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# If xy < 3, is x < 3 ?

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Manager
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If xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 02:23
1
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55% (hard)

Question Stats:

59% (02:19) correct 41% (01:26) wrong based on 155 sessions

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If xy < 3, is x < 3 ?

(1) |y|> 1
(2) |x| < 3
[Reveal] Spoiler: OA
Math Expert
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Kudos [?]: 85341 [3] , given: 10236

Re: If xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 02:33
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Expert's post
If xy < 3, is x < 3 ?

(1) |y|> 1. Probably the easiest way to deal with this statement would be to plug some numbers. Notice that $$|y|> 1$$ means that $$y<-1$$ or $$y>1$$. Now, if $$y=2$$ and $$x=-4$$ then the answer is YES but if $$y=-2$$ and $$x=4$$ then the answer is NO. Not sufficient.

(2) |x| < 3 --> $$-3<x<3$$: directly gives an YES answer to the question. Sufficient.

Hope it's clear.
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Re: Is xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 02:35

From the question:
xy<3 => x,y can be both positive and negative or, opposite signs. x(-2)y(3)<3
1. |y| > 1 => y>1 y<-1 => y can take 2, 3, 4, 5 or -2, -3, -4, -5.. if y=-6 and x=6 xy is -36 <3. If y=-1, x=-2 xy<3.
here x = 6 in one case and -2 in another case.
Hence Insufficient.
2. |x|<3 => -3<x<3 . No matter what the values of x are, it will be <3. Sufficient.
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Re: Is xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 04:46
I'm not quite sure that I've understood the question.

"Is xy < 3" This part I read as one question, "is x < 3?" This as another one.

Was the question "If xy<3, is x<3?"?

If I'm completely wrong please let me know why i might've misunderstood the semantics.

Thanks!
Math Expert
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Kudos [?]: 85341 [0], given: 10236

Re: Is xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 04:49
Markusosv wrote:
I'm not quite sure that I've understood the question.

"Is xy < 3" This part I read as one question, "is x < 3?" This as another one.

Was the question "If xy<3, is x<3?"?

If I'm completely wrong please let me know why i might've misunderstood the semantics.

Thanks!

Yes, the question reads: "If xy < 3, is x < 3 ?"

Hope it's clear.
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Re: Is xy < 3, is x < 3 ? [#permalink]

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18 Jun 2012, 04:51
Bunuel wrote:
Markusosv wrote:
I'm not quite sure that I've understood the question.

"Is xy < 3" This part I read as one question, "is x < 3?" This as another one.

Was the question "If xy<3, is x<3?"?

If I'm completely wrong please let me know why i might've misunderstood the semantics.

Thanks!

Yes, the question reads: "If xy < 3, is x < 3 ?"

Hope it's clear.

Noticed it now. I must've misread earlier.

Thanks!
Math Expert
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Re: If xy < 3, is x < 3 ? [#permalink]

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23 Feb 2014, 06:39
Bumping for review and further discussion.
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Re: If xy < 3, is x < 3 ? [#permalink]

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04 Apr 2014, 22:31
I missed the question. Had to read the question again after arriving at wrong answer.

Last edited by email2vm on 05 Apr 2014, 00:05, edited 1 time in total.
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Re: If xy < 3, is x < 3 ? [#permalink]

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04 Apr 2014, 23:05
Ankit04041987 wrote:
If xy < 3, is x < 3 ?

(1) |y|> 1
(2) |x| < 3

Statement I is insufficient:

y = 0.1 then x < 30 it can be equal to 5 or -5.

Statement II is sufficient:

|x| < 3 means x is between -3 and 3 hence x will always be less than 3

Answer will be B.
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Re: If xy < 3, is x < 3 ? [#permalink]

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13 Mar 2016, 09:25
Here statement 2 is sufficient as if |x|<3 => x lies in the range of (-3,3)
hence x<3 is always true.
So B
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Re: If xy < 3, is x < 3 ?   [#permalink] 13 Mar 2016, 09:25
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# If xy < 3, is x < 3 ?

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