tabsang wrote:If x,y and z are non-zero integers and m and n are positive even integers, where m > n.
Is ((x^m)*z)/(y^n) > 1 ?
(1) |z| > |x| > |y|
(2) x^m > (y^n)/z
Statement 2: x^m > (y^n)/z
Since z is nonzero, z² must be positive.
Thus, we can multiply each side by z² without having to worry about the direction of the inequality:
(x^m)z² > ((y^n)/z) * z²
(x^m)z² > (y^n)z
(x^m)z² - (y^n)z > 0
z * ((x^m)z - y^n) > 0.
The result above implies two cases.
Case 1:
If z>0, then (x^m)z - y^n) > 0, implying that (x^m)z > y^n and that ((x^m)*z)/(y^n) > 1.
The following combination satisfies the conditions in the question stem and those in the two statements:
x=2, m=4, z=10, y=1, and n=2.
When we plug these values into the question stem, we get:
(2�)(10) / 1² > 1.
Case 2:
If z<0, then (x^m)z - y^n < 0, implying that (x^m)z < y^n and that ((x^m)*z)/(y^n) < 1.
The following combination satisfies the conditions in the question stem and those in the two statements:
x=2, m=4, z=-10, y=1, and n=2.
When we plug these values into the question stem, we get:
(2�)(-10) / 1² < 1.
Since in the first case ((x^m)*z)/(y^n) > 1, and in the second case ((x^m)*z)/(y^n) < 1, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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