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What is the value of xy? [#permalink]
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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? [#permalink]
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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? [#permalink]
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06 Mar 2014, 00:49
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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? [#permalink]
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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? [#permalink]
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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? [#permalink]
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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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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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Re: What is the value of xy? [#permalink]
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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? [#permalink]
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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? [#permalink]
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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




Re: What is the value of xy?
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