Bunuel
If xy < 0, is x > y ?
(1) x/y < 1
(2) |x| < |y|
Given: xy < 0
Inference:
x and y lie on opposite sides of 0.Question: x > y
Inference:
Does x lie to the right of y when plotted over a number line------------ y ------------ x ------------
Let's start with Statement 2 first as that's a bit easier than Statement 1
Statement 2: |x| < |y|
Inference:
The distance of x from 0 is greater than the distance of y from 0We do not know on which side of 0 does x and y lie , so we will have two scenarios -
CASE 1 : x lie to the left of 0 and y lie to the right of zero
------------ x ------------ 0------------------------ y ------------
CASE 2 : x lie to the right of 0 and y lie to the left of zero
------------ y ------------------------ 0 ------------ x ------------
As we have two different possibilities, this statement is not sufficient on its own and we can rule out B and D
Statement 1: \(\frac{x}{y}\) < 1
\(\frac{x - y }{ y }< 0\)
CASE 1 : y > 0
If y > 0, then x - y < 0
Hence if y > 0; x < y
CASE 2 : y < 0
If y < 0, x - y > 0
Hence if y < 0; x > y
If y > 0, x - y > 0
Hence if y > 0; x < y
As we have two cases possible depending on the positive negative nature of y, this statement is also not sufficient and we can eliminate A.
CombinationThe combination doesn't help us resolve the ambiguity as Statement 2 merely provides us with the information of distances and not the sign (positive - negative nature of y). Hence we can eliminate C.
Option E