SOLUTION: If (x^2)(y^3)(z^5) is positive, which product is always positive? A) xz B) (y^2)z C) yz D) xy E) y(z^2) Please explain how I could approach this probelem (ie. plugging in

Question 472220: If (x^2)(y^3)(z^5) is positive, which product is always positive?
A) xz
B) (y^2)z
C) yz
D) xy
E) y(z^2)
Please explain how I could approach this probelem (ie. plugging in numbers...?) and why the answer is correct.
Thanks!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assuming x,y,z are real numbers not equal to zero, we can say that x^2 is always positive, so x can be either positive or negative. This, however, eliminates choices A and D from always being positive, because if z or y were positive, x could be negative, and vice versa.

We can infer that (y^3)(z^5) is always positive. Hence, y and z must have the same sign. This eliminates choices B and E, because squares are always positive (in this case), and y or z could be negative. This leaves answer choice C as our only option (which must be positive anyway, because y,z have the same sign).
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