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# Is xy > 0 ? (1) x – y > 2 (2) x + y > –2

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Is xy > 0 ? (1) x – y > 2 (2) x + y > –2  [#permalink]

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26 Feb 2017, 09:12
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:07) correct 37% (01:54) wrong based on 92 sessions

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Is xy > 0 ?

(1) x – y > 2
(2) x + y > –2

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Joined: 12 Sep 2015
Posts: 4009
Re: Is xy > 0 ? (1) x – y > 2 (2) x + y > –2  [#permalink]

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26 Feb 2017, 10:34
Top Contributor
1
Bunuel wrote:
Is xy > 0 ?

(1) x – y > 2
(2) x + y > –2

Target question: Is xy > 0 ?

Statement 1: x – y > 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 5 and y = 1, in which case xy = (5)(1) = 5. So, xy > 0
Case a: x = 5 and y = -1, in which case xy = (5)(-1) = -5. So, xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x + y > –2
This statement doesn't feel sufficient either.
IMPORTANT: Before I start plugging in new values for x and y, let's see if I can first REUSE my x- and y-values from statement 1.
YES! Those values also satisfy the conditions in satisfy statement 2. That is:
Case a: x = 5 and y = 1, in which case xy = (5)(1) = 5. So, xy > 0
Case a: x = 5 and y = -1, in which case xy = (5)(-1) = -5. So, xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since the SAME x- and y-values were used to show that ether statement ALONE is not sufficient, we can conclude that, the SAME x- and y-values will satisfy BOTH statements. That is:
Case a: x = 5 and y = 1, in which case xy = (5)(1) = 5. So, xy > 0
Case a: x = 5 and y = -1, in which case xy = (5)(-1) = -5. So, xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Is xy > 0 ? (1) x – y > 2 (2) x + y > –2  [#permalink]

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26 Feb 2017, 21:08
Bunuel wrote:
Is xy > 0 ?

(1) x – y > 2
(2) x + y > –2

Question: Is xy > 0 ?

Statement 1: x – y > 2

Case 1: x =4, y=1 and xy >0
Case 2: x =0, y=-3 and xy =0
Case 3: x =1, y=-4 and xy <0
NOT SUFFICIENT

Statement 2: x + y > -2
Case 1: x =4, y=1 and xy >0
Case 2: x =0, y=-1 and xy =0
Case 3: x =3, y=-4 and xy <0
NOT SUFFICIENT

Combining the two statements
x – y > 2
x + y > -2
2x>0
i.e. x > 0
Case 1: x =4, y=1 and xy >0
Case 2: x =3, y=-4 and xy <0
NOT SUFFICIENT

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Re: Is xy > 0 ? (1) x – y > 2 (2) x + y > –2  [#permalink]

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27 Feb 2017, 10:52
Bunuel wrote:
Is xy > 0 ?

(1) x – y > 2
(2) x + y > –2

(1) x>2+y
if x=4 , y= -1 then NO
if x=4 , y=1 then YES

insuff

(2) x>-2-y
same as above...insuff

combined ...same examples as in (1)
insuff

Ans E
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Re: Is xy > 0 ? (1) x – y > 2 (2) x + y > –2  [#permalink]

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09 Oct 2018, 09:50
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Re: Is xy > 0 ? (1) x – y > 2 (2) x + y > –2   [#permalink] 09 Oct 2018, 09:50
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