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# x is a nonzero number. Is xy < 0?

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Math Expert
Joined: 02 Sep 2009
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x is a nonzero number. Is xy < 0?  [#permalink]

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04 Feb 2015, 08:43
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72% (01:05) correct 28% (01:13) wrong based on 84 sessions

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x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

Kudos for a correct solution.

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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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04 Feb 2015, 10:11
1
Zero is neither positive or negative.

Statement 1: If y is not negative, then y could either be 0 (and xy = 0) or positive (and xy could be anything, depending on what x is) [INSUFFICIENT]
Statement 2: If y is not positive, then y could either be 0 (and xy = 0) or negative (and xy could be anything, depending on what x is) [INSUFFICIENT]

Combining both statement reveals that y = 0 so the product xy = 0 which is sufficient to answer the question.
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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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04 Feb 2015, 10:16
1
ans C..
combined the two statements give a value for y as 0.. sufficient
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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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04 Feb 2015, 10:34
Bunuel wrote:
x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

Kudos for a correct solution.

Statement 1: y can either be 0 or be positive. Not sufficient.

Statement 2: y can be either 0 or negative.

1+2) the only one that matches is 0. y=0 and xy=0.

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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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04 Feb 2015, 19:28
Bunuel wrote:
x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

Kudos for a correct solution.

Statement 1:
y is positive or 0
no mention of x

Statement 2:
y is negative or 0
no mention of x

Combined, y = 0. Hence, xy = 0 and cannot be < 0. Sufficient.

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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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05 Feb 2015, 04:41
1
Both 1) and 2) are not sufficient since different values lead to different results.
Also note that x and y can be fractions.

Together --> y is neither positive nor negative --> y has to be zero --> sufficient --> Answer C
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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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09 Feb 2015, 06:15
Bunuel wrote:
x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Statement (1) tells us that y must be greater than or equal to 0. If, for instance, y is 1, then x^y will retain whatever sign x itself carries. So (1) is insufficient because it can yield both positive and negative results. Statement (2) alone allows for y to be either negative or 0. If y is -1, for instance, then again, x^y will retain x’s own original sign. Coupling the two statements leaves the sole possible explanation that y = 0. Anything nonzero number raised to the power of 0 will be 1. Therefore, we can answer the question with a definitive “no.” (Note: this question also serves as a good reminder that Statements (1) and (2) can NEVER contradict each other. If you initially inferred from Statement (1) that y was definitely positive and subsequently inferred from Statement (2) that y was definitely negative, this contradiction should have alerted you to the fact that you missed some possibility and needed to go back and find it!)
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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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19 Apr 2016, 15:06
Question stem gives us the information that x can be a positive or negative number
from statement 1 we can infer that y must be greater than or equal to 0. sign of xy will depend on sign of x . so value of xy can be 0 or any other value. insufficient
from statement 2 we can infer that y must be less than or equal to 0. sign of xy will depend on sign of x . so value of xy can be 0 or any other value. insufficient
combining both statements, we can clearly infer that y is 0 thus making xy = 0 irrespective of value of x
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Re: x is a nonzero number. Is xy < 0?  [#permalink]

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23 Mar 2018, 12:49
Bunuel wrote:
x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

We are given that x is a nonzero number and need to determine whether xy < 0.

Statement One Alone:

y is not negative.

If y is zero, then xy is not less than zero. If y is positive and x is negative, then xy is less than zero. Statement one alone is not sufficient.

Statement Two Alone:

y is not positive.

If y is zero, then xy is not less than zero. If y is negative and x is positive, then xy is less than zero. Statement two alone is not sufficient.

Statements One and Two Together:

Using our statements together we see that y is not negative and also not positive so y must be zero, thus xy must be zero, which is not less than 0. The two statements together are sufficient to answer the question.

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Re: x is a nonzero number. Is xy < 0?   [#permalink] 23 Mar 2018, 12:49
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