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kingflo
Current Student
Joined: 26 Jun 2012
Last visit: 06 Jul 2021
Posts: 24
Given Kudos: 1
Location: Germany
Concentration: Leadership, Finance
Schools: IMD '15 (M) INSEAD Jan '15 (A) LBS '16
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
21 Jul 2013, 08:14
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
71% (02:24) correct
29%
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Not Attempted Yet
If x, y and z are integers, what is y – z?
(1) \(100^x = 2^y5^z\)
(2) \(10^y = 20^x5^{z+1}\)
(1) \(100^x = 2^y5^z\)
(2) \(10^y = 20^x5^{z+1}\)
21 Jul 2013, 08:41
Kudos
Bookmarks
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
(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
30 Aug 2013, 04:46
Kudos
Bookmarks
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.
(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.
