Given: (xy)^3 * y = (10)^3 * 5;
is y = 5 ?

Workout:
xy = 10 , x.y = (2,5) or (-2,-5) , (5,2) ,(-5,-2)
when y =2;
(10)^3 * 2 = 2000 != 5000 hence = y = (5,-5);

1.Y is positive => y = 5 : A sufficient
2. X is an integer : This is of no use.

Ans;A

Sorry...the answer is different.

Can anyone help?

.. Me going with C ..

5000 when factorized can be written as 2^3*5^4 ..

... the first statement says that y is a positive integer .. but it does not say anything about x .. so y could be 5 ( in which case x will be an integer i.e. 2) or y could be some other positive integer like 6,7,8 etc which will make x a fraction .. so this statement is insufficient .

the second statement says x is an integer .. again nothing is said about y so the 2nd statement is also insufficient ..

Combine the 2 statements and we get both x,y are integers and both are positive and the only possibility is x =2 and y = 5 .. so C ..

I agree with gabriel, the ans should be C

5000 =2^3 * 5 ^4

however the question doesn't mention that x & y are integers
which is a must on the GMAT to work with integers

so here we cannot assume that x & y are integers, hence they can be fractions (decimals)

so stmt 1 : says that y is +ve integer , but we cannot assume that x is an integer, it may still be a fraction, In these cases one should just assume and not try to solve as when we use fractions specially with exponents there is very high probabilty that we may get a decimal nos, suppose in this case if we assume that x is fraction we may get a value like 4999.9..
or 5000.0... when multiplied with integer value of y which may not be 5.
Now such a decimal value can be considered 5000.
So it is NOT SUFF

stm2 : this reassures us that x is an integer but same logic above can be used to convey that y is a decimal.

combined: then we can say that both are integers and then x=2 & y=5

ONE IMPORTANT thing that I would like to add through my observations, here is that if you causually let off a DATA SUFFICIENCY statement like the second one here, there is a good chance that your answer will be incorrect. So before locking an answer one needs to carefully analyse what role a statement plays in the context of the problem, no matter how adjunct the statement may seem.

Thanks
Samir

Thank you - OA is C.