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Manager  Joined: 14 Jun 2011
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What is the value of xy?  [#permalink]

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Question Stats: 27% (01:43) correct 73% (01:33) wrong based on 296 sessions

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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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Kudos always encourages me

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.
Math Expert V
Joined: 02 Sep 2009
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What is the value of xy?  [#permalink]

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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.

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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GMAT 1: 780 Q51 V46 Re: What is the value of xy?  [#permalink]

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

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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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Joined: 19 Mar 2014
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Re: What is the value of xy?  [#permalink]

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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.

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
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

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

Math Expert V
Joined: 02 Sep 2009
Posts: 53738
Re: What is the value of xy?  [#permalink]

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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.

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

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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

Posted from my mobile device

Posted from my mobile device
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

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

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Joined: 26 Mar 2013
Posts: 2098
What is the value of xy?  [#permalink]

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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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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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What is the value of xy?  [#permalink]

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Bunuel ydmuley
Sorry guys, I still have a problem with this:
In statement 2, why we assumed that (x-1)(y-2) is an integer (zero)? it might be any ir/rational number that when powered to 3 equals 1.
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Joined: 02 Sep 2009
Posts: 53738
Re: What is the value of xy?  [#permalink]

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HisHo wrote:
Bunuel ydmuley
Sorry guys, I still have a problem with this:
In statement 2, why we assumed that (x-1)(y-2) is an integer (zero)? it might be any ir/rational number that when powered to 3 equals 1.

No. Only 3 in the power of 0 equals to 1.
_________________ Re: What is the value of xy?   [#permalink] 11 Sep 2018, 05:57
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# What is the value of xy?

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