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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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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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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 \(yz=2x2x=0\). 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 yz. Consider y=4,x=2 and z=1 so yz=3; or y=8,x=4 and y=3 so yz=5. Not sufficient A
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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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Re: If x, y and z are integers, what is y – z? [#permalink]
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02 May 2016, 04:07
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 \(2x2x=yz=0\). 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 yz 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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Re: If x, y and z are integers, what is y – z? [#permalink]
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02 May 2016, 16:58
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I think what's confusing some folks is the second equation is giving y = x+z+1 bringing z to the left side. yz = x+1. This still doesn't give a value for yz. Question is asking for a value for yz and not if you can deduce an expression for yz. 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]
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17 Nov 2016, 18:58
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 \(2x2x=yz=0\). Sufficient. Answer: A. Hope it's clear. If yz=0, then y=z. If i put the value of y=z, how can we legitimate the statement 1? statement 1: \(100^x = 2^y5^z\) \(2^{2x}5^{2x}=2^z5^z\) To legitimate the statement 1 we still need the value of x and z. But, they are still unknown here. How can you make known it for all? Then, how can we conclude it? BunuelThank you...
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Re: If x, y and z are integers, what is y – z? [#permalink]
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17 Nov 2016, 21:50
iMyself 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 \(2x2x=yz=0\). Sufficient. Answer: A. Hope it's clear. If yz=0, then y=z. If i put the value of y=z, how can we legitimate the statement 1? statement 1: \(100^x = 2^y5^z\) \(2^{2x}5^{2x}=2^z5^z\) To legitimate the statement 1 we still need the value of x and z. But, they are still unknown here. How can you make known it for all? Then, how can we conclude it? BunuelThank you... The question asks the value of y  z, not the individual value of x, y, and z. From the solution we got that y  z = 0.
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Re: If x, y and z are integers, what is y – z? [#permalink]
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17 Nov 2016, 22:06
But how did you get the value of yz , i did not get from your explanation actually. Thank you... Sent from my iPhone using GMAT Club Forum mobile app
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Re: If x, y and z are integers, what is y – z? [#permalink]
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Re: If x, y and z are integers, what is y – z? [#permalink]
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18 Nov 2016, 07:57
Bunuel wrote: iMyself wrote: But how did you get the value of yz , i did not get from your explanation actually. Thank you... Sent from my iPhone using GMAT Club Forum mobile appx, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) > equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z. This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y > 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos'
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Re: If x, y and z are integers, what is y – z? [#permalink]
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20 Nov 2016, 03:22
iMyself wrote: Bunuel wrote: iMyself wrote: But how did you get the value of yz , i did not get from your explanation actually. Thank you... Sent from my iPhone using GMAT Club Forum mobile appx, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) > equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z. This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y > 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos' We can only do this here because we know that x, y, and z are integers.
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Re: If x, y and z are integers, what is y – z? [#permalink]
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20 Nov 2016, 03:30
Bunuel wrote: iMyself wrote: Bunuel wrote: x, y, and z are given to be integers. We have \(2^{2x}5^{2x}=2^y5^z\) > equate the exponents of 2 and 5: \(2x=y\) and \(2x=z\). Thus 2x = y = z.
This is the first time i learn that i can equate the exponent after having multiple variables on both side. I, normally, equate the exponent when i have only one part in the right hand side and the other one in the left hand side. like below... 2^{2x}=2^y > 2x=y it is ok. But when it is something like below then it is the first time i learn. \(2^{2x}5^{2x}=2^y5^z\) \(2x=y\) and \(2x=z\). Anyway, many many thanks with 'kudos' We can only do this here because we know that x, y, and z are integers. That means: we can't equate this type of things if the variable is NOT integer, right Bunuel?
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Re: If x, y and z are integers, what is y – z? [#permalink]
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Re: If x, y and z are integers, what is y – z? [#permalink]
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20 Nov 2016, 03:40
Bunuel wrote: iMyself wrote: That means: we can't equate this type of things if the variable is NOT integer, right Bunuel? _______________________ Yes... Thank you Brother with kudos!
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Re: If x, y and z are integers, what is y – z? [#permalink]
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29 Nov 2016, 16:33
kingflo wrote: If x, y and z are integers, what is y – z?
(1) \(100^x = 2^y5^z\)
(2) \(10^y = 20^x5^{z+1}\) We need to determine the value of y – z. Statement One Alone:100^x = 2^y * 5^z Notice that 100^x = (2^2 * 5^2)^x = 2^(2x) * 5^(2x). Equate this with 2^y * 5^z and we have: 2^(2x) * 5^(2x) = 2^y * 5^z Therefore, 2^(2x) = 2^y and 5^(2x) = 5^z. Thus, 2x = y and 2x = z. Therefore, y  z = 2x  2x = 0. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E. Statement Two Alone:10^y = 20^x * 5^(z+1) Since 20^x = (2^2 * 5)^x = 2^(2x) * 5^x, that means 20^x * 5^(z+1) = 2^(2x) * 5^x * 5^(z+1) = 2^(2x) * 5^(x+z+1). Notice that 10^y = (2 * 5)^y = 2^y * 5^y, so we have: 2^y * 5^y = 2^(2x) * 5^(x+z+1) Therefore, 2^y = 2^(2x) and 5^y = 5^(x+z+1). Thus, y = 2x and y = x + z + 1. From the second equation, we have y  z = x + 1. However, since we do not know the value of x, we cannot determine the value of y  z. Statement two alone is not sufficient to answer the question. Answer: A
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Re: If x, y and z are integers, what is y – z? [#permalink]
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05 Dec 2017, 02:25
kingflo wrote: If x, y and z are integers, what is y – z?
(1) \(100^x = 2^y5^z\)
(2) \(10^y = 20^x5^{z+1}\) Agree to the explanations given. However, if x=y=z=0, then the answer must be E. Neither the initial question task nor each of the two conditions stipulate that x can't equal y and z or 0. Why am I not correct?



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