by n00bpron00bpron00b Fri Sep 26, 2014 7:50 am
Hey,
X,Y,R,T are integers
#1) x^y is negative
which means,
value of X is negative (can be even or odd ; does not matter)
value of Y is Odd
pick any random integer values satisfying the above conditions,
if x = -3 & y = 3
(-3)^3 = -27
if x= -2 & y = 1
(-2)^1 = -2
Y cannot be "even" in this case (negative base with an even exponent will make it positive) and X cannot be positive
#2) r^t is positive and t is not a multiple of 2
t is not a multiple of 2 => value of "t" is odd
if "t" is odd then the base (i.e. "r") has to be positive for the end result (r^t) to be positive
Because a negative base raised to and odd exponent will give us a negative end result (-3)^3 = -27
pick any random integer values satisfying the above conditions,
r = 2 (can be even or odd, must strictly positive)
t = 3
r^t = (2)^3 = 8
Let's see the answer choices using the following info -
#) X is negative and Y is ODD
#) R is positive and T is ODD
1) xr > 0
from above we know,
x is negative and r is positive
so "x * r" will be negative
2) x - r < 0
x is negative
r is positive
if x = -1 and r = 5 then,
(-1) - (+5) = -1-5 = -6 (which is less than 0)
3) Y is a multiple of 2
from 1st condition we know, "Y" is odd (so cannot be multiple of 2)
4) x^t > 0
x is negative
t is odd
Negative base raised to an odd exponent will always be odd
(-3)^3 = -27
So answer B
hope this helps