its 5 raise to the power 2. And the solution you have provided considers it as 5 raise to the power z.
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Re: If x, y and z are integers, what is y – z? [#permalink]

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02 May 2016, 04:07
Expert's post
Bunuel wrote:
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.

How can 1 be sufficient??? In the given statement, its 5 raise to the power 2. And the solution you have provided considers it as 5 raise to the power z.

It's 5^z both in the question and in the solution.
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Re: If x, y and z are integers, what is y – z? [#permalink]

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02 May 2016, 16:58
I think what's confusing some folks is the second equation is giving y = x+z+1 bringing z to the left side. y-z = x+1.
This still doesn't give a value for y-z. Question is asking for a value for y-z and not if you can deduce an expression for y-z. I made this silly mistake once in the heat of the moment so sharing it here.
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Re: If x, y and z are integers, what is y – z?   [#permalink] 02 May 2016, 16:58
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