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!?
tough inequality
This topic has expert replies
It's simple, as you endup with two answers from using statement 1, that's the reason why it's not sufficient.Gurpinder 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!?
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.
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thx.
i see what i was doing wrong. i need some coffee!
i see what i was doing wrong. i need some coffee!
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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 sameGurpinder 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!?
All we get from statement 1 is, Is 1/x >0 ?. x could be positive or negative. Insufficient