DS question

To me, Answer should be E.

(1) xy > 1

Assume x=2 & y=3, xy = 6 >1. But x/y <1.
If x=3 & y=2, xy =6>1 and x/y >1. So, A is NOT SUFFICIENT.


(2) x - y > 0

Lets say x= 3, y =2. 3-2=1 > 0. x/y >1
When x=-2 & y = -3, x-y = 1 >0. But x/y <1. NOT SUFFICIENT.

Combining together does not help rather. So, both are NOT SUFFICIENT and answer is E.

If you just re- word the equation its saying " is x>y?

Statement one is not sufficient because those numbers could be anything.

Statement two says x>y, hence sufficient.

let show my calculation

in question it say X/Y>1 so it must be X>Y or we can proof it from both st.

now in st 1 we can not find wether X>Y because X & Y can take different sing so it out

but in st 2 as X-Y>0 it must be X>y
in other way
let X=-3 & Y=-1
we get X-Y=-3-(-1)=-3+1=-3 so it can not satisfy X-Y>0 to satisfy X-y>o X must hold greater value in what ever sing
let X=3 y=1 so X-y=2>o so we find x>y
in others way
let X=-1 & y=-3
so X-y=-1-(-3)=-1+3=2>0
so in number line we can get -1 is greater than -3 so X>y

now let x=1 y=3
so x-y=1-3=-2<0 so no way
in my think to satisfy x-Y>o , X must by greater than Y so obly b is enough

x/y > 1 does not necessarily mean that x > y.
This is a very common mistake.

If x/y > 1, and 'y' is a positive integer, ONLY THEN can we multiply both sides of the inequality with 'y' and the sign of inequality will not change.
Thus,
x > y

If 'y' is a negative integer, when we multiply both sides of the inequality 'y' the sign of inequality WILL REVERSE. And, we will have
x < y

The problem does not mention anywhere that 'y' is positive, and thats why both the possibilities are to be considered.

You can see even plug in values to understand this:

x/y > 1 for say x = 3 and y = 2. (x > y when y > 0)
x/y > 1 also for x = - 3 and y = - 2. (x < y when y < 0)

So, what did we learn here?

An inequality behaves a little differently from an equation. We have to be careful while multiplying with a number on both sides of the inequation.
If the quantity being multiplied in postive, the sign of inequality WILL NOT CHANGE.
If the quantity being multiplies is negative, the sign of inequality WILL REVERSE.