anantbhatia wrote:Is y - x > 1/(x-y) ?

(1) ┃x - y┃ > 1

(2) y > x


[spoiler]OA: B Grockit[/spoiler]

my soln:

same as:-

is ((x-y)^2+1)/(x-y) <0

with (1), I get a firm No.

with 2, I get a firm Yes. So I chose D

What was my mistake?

i dont understand why the answer is B. i think it should be A because
y-x>1/x-y <=> x-y<-1/(x+y) <=> x-y+1/x-y <=> ((x-y)^2+1)/x-y
since x-y>1 and x-y)^2 is always positive
thus A is sufficient
and B cant

Is y - x > 1/(x-y) ?

(1) x-y > 1

(2) y > x

Reposted the question.

@Rahul: Please help me with the generic and quick approach to the inequalities in DS. I feel like I am struggling while giving mocks.

anantbhatia wrote:Is y - x > 1/(x-y) ?

(1) x-y > 1

(2) y > x

Reposted the question.

@Rahul: Please help me with the generic and quick approach to the inequalities in DS. I feel like I am struggling while giving mocks.

I think it should be A,

y - x > 1/(x-y)

(y-x) (x-y) > 1
xy - y^2 - x^2 + xy > 1
2xy - y^2 - x^2 > 1
multiplied by -ve on both sides
- 2xy + y^2 + x^2 < - 1 ( AS i know equality sign flips when we multiply by -ve )

( x - y ) ^ 2 < - 1 or ( y - x ) ^ 2 < - 1 This is question for me know ( Please correct if i am wrong because i am still not sure with -ve multiplication )

(1) x-y > 1 Then we have a positive value which is sufficient to answer

(2) y > x

let y = - ( 1/2 )
let x = - (1/3 )

or let y = 2
let x = 1

Gives us different value when we substitute it above equation so its insufficient.

HOPE this Helps..

Goyal sahib, you have taken a value from RHS to the LHS without considering if it was positive or negative, which is incorrect. If you want to take it to the left, you should subtract it without affecting the inequality.

anantbhatia wrote:Goyal sahib, you have taken a value from RHS to the LHS without considering if it was positive or negative, which is incorrect. If you want to take it to the left, you should subtract it without affecting the inequality.

Thanks Dear,
as you said you struggling in inequalities, I don't know what i should call about my inequalities

After going through GOYALSU and ANANTBHATIA discussion:

1: is insufficient as we cannot say whether x-y is +ve or -ve. So we ar not sure about the sign.
2: y>x
=> y - x > 0 ......(a)

so x-y < 0
so 1/(x-y) < 0 ......(b)

from (a) and(b) we can say 1/(x-y) < 0 < y - x => y-x > 1/(x-y) (Sufficient)

Now try with some values:
x=2,y=3 => y-x = 1 and x-y = -1 so 1/(x-y) = -1 (Satisfied)
x=-3,y=-2 => y-x = 1 and x-y = -1 (Satisfied)

B is Sufficient.

goyalsau wrote: (2) y > x

let y = - ( 1/2 )
let x = - (1/3 )

Gives us different value when we substitute it above equation so its insufficient.

HOPE this Helps..

here y < x so u missed it