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(i) x^2 is a positive number \(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number \(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number. Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative. Not sufficient E _________________

It is beyond a doubt that all our knowledge that begins with experience.

(i) x^2 is a positive number \(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number \(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number. Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative. Not sufficient E

Hi Zarrolou, I thought mod of Zero was illegal. in (ii) x could be zero. But together we know x cannot be zero hence negative.
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(i) x^2 is a positive number \(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number \(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number. Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative. Not sufficient E

Hi Zarrolou, I thought mod of Zero was illegal. in (ii) x could be zero. But together we know x cannot be zero hence negative.

\

|0|=0.

Is x negative?

(1) x^2 is a positive number. This statement implies that \(x\neq{0}\). Not sufficient.

(2) x * |y| is not a positive number --> \(x * |y|\leq{0}\). If \(y=0\), then \(x\) could be ANY number. Not sufficient.

(1)+(2) Again, if \(y=0\), then \(x\) could be ANY number but 0 (excluded because of the first statement). Not sufficient.

x^2 = + |x| = + x could be any number aside from zero and |x| will be positive. x = positive or negative INSUFFICIENT

(2) x * |y| is not a positive number |y| will always be a positive number so for x * |y| to be negative x must be negative. HOWEVER, the answer could be zero too. 0 is not positive or negative. So, 0 * |y| = 0 OR x * |0| = 0. x = positive, zero or negative INSUFFICIENT

1+2) # 1 tells us that x could be positive or negative. # 2 tells us that c could be positive, negative or zero. In other words, x could be positive or negative. INSUFFICIENT

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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