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tough inequality

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by Gurpinder » Thu Oct 06, 2011 12:05 pm
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!?
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
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Source: — Data Sufficiency |

by n@resh » Thu Oct 06, 2011 12:23 pm
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!?
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.
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by Gurpinder » Thu Oct 06, 2011 12:25 pm
thx.

i see what i was doing wrong. i need some coffee!
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
Join the discussion

by sl750 » Fri Oct 07, 2011 2:28 am
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!?
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
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