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Is x a negative number? (1) x^2 is a positive number.

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Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 16 Jul 2019, 08:47
2
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

37% (00:59) correct 63% (00:39) wrong based on 117 sessions

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Is x a negative number?

(1) \(x^2\) is a positive number.

(2) \(x · |y|\) is not a positive number.

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Re: Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 16 Jul 2019, 08:54
From A, we cannot derive anything. SO insufficient.
From B, we can say x is always negative, as |y| is always positive. Sufficient Hence, B is the correct answer.
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Re: Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 16 Jul 2019, 11:14
Is x a negative number?

(1) x^2 is a positive number.

x can be both positive or negative but square of either is still a positive, not sufficient enough.

(2) x·|y| is not a positive number.

mod y is always positive and total sum is negative implies no other option than x to be negative. Sufficient enough.

Hence B is correct
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Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 16 Jul 2019, 13:48
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The correct answer should be E. Note that we must not forget the case that x can equal 0 for statement 2, which means that x can be either 0 or negative.

Combining both statements, we know that x^2 is positive, but if y is 0, then x can be either positive or negative.

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Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 21 Jul 2019, 05:50
1
1) x can be either positive or negative --> insufficient

2) if y = 0 --> then for any x, the product of x*|y| will not be positive. --> insufficient

Combined) no new information --> insufficient.

Hence, the answer is E.
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Re: Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 22 Jul 2019, 10:28
2
Is x a negative number?

(1) x^2 is a positive number.

(2) x⋅|y| is not a positive number.

Solution:-

There is no information in the question stem to process so we move to the statements directly.

(1) x^2 is a positive number.

Square of any number is positive, be it a negative or a positive number.
So, X can be a negative number or a positive number as well. Hence, INSUFFICIENT

(2) x⋅|y| is not a positive number.

Now, We need to read this statement very carefully. It says x⋅|y| is NOT A POSITIVE number. It does not say that x⋅|y| is A NEGATIVE number. So, There are 2 possibilities now, x⋅|y| can either be a Negative number or it can be ZERO. (Because Zero is neither positive nor negative)
Lets say x⋅|y|=0
So, if |y|=0, X can either be positive or negative.
Lets say x⋅|y|= Negative
So, here X can only be negative.

Since, This statement is also not providing us a clear answer, Its INSUFFICIENT

Taking both statements together will do us no good because both statements suggest the same thing that X can either be positive or negative.

So the answer is E.


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Re: Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 23 Jul 2019, 05:55
nlx23 wrote:
Is x a negative number?

(1) x^2 is a positive number.

x can be both positive or negative but square of either is still a positive, not sufficient enough.

(2) x·|y| is not a positive number.

mod y is always positive and total sum is negative implies no other option than x to be negative. Sufficient enough.

Hence B is correct


I do agree X has to be negative on combining both options A and B and hence ans has to be C and not E.
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Re: Is x a negative number? (1) x^2 is a positive number.  [#permalink]

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New post 29 Jul 2019, 11:56
Question: Is X a negative # -> is X<0?

1. x^2 is +
x=/=0 NS
2. x⋅|y| is not +
X<=0 or Y is 0
NS

By combing both we see that if Y is not 0 then X must be negative, but there is nothing in the question saying that Y=/=0.
.: E
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Re: Is x a negative number? (1) x^2 is a positive number.   [#permalink] 29 Jul 2019, 11:56
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