If X and Y are positive Integers and x^3y^4 = 2,000, which

[MaxF412]

If X and Y are positive Integers and x^3y^4 = 2,000, which of the followiung is the value of xy?

A. 2
B. 4
C. 8
D. 10
E. 20

I found out the answer in an untimed environment to be 10 by testing each answer choice and then settling on C by breaking it down into 5^3 X 2^4, however I was wondering if there is an easier/quick way to get through this problem. Thank you!

[slaughterGMAT]

Factor 2000 = 2*2*2*2*5*5*5, which clearly show that x=2 and y=5, so xy = 10.

[RonPurewal]

If X and Y are positive Integers and x^3y^4 = 2,000, which of the followiung is the value of xy?

A. 2
B. 4
C. 8
D. 10
E. 20

I found out the answer in an untimed environment to be 10 by testing each answer choice and then settling on C by breaking it down into 5^3 X 2^4, however I was wondering if there is an easier/quick way to get through this problem. Thank you!

you should do that factoring at the beginning.

you have 2 to the fourth power, so 2 needs to be part of "y"; you have 5 to the third power, so 5 needs to be part of "x". the only way to accomplish both of these things is to have y = 2 and x = 5.