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Manager  Joined: 06 Jun 2012
Posts: 122

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5 00:00

Difficulty:   65% (hard)

Question Stats: 38% (00:59) correct 62% (00:43) wrong based on 211 sessions

HideShow timer Statistics Is x negative?

(1) x^2 is a positive number
(2) x * |y| is not a positive number

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Originally posted by summer101 on 02 Jun 2013, 04:40.
Last edited by Bunuel on 02 Jun 2013, 04:46, edited 1 time in total.
Edited the question and added the OA.
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1
Is x negative?

(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
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Zarrolou wrote:
Is x negative?

(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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summer101 wrote:
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.

Mod of 0 is legit.

$$|0|=0$$
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summer101 wrote:
Zarrolou wrote:
Is x negative?

(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.

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Is x negative?

(1) x^2 is a positive number

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

(E)
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_________________ Re: Is x negative?   [#permalink] 13 Jan 2019, 12:48
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