Bunuel wrote:
If none of x, y, & z equals to 0, is \(x^4y^5z^6 > 0\)?
(1) \(y > x^4\)
(2) \(y > z^5\)
For \(x^4y^5z^6 > 0\) to be true, \(x^4\), \(y^5\) and \(z^6\) have to be all positive numbers.
x and z could be negative numbers themselves but their positive even powers will turn them into positive numbers.
The real question here is if y is a positive number or negative.
(1) \(y > x^4\)
\(x^4\) we know is an even number because of the positive even power of x and if y is greater than that, it means y is a positive number.
Thus, Positive x Positive x Positive > 0
SUFFICIENT(2) \(y > z^5\)
If z is positive, \(z^5\) will be positive and a y greater than that will be positive too. That will result in Even x Even x Even > 0
However, if z is negative, \(z^5\) will be negative as well and a y greater than that could either be negative or positive.
Thus, Positive x Negative x Positive < 0
INSUFFICIENTThe answer is A.
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