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# If x and y are positive integers, what is the

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Joined: 12 Feb 2017
Posts: 70
If x and y are positive integers, what is the  [#permalink]

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Updated on: 03 Dec 2017, 10:12
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Difficulty:

75% (hard)

Question Stats:

51% (01:38) correct 49% (01:47) wrong based on 82 sessions

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If x and y are positive integers, what is the value of x^y?

1) y^x= 9
2) x^(2y)= 64

Kudos if it helps.

Originally posted by pushkarajnjadhav on 03 Dec 2017, 09:34.
Last edited by pushkarajnjadhav on 03 Dec 2017, 10:12, edited 1 time in total.
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Re: If x and y are positive integers, what is the  [#permalink]

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03 Dec 2017, 09:53
2
If x and y are positive integers, what is the value of x^y?

1) y^x= 9
2) x^(2y)= 64

I do not agree with the Official answer provided for this question. That is why I am posting this one to have a discussion.
Kudos if it helps.

Statement 1: if $$y=9$$ & $$x=1$$, then $$x^y=1$$

and if $$y=3$$ & $$x=2$$, then $$x^y=8$$. Hence Insufficient

Statement 2: $$x^{2y}=(x^y)^2=64$$

Taking square root of both sides $$x^y=8$$ (as $$x$$ & $$y$$ are positive so $$-8$$ is not possible). Sufficient

Option B
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Re: If x and y are positive integers, what is the  [#permalink]

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26 Feb 2018, 13:54
If x and y are positive integers, what is the value of x^y?

1) y^x= 9
2) x^(2y)= 64

Statement 2:
y^x = 9 have many different solutions: 9^1 =9; 3^2 = 9; -3^2 = 9...

Statement 2:
x^2y = 64 also has many solutions but they all give you the same result for x^y. Let's check:
2^6 = 64; so x=2 and y = 3 =>x^y =8
4^3 = 64; so x=4 and y = 3/2 => x^y = 8
8^2 = 64; so x =8 and y =1 => x^y = 8

Statement 2 is sufficient! B
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Re: If x and y are positive integers, what is the   [#permalink] 26 Feb 2018, 13:54
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