Hi All,
We're told that X, Y and Z are NEGATIVE numbers such that Z = 40X + 80Y and X+Y = -1. We're asked if Z is LESS than -60. This is a YES/NO question and can be solved by TESTing VALUES and/or using a bit of logic.
To start, this question has some interesting limitations to it. Since all 3 variables MUST be negative, and (X+Y) must equal -1, we know that X and Y are both NEGATIVE FRACTIONS. As one variable gets closer to -1, the other variable gets closer to 0....thus the value of Z will be something BETWEEN -40 and -80 (depending on the relative values of X and Y. If X and Y are BOTH equal to -1/2, then Z = 40(-1/2) + 80(-1/2) = -60 exactly.
1) X > Y
With the information in Fact 1, we know that X is GREATER than Y, meaning that it is closer to 0 than Y is. By definition, that means that X > -1/2 and Y < -1/2. Thus, Z MUST be LESS than -60 (you can TEST any pairs of values for X and Y and you'll see).
Fact 1 is SUFFICIENT
2) Y < -0.5
With the information in Fact 2, we know that Y < -1/2, so X > -1/2. This is the exact same pattern that we had in Fact 1, so no additional work is necessary.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
