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

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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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New post 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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New post 30 Aug 2013, 04:46
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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]

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

Can someone please clarify this??
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Re: If x, y and z are integers, what is y – z? [#permalink]

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

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New post 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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Extra-hard Quant Tests with Brilliant Analytics

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

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

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