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What is the value of xy?

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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
[Reveal] Spoiler: OA

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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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Re: gmat club test question M27-22 [#permalink]

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New post 05 Mar 2014, 23:08
swati007 wrote:
What is the value of xy?

(1) 3x∗5y=75

(2) 3^(x−1)(y−2)=1



A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.


B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.


C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


D) EACH statement ALONE is sufficient.


E) Statements (1) and (2) TOGETHER are NOT sufficient[/list]


I could not find the explanation anywhere on gmat club hence posting the question.


There seems to be a typo here. Kindly put up the correct question.
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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.

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?

Posted from my mobile device
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Re: What is the value of xy? [#permalink]

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New post 30 Aug 2017, 05:02
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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.

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

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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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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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