shivanigs wrote:If x^3 y^4= 5,000, is y = 5?

(1) y is a positive integer.
(2) x is an integer.

5000 = 5*5*5*5*2*2*2
= (2^3)(5^4)

Statement 1: y is a positive integer.
This one looks promising, but we aren't told whether or not x is an integer.
So, we have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=1 and x= the cube root of 5000. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: x is an integer.
We have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=-5 and x=3. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2:
If x and y are both integers and y is a positive integer, it must be the case that x=3 and y=5
SUFFICIENT

Answer = C

Cheers,
Brent