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Bunuel
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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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Bunuel

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


(1) x = 2
Since y is unknown
Not sufficient

(2) \(128^x*6^{(x + y)} = 48^{(2x)}*3^{(-x)}\)
2^{7x}*2^{x+y}*3^{x+y}=2^{8x}*3^{2x}*3^{-x}
2^{8x+y}*3^{x+y} = 2^{8x}*3^{x}
y=0
xy=0
Sufficient

IMO B
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