is x negative ?

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is x negative ?

by vikram4689 » Sun Feb 28, 2010 10:47 pm
Is x negative?

1) x^3 (1-X^2) < 0

2) x^2 - 1 < 0


My Anwser:
for 1) take x as +ve =3 (say) then x^3 (1-X^2) <0
now take x as -ve =-3 (say) then x^3 (1-X^2) >0 which contradicts the given statement so we can deduce that x is +ve which an answere so this statement (given in 1) is sufficient

for 2) take x as +ve =3 (say) then x^2 - 1<0
now take x as -ve =-3 (say)then x^2 - 1<0 .so ths statement is insufficient as we cant deduce whether x is -ve or +ve

so Answer should be A but OA is C
Source: — Data Sufficiency |

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by fibbonnaci » Mon Mar 01, 2010 2:53 am
Hey u have fallen for a trap.
you have taken X as only integers in statement 1.

i could take x= -0.5 then (1- x^2) is positive and x^3 is negative.
Thus x^3 (1-x^2) is still < 0

But when x = 3, the statement 1 still hold good.

so we have 2 values of x, one positive and one negative. Thus insufficient.

Statement 2: x^2 <1
so x could again be positive or negative. Insufficient

Combine both, you definitely know that x^2 < 1,
then 1- x^2 is definitely positive. So inorder for the statement 1 to be true, x^3 has to be negative.
Therefore X is negative.
Thus you need both the statements to determine whether x is negative.

Thus the answer is C.

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by vikram4689 » Mon Mar 01, 2010 4:43 am
yeah right,i forgot that...thanks