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What is the value of xy?
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Updated on: 06 Mar 2014, 00:03
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What is the value of xy? (1) \(3^x*5^y=75\) (2) \(3^{(x1)(y2)}=1\) M2722
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Originally posted by swati007 on 05 Mar 2014, 20:12.
Last edited by Bunuel on 06 Mar 2014, 00:03, edited 1 time in total.
Renamed the topic and edited the question.



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What is the value of xy?
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06 Mar 2014, 00:05
swati007 wrote: What is the value of xy?
(1) \(3^x*5^y=75\)
(2) \(3^{(x1)(y2)}=1\)
M2722 What is the value of \(xy\)?Notice that we are not told that the \(x\) and \(y\) are integers.(1) \(3^x*5^y=75\) > if \(x\) and \(y\) are integers then as \(75=3^1*5^2\) then \(x=1\) and \(y=2\) BUT if they are not, then for any value of \(x\) there will exist some noninteger \(y\) to satisfy given expression and viseversa (for example if \(y=1\) then \(3^x*5^y=3^x*5=75\) > \(3^x=25\) > \(x=some \ irrational \ #\approx{2.9}\)). Not sufficient. (2) \(3^{(x1)(y2)}=1\) > \((x1)(y2)=0\) > either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient. (1)+(2) If from (2) \(x=1\) then from (1) \(3^x*5^y=3*5^y=75\) > \(y=2\) and if from (2) \(y=2\) then from (1) \(3^x*5^y=3^x*25=75\) > \(x=1\). Thus \(x=1\) and \(y=2\). Sufficient. Answer: C. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank youl.
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Re: What is the value of xy?
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06 Mar 2014, 00:49
swati007 wrote: What is the value of xy? (1) \(3^x*5^y=75\)
(2) \(3^{(x1)(y2)}=1\)
M2722 Since we do not know that x and y are integers hence statement I and II will be insufficient as we can have multiple answers. Combining will be sufficient here as we will have two equations and two answers.
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Re: What is the value of xy?
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01 Jun 2014, 13:33
CrackVerbalGMAT wrote: swati007 wrote: What is the value of xy? (1) \(3^x*5^y=75\)
(2) \(3^{(x1)(y2)}=1\)
M2722 Since we do not know that x and y are integers hence statement I and II will be insufficient as we can have multiple answers. Combining will be sufficient here as we will have two equations and two answers. Very nice and easy explanation.



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Re: What is the value of xy?
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30 Aug 2017, 04:56
Bunuel wrote: swati007 wrote: What is the value of xy?
(1) \(3^x*5^y=75\)
(2) \(3^{(x1)(y2)}=1\)
M2722 What is the value of \(xy\)?Notice that we are not told that the \(x\) and \(y\) are integers.(1) \(3^x*5^y=75\) > if \(x\) and \(y\) are integers then as \(75=3^1*5^2\) then \(x=1\) and \(y=2\) BUT if they are not, then for any value of \(x\) there will exist some noninteger \(y\) to satisfy given expression and viseversa (for example if \(y=1\) then \(3^x*5^y=3^x*5=75\) > \(3^x=25\) > \(x=some \ irrational \ #\approx{2.9}\)). Not sufficient. (2) \(5^{(x1)(y2)}=1\) > \((x1)(y2)=0\) > either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient. (1)+(2) If from (2) \(x=1\) then from (1) \(3^x*5^y=3*5^y=75\) > \(y=2\) and if from (2) \(y=2\) then from (1) \(3^x*5^y=3^x*25=75\) > \(x=1\). Thus \(x=1\) and \(y=2\). Sufficient. Answer: C. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank youl. Hello Bunuel  I have a question on this solution, I remember reading somewhere on ur post that GMAT always prefers rational numbers, in that case will this solution still exist? Not sure if I am getting it wrong? Posted from my mobile device
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Re: What is the value of xy?
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30 Aug 2017, 05:02
ydmuley wrote: Bunuel wrote: swati007 wrote: What is the value of xy?
(1) \(3^x*5^y=75\)
(2) \(3^{(x1)(y2)}=1\)
M2722 What is the value of \(xy\)?Notice that we are not told that the \(x\) and \(y\) are integers.(1) \(3^x*5^y=75\) > if \(x\) and \(y\) are integers then as \(75=3^1*5^2\) then \(x=1\) and \(y=2\) BUT if they are not, then for any value of \(x\) there will exist some noninteger \(y\) to satisfy given expression and viseversa (for example if \(y=1\) then \(3^x*5^y=3^x*5=75\) > \(3^x=25\) > \(x=some \ irrational \ #\approx{2.9}\)). Not sufficient. (2) \(5^{(x1)(y2)}=1\) > \((x1)(y2)=0\) > either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient. (1)+(2) If from (2) \(x=1\) then from (1) \(3^x*5^y=3*5^y=75\) > \(y=2\) and if from (2) \(y=2\) then from (1) \(3^x*5^y=3^x*25=75\) > \(x=1\). Thus \(x=1\) and \(y=2\). Sufficient. Answer: C. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank youl. Hello Bunuel  I have a question on this solution, I remember reading somewhere on ur post that GMAT always prefers rational numbers, in that case will this solution still exist? Not sure if I am getting it wrong? Posted from my mobile deviceIt's not a matter of preferences, If a solution exits, it exists and if it does not then well it does not. Here, for (1) x and y could be irrational, so the statement is not sufficient.
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Re: What is the value of xy?
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30 Aug 2017, 06:06
Bunuel wrote: P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to rule 3. Thank youl. Hello Bunuel  I have a question on this solution, I remember reading somewhere on ur post that GMAT always prefers rational numbers, in that case will this solution still exist? Not sure if I am getting it wrong? Posted from my mobile device[/quote] It's not a matter of preferences, If a solution exits, it exists and if it does not then well it does not. Here, for (1) x and y could be irrational, so the statement is not sufficient.[/quote] Got it thanks Bunuel Posted from my mobile devicePosted from my mobile device
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What is the value of xy?
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31 Aug 2017, 03:35
Bunuel wrote: (2) \(3^{(x1)(y2)}=1\) > \((x1)(y2)=0\) > either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient.
Dear BunuelI know that 3^0 = 1. But why did you limited \((x1)(y2)=0\). Why did not you consider \((x1)(y2)=10\) or any value. 1^ (any value) = 1. Thanks



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Re: What is the value of xy?
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31 Aug 2017, 04:27
Mo2men wrote: Bunuel wrote: (2) \(3^{(x1)(y2)}=1\) > \((x1)(y2)=0\) > either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient.
Dear BunuelI know that 3^0 = 1. But why did you limited \((x1)(y2)=0\). Why did not you consider \((x1)(y2)=10\) or any value. 1^ (any value) = 1. Thanks Hello, let me try to explain here: Given is  \(3^{(x1)(y2)}=1\) This is only possible when the power of 3 is ZERO. Hence, we have equate the power of three, in this case \((x1)(y2)\) as ZERO and it cannot be equal to any other number. Hope this is clear. Posted from my mobile device



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What is the value of xy?
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11 Sep 2018, 05:45
Bunuel ydmuleySorry guys, I still have a problem with this: In statement 2, why we assumed that (x1)(y2) is an integer (zero)? it might be any ir/rational number that when powered to 3 equals 1.



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