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If xy < 3, is x < 3 ?

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If xy < 3, is x < 3 ?  [#permalink]

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18 Jun 2012, 02:23
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If xy < 3, is x < 3 ?

(1) |y|> 1
(2) |x| < 3
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Joined: 02 Sep 2009
Posts: 54434
Re: If xy < 3, is x < 3 ?  [#permalink]

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18 Jun 2012, 02:33
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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!
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Posts: 54434
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!
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Joined: 20 Dec 2013
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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

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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]

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30 Jul 2017, 17:46
Ankit04041987 wrote:
If xy < 3, is x < 3 ?

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

We are given that the product of x and y is less than 3 and need to determine whether x is less than 3.

Statement One Alone:

|y| > 1

Since |y| > 1, either y > 1 or -y > 1, which means y < -1. We will pick a number for y in each interval to see what the value of x will be.

First, if y > 1, say y = 2, and then we have:

2x < 3

x < 3/2

Here x < 3.

However, if y < -1, say y = -3, and then we have:

-3x < 3

x > -1

Since x is greater than -1, we see that x could be greater than 3.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

|x| < 3

Since |x| < 3, either x < 3 or -x < 3, which means x > -3. So, we have:

-3 < x < 3

Thus, we see that x will always be less than 3.

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Re: If xy < 3, is x < 3 ?   [#permalink] 30 Jul 2017, 17:46
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