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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

1

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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 _________________

It is beyond a doubt that all our knowledge that begins with experience.

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,

Answer: A.

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.

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

ashutoshyadav1707 wrote:

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,

Answer: A.

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. _________________

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. _________________

Give Kudos if you want to say thanks

gmatclubot

Re: If x, y and z are integers, what is y – z?
[#permalink]
02 May 2016, 16:58

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