386390 wrote:

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!?

You can't multiply both sides of an inequality by a variable unless the variable is positive. The inequality may be reversed

e.g.

1>-4

Multiplying both sides by -1 we get-

-1<4 & not -1>4

Another way to solve this is to just simplify the equation

(x^2+1)/x>Y

or x+1/x>y

Start with statement 2, to make the solution simpler.

2. y>0

we have no idea what the value of x is. x can be positive but lesser/greater than y or negative which would make the expression negative.

Eliminate B & D

1. x=y

We don't know what are x & y so it's hard to precisely determine whether the expression will be greater or lesser than y

1+2

y>0 & x=y

Positive+Positive is Positive.

x+1/x=y+1/y

i.e. positive number + some fraction

so y+1/y>y

Hence C

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