tough inequality

[Gurpinder]

if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?

[n@resh]

if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?

It's simple, as you endup with two answers from using statement 1, that's the reason why it's not sufficient.
Even statement 2, isn't enough.

Using both statements: x = y and y>0, we can confirm (x^2 +1)/x > Y. for all the values of x and y.
Answer C.

[Gurpinder]

thx.

i see what i was doing wrong. i need some coffee!

[sl750]

if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?

In statement, all it says is x=y, but we don't know the sign of x or y. So you can't multiply the right hand side by x and assume the inequality sign will remain the same

All we get from statement 1 is, Is 1/x >0 ?. x could be positive or negative. Insufficient