Gmat_mission wrote: ↑

Sat Nov 23, 2019 3:36 am

Is \((x^7)(y^2)(z^3)>0?\)

(1) \(yz<0\)
(2) \(xz>0\)

[spoiler]OA=C[/spoiler]

Source: GMAT Club Tests

This question is tricky in that it exploits a common belief that the square of a number will always be positive.
Examples: 3^2 = 9, (-5)^2 = 25, 1^2 = 1, etc.
However, 0^2 is not positive. So, the belief falls apart here.

What we can say is: the square of a number will always be greater than or equal to zero.

Now on to the question.

Statement 1: yz < 0
consider 2 cases:
case a) x=1, y=-1, z=1. In this case, (x^7)(y^2)(z^3) is greater than 0
case b) x=-1, y=-1, z=1. In this case, (x^7)(y^2)(z^3) is not greater than 0
INSUFFICIENT

Statement 2: xz > 0
consider 2 cases:
case a) x=1, y=1, z=1. In this case, (x^7)(y^2)(z^3) is greater than 0
case b) x=1, y=0, z=1. In this case, (x^7)(y^2)(z^3) is not greater than 0
INSUFFICIENT

Statements 1& 2
Statement 1 eliminates the possibility that y=0 and z=0
Statement 2 eliminates the possibility that x=0 and z=0
So, we know that no variable equals 0

At this point, we can use two nice rules:
If k does not equal zero, then k^(even #) is positive
If k does not equal zero, then k^(odd #)has the same sign as k

So, if xz > 0 (from statement 1), then (x^7)(z^3) > 0
In other words, (x^7)(z^3) is positive
Also, if y does not equal 0, we know that (y^2) is positive.

So, altogether, we can see that (x^7)(y^2)(z^3) = (positive)(positive) = positive
In other words, (x^7)(y^2)(z^3) > 0

SUFFICIENT

Answer: C

Cheers,
Brent