If none of x, y, & z equals to 0, is x^4y^5z^6 0?

Question

If none of x, y, & z equals to 0, is  x^4y^5z^6 > 0 ?

(1)  y > x^4

(2)  y > z^5

MikeScarn · Answer

Statement (1) tells us that y >0 because x^4 must be positive.

This is sufficient. If neither x, y, or z = 0  and y is positive , then we know that  x^4y^5z^6 > 0  = positive

Statement (2) does not tell us that y is positive or negative. z could be negative which would make  z^5  negative.

Not Sufficient.

Answer = A

LevanKhukhunashvili · Answer

x and z will always be positive, despite the +- nature of x,z as they have even powers.
We have to detect weather y is + or -

1. y is greater than positive  x^4 . y is positive. suff.
2. as we dont know the +- nature of z, we cant say for sure y is positive or not. not suff

IMO
Ans:  A

MsInvBanker · Answer

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

INSUFFICIENT

The answer is A.

KSBGC · Answer

x^4  and  z^6 yields a positive result . thus we all about need to know whether y is positive.

Statement 1:  y>x^4 .  x^4  will always be positive. thus y has to be positive. Sufficient.

Statement :  y>z^5 . NOT clear. z= -2. z^5 = -32  and y = -2. NOT sufficient.

The best answer is A.

If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?