If xy does not equal zero, what is the value of xy?

Question

Tough and Tricky questions: Algebra.

(1) 2/x + 2/y = 3 
(2) x^3 – (2/y)^3 = 0

Kudos for a correct  solution .

sarjve · Answer

first is obviously not enough. but the second gives us an answer.
x^3-(2/y)^3=0
x^3=2^3/y^3
x^3*y^3=2^3
(xy)^3=2^3
xy=2

answer is B

kinghyts · Answer

Statement 1 is clearly insufficient since 
1/x+1/y = 3/2 --> from this we can't get the value of xy

Statement 2 is sufficient 
(xy)^3 = 8

therefore xy = 8

siddharthkapoor · Answer

If xy does not equal zero, what is the value of xy?

(1) 2/x + 2/y = 3
(2) x^3 – (2/y)^3 = 0

If xy is not equal to 0, it implies that both x and y are not 0, so x and y belong to real numbers, except 0.

(1) => 2y+2x=3xy
=> 2(x+y)=3xy
=> xy=2(x+y)/3
Since we don't know the value of (x+y), we can't find the value of xy from this statement.
Thus, insufficient.

(2) => (xy)^3-8=0
=> xy=(8)^1/3
=> xy=2
Thus, sufficient.

So, the answer is option B.

chiragmaniar · Answer

Is there a way we can rule out statement 1.?

2/x + 2/y = 3
2x + 2y / xy = 3
x + y / xy = 3/2

Doesn't this imply that xy=2 as this is the only combination that fits in the above equation. Not sure if I am missing something here.

Bunuel · Answer

You are assuming that x and y are integers, which is not given here. For non-integer solutions xy is not 2.

hemantbafna · Answer

xy not equal to 0.
(1) 2/x+2/y=3
2y+2x/xy=3

We have value of xy in terms of x+y, which is not defined.

Not Sufficient.

(2) x^3-(2/y)^3=0
x^3- 8/y^3=0
(xy)^3-8=0
xy=2

Sufficient.

B

Zarky · Answer

Bunuel  In the second statement, why are we cross multiplying x^3 with y^3 when we do not know the signs of x and y? Isn't the rule to cross multiply only when the variables are explicitly mentioned to be positive or carry even powers?

Bunuel · Answer

We are concerned with the sign when we are dealing with inequalities. If you multiply an inequality by a negative number you should flip the sign but when you multiply an inequality by a positive number you should keep the sign. Here we have an equation, not an inequality, so it's ok to cross-multiply.

Harsh9676 · Answer

IMO B

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If xy does not equal zero, what is the value of xy?

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