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# Is xy < 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445

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18 Jun 2015, 02:56
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:45) correct 52% (01:25) wrong based on 115 sessions

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Is xy < 1?

(1) 2/x > 3y
(2) x > 0

Kudos for a correct solution.

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Joined: 13 May 2011
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Updated on: 18 Jun 2015, 07:53
Is xy < 1?

I made a mistake in a solution, hence deleting it.

(1) 2/x > 3y
If x=1, y=0,5, then xy>1
If x=1, y=-2, then xy<1. Not sufficient.

(2) x > 0
No info on y. Not sufficient.

Together (1) & (2)
The issue in Statement 2 is still unresolved. Not sufficient.

[/spoiler]
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Originally posted by kvazar on 18 Jun 2015, 07:18.
Last edited by kvazar on 18 Jun 2015, 07:53, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 7984
Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 07:41
kvazar wrote:
Is xy < 1?

(1) 2/x > 3y
If x=1, y=0,5, then xy>1
If x=1, y=-2, then xy<1. Not sufficient.

(2) x > 0
No info on y. Not sufficient.

Together (1) & (2)
The issue in Statement 2 is still unresolved. Not sufficient.

Hi
coloured portion not clear..
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Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 07:43
1
1
Bunuel wrote:
Is xy < 1?

(1) 2/x > 3y
(2) x > 0

Kudos for a correct solution.

Question : Is xy < 1?

Statement 1: 2/x > 3y
@x=1, y can be 1/3 i.e. xy(1/3) < 1
@x=-1, y can be -3 i.e. xy(3) > 1

Hence, NOT SUFFICIENT

Statement 2: x > 0

Hence, NOT SUFFICIENT

Combining the two statements

2/x > 3y and x>0

Since x is positive, therefore we can re-write the expression of first statement as

2 > 3xy
i.e. xy < 2/3

i.e. xy is always less than 1

Hence, SUFFICIENT

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Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 07:49
kvazar wrote:
Is xy < 1?

(1) 2/x > 3y
If x=1, y=0,5, then xy>1
If x=1, y=-2, then xy<1. Not sufficient.

(2) x > 0
No info on y. Not sufficient.

Together (1) & (2)
The issue in Statement 2 is still unresolved. Not sufficient.

Highlighted part has a mistake that has already been referred by Chetan

Also, looks like you have combined the two equations in jiffy which has resulted in a wrong answer

Please Note: Never say NOT SUFFICIENT until/unless you have proven that the information is insufficient to answer the question.
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Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 07:56
GMATinsight wrote:
kvazar wrote:
Is xy < 1?

(1) 2/x > 3y
If x=1, y=0,5, then xy>1
If x=1, y=-2, then xy<1. Not sufficient.

(2) x > 0
No info on y. Not sufficient.

Together (1) & (2)
The issue in Statement 2 is still unresolved. Not sufficient.

Highlighted part has a mistake that has already been referred by Chetan

Also, looks like you have combined the two equations in jiffy which has resulted in a wrong answer

Please Note: Never say NOT SUFFICIENT until/unless you have proven that the information is insufficient to answer the question.

Hi! Yep, thanks to Chetan, I've hidden the solution not to confuse people.
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Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 09:43
1
Bunuel wrote:
Is xy < 1?

(1) 2/x > 3y
(2) x > 0

Kudos for a correct solution.

1) 0.66/x > y. If x= -1 & y= -0.67 then YES
If x=-1 & y= -2 then No

Not sufficient

2) If x=0.25 & y=1 Then YES
If x=1 & y=1 then NO.

1+2 gives xy<0.66. Hence C
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Re: Is xy < 1?  [#permalink]

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18 Jun 2015, 18:41
1
Given expression: $$\frac{(2-3xy)}{x} > 0$$

If x >0 :
2-3xy > 0 therefore xy < 2/3
This is provided by .
Both are necessary

If x <0:
2-3xy < 0 therefore xy > 2/3
Cannot be decided with only this choice.

So

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Re: Is xy < 1?  [#permalink]

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19 Jun 2015, 00:00
Bunuel wrote:
Is xy < 1?

(1) 2/x > 3y
(2) x > 0

Kudos for a correct solution.

1: Assume x>0: 2 > 3xy, 2/3 > xy. If x < 0, reverse the sign so 2/3 < xy. So insufficient.
2: Tells nothing about y, insufficient.

Together it is sufficient, since 1 has the x > 0 criteria in it. Therefore, answer is C.
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Posts: 58445
Re: Is xy < 1?  [#permalink]

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22 Jun 2015, 05:50
Bunuel wrote:
Is xy < 1?

(1) 2/x > 3y
(2) x > 0

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Statement (1) might imply that xy < 2/3, but only if x is positive. If it is negative, we would need to flip the sign: xy > 2/3.

Thus we cannot answer the question without knowing the sign of x—information that is provided in Statement (2). The correct answer is C.

These types of questions may have an A or B trap, in that you might fail to realize that you have to set up negative and positive cases when you multiply or divide an inequality by a variable.

Watch out! In some GMAT problems, you can assume the sign of the variables, because the variables represent countable quantities of physical things. In those cases, you can assume that the variables are positive, and you can cross-multiply inequalities involving those variables at will.
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Re: Is xy < 1?  [#permalink]

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03 Jan 2019, 05:25
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Re: Is xy < 1?   [#permalink] 03 Jan 2019, 05:25
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