Bunuel wrote:
TRICKY
If \(xy < 0\) and \(x + y < 0\), then which of the following must be true?
I. \(x - y > 0\)
II. \(x > 0\) or \(y > 0\)
III. \(\frac{x}{y} < 1\) or \(\frac{y}{x} < 1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
IMO D
If \(xy < 0\) and \(x + y < 0\), for these statements to be true together
x < 0 or y > 0, also magnitude of x has to be greater than y
x = -2 and y = 1, -2< 0 and -1<0 (a)
x > 0 or y < 0, also magnitude of y has to be greater than y
x = 1 and y = -2, -2<0 and -1<0 (b)
I. \(x - y > 0\) => False when (a), True when (b)
We can eliminate A and E
II. \(x > 0\) or \(y > 0\)
Now this is an "or" statement, if either one of the condition is met we are good. As per my cases in (a) and (b), this holds good.
Now IMO this the tricky option, but still i will go with this.
III. \(\frac{x}{y} < 1\) or \(\frac{y}{x} < 1\)
This will always be true, because we will get a negative term.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.