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If x is a non-zero integer, what is the value of xy?

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Bunuel
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If x is a non-zero integer, what is the value of xy? [#permalink] New post   06 Nov 2014, 09:20
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Tough and Tricky questions: Algebra.



If x is a non-zero integer, what is the value of xy?


(1) x = 2

(2) \(128^x*6^{(x + y)} = 48^{(2x)}*3^{(-x)}\)


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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   06 Nov 2014, 10:24
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Statement 1 is clearly insufficient.
Statement 2: You can combine all the bases with the exponent "x". They all end up cancelling out and yielding 6^y=1^x. Here, 1^x is always equal to 1, so 6^y=1 and that should be sufficient.

Answer B
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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   06 Nov 2014, 13:15
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Statement 1 not sufficient since we clearly dont know value of y
Statement 2 can be simplified to reach 2^y*3^y=1, 6^y=1
This means y=0
This is enough to find xy that is 0

Answer B
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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   06 Nov 2014, 20:06
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Statement 1 is clearly insufficient, since we don't know the value of y

Statement 2:
128^x*6^(x + y) = 48^(2x)*3^(-x)

This can be simplified as

2^8x * 2^y * 3^x*3^y = 2^8x*3^x
=> 2^y *3^y=1
Only possible if y = 0

Therefore xy = 0. Sufficient

Hence B) is the answer
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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   06 Nov 2014, 23:58
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If x is a non-zero integer, what is the value of xy?

(1) x = 2
(2) 128^x*6^(x + y) = 48^(2x)*3^(-x)

Kudos for a correct solution.



Statmnt1) Nothing we know about Y...Insuff

Statmnt2)
2^7x * 2^(x+y) * 3^(x+y) = 3^2x*2^8x*3^(-x)
2^8x+y * 3^(x+y) = 3^x * 2^8x

so y=0 -> xy=0

Suff, IMO B
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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   29 Jan 2017, 03:50
If x is a non-zero integer, what is the value of xy?

x could negative or positive integer. y could be any number

(1) x = 2

No info about y.

Insufficient

(2) 128^x*6^(x + y) = 48^(2x)*3^(-x)

Simplifying the equation above keeping an eye of 3 as it has x & y......... 3^(x+y) = 3^x

x+y=x............then y=0

xy=0

Sufficient

Answer: B
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Re: If x is a non-zero integer, what is the value of xy? [#permalink] New post   12 Oct 2023, 09:34
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Re: If x is a non-zero integer, what is the value of xy? [#permalink]
12 Oct 2023, 09:34
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