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What is the value of xy?

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What is the value of xy? [#permalink]

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What is the value of xy?

(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22

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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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New post 06 Mar 2014, 00:05
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swati007 wrote:
What is the value of xy?

(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22


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 non-integer \(y\) to satisfy given expression and vise-versa (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) \(3^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> 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/rules-for-pos ... 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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New post 06 Mar 2014, 00:49
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swati007 wrote:
What is the value of xy?
(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22


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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New post 01 Jun 2014, 13:33
CrackVerbalGMAT wrote:
swati007 wrote:
What is the value of xy?
(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22


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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New post 30 Aug 2017, 04:56
Bunuel wrote:
swati007 wrote:
What is the value of xy?

(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22


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 non-integer \(y\) to satisfy given expression and vise-versa (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) \(5^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> 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/rules-for-pos ... 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?

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Re: What is the value of xy? [#permalink]

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New post 30 Aug 2017, 05:02
ydmuley wrote:
Bunuel wrote:
swati007 wrote:
What is the value of xy?

(1) \(3^x*5^y=75\)

(2) \(3^{(x-1)(y-2)}=1\)

M27-22


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 non-integer \(y\) to satisfy given expression and vise-versa (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) \(5^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> 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/rules-for-pos ... 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


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.
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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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New post 30 Aug 2017, 06:06
Bunuel wrote:

P.S. Please read carefully and follow: http://gmatclub.com/forum/rules-for-pos ... 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

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Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

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What is the value of xy? [#permalink]

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New post 31 Aug 2017, 03:35
Bunuel wrote:

(2) \(3^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient.


Dear Bunuel

I know that 3^0 = 1. But why did you limited \((x-1)(y-2)=0\). Why did not you consider \((x-1)(y-2)=10\) or any value. 1^ (any value) = 1.

Thanks
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Re: What is the value of xy? [#permalink]

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New post 31 Aug 2017, 04:27
Mo2men wrote:
Bunuel wrote:

(2) \(3^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient.


Dear Bunuel

I know that 3^0 = 1. But why did you limited \((x-1)(y-2)=0\). Why did not you consider \((x-1)(y-2)=10\) or any value. 1^ (any value) = 1.

Thanks


Hello, let me try to explain here:

Given is - \(3^{(x-1)(y-2)}=1\)

This is only possible when the power of 3 is ZERO.

Hence, we have equate the power of three, in this case


\((x-1)(y-2)\) as ZERO and it cannot be equal to any other number.

Hope this is clear.

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Re: What is the value of xy?   [#permalink] 31 Aug 2017, 04:27
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