if x is NOT = 0, is (x^2 +1)/x > Y?
(1) x = y
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
Multiplying both sides by -1 we get-
-1<4 & not -1>4
Another way to solve this is to just simplify the equation
Start with statement 2, to make the solution simpler.
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
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
y>0 & x=y
Positive+Positive is Positive.
i.e. positive number + some fraction
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