Is xy 0 ? (1) x – y 2 (2) x + y –2

Question

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

BrentGMATPrepNow · Answer

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: https://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 Answer: E Cheers, Brent

GMATinsight · Answer

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 Adding the two equation 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 Answer: Option E

rohit8865 · Answer

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

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