Inequality

[vinodhinir]

Is 1/x-y < y - x ?
(1) y is positive.
(2) x is negative.

I have a doubt regarding the above problem.

Obviously each statement alone is not sufficient.
When taken together the stmts are still not sufficent(per my reasoning).

Since y is positive and x is negative we can re-write the equation as

Is 1/-x-y < y+x --> -(1/x+y) < x+y
If x+y is positive For eg if x+y =1 then -1 < 1 --->true
If x+y is negative For eg if x+y= -1 then 1 > -1 ---->false

So my answer is E.

But the OA is C and they have solved it in a different way.

Can someone let me know what am I missing here.

TIA

[rijul007]

Is 1/x-y < y - x ?
(1) y is positive.
(2) x is negative.

I have a doubt regarding the above problem.

Obviously each statement alone is not sufficient.
When taken together the stmts are still not sufficent(per my reasoning).

Since y is positive and x is negative we can re-write the equation as

Is 1/-x-y < y+x --> -(1/x+y) < x+y
If x+y is positive For eg if x+y =1 then -1 < 1 --->true
If x+y is negative For eg if x+y= -1 then 1 > -1 ---->false

So my answer is E.

But the OA is C and they have solved it in a different way.

Can someone let me know what am I missing here.

TIA

If x is -ve, you cant really substitute -x in place of x

Lets say for example,
x = -3
y = 2

x-y = -5

As per your logic,
x is negative so substitute x by -x

-x-y = -5
-(-3)-2 = -5
3-2 = -5 (Not true)

Hence, we can't do this



Solution to the problem

Is 1/x-y < y - x ?


Statement 1
y is postive

lets plug in nos

y = 3
x = 1
1/x-y < y - x
-1/2 < 2

Is 1/x-y < y - x ? -- Yes

Lets plug in another set of nos
y = 3
x = 5
1/x-y < y - x
1/2 < -2

Is 1/x-y < y - x ? -- NO

Hence, Not sufficient


Statement 2
x is negative

x = -2
y = -3

1/x-y < y - x
1 < -1

Is 1/x-y < y - x ? -- No

x = -2
y = -1

1/x-y < y - x ?
-1 < 1

Is 1/x-y < y - x ? -- Yes

Not sufficient

Lets combine the two statements
y is positive
and
x is negative

positive subtrated from negative is always negative
hence, x-y is negative

1/x-y < y - x
(negative) < (positive)

Is 1/x-y < y - x ? -- Yes


Option C

[Shalabh's Quants]

Is 1/x-y < y - x ?
(1) y is positive.
(2) x is negative.

I have a doubt regarding the above problem.

Obviously each statement alone is not sufficient.
When taken together the stmts are still not sufficent(per my reasoning).

Since y is positive and x is negative we can re-write the equation as

Is 1/-x-y < y+x --> -(1/x+y) < x+y
If x+y is positive For eg if x+y =1 then -1 < 1 --->true
If x+y is negative For eg if x+y= -1 then 1 > -1 ---->false

So my answer is E.

But the OA is C and they have solved it in a different way.

Can someone let me know what am I missing here.

TIA

I think you made a mistake here. Highlighted in Red. I put it again.

Is 1/-x-y < y+x --> -(1/x+y) < x+y ------(1)
If x+y is positive For eg if x+y =1 then -1 < 1 --->true
If x+y is negative For eg if x+y= -1 then 1 > -1 ---->false

As you have already taken into consideration sign of x as negative, then there is no question of x+y be negative. It will always be +ive.

Inequality (1) should better be put up as 1/-|x|-y < y+|x| --> -(1/|x|+y) < |x|+y after taking x as negative.

Now there is no question of contemplating |x|+ y as negative, as x is in mod and y is +ive only.