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Is xy < 0 ?

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Is xy < 0 ? [#permalink] New post 04 Aug 2010, 14:17
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:53) correct 38% (00:45) wrong based on 77 sessions
Is xy < 0 ?

(1) 1/x < 1/y
(2) x > 0
[Reveal] Spoiler: OA

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Re: Need solution ! [#permalink] New post 04 Aug 2010, 22:01
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nusmavrik wrote:
Is xy < 0 ?
1. 1/x < 1/y
2. x > 0


Is xy < 0 ?

Notice that the question basically asks whether x and y have the opposite signs.

(1) \frac{1}{x}<\frac{1}{y} --> x and y can have the same sign (x=2 and y=1) as well as opposite signs (x=-2 and y=1). Not sufficient.

(2) x>0 --> no info about y. Not sufficient.

(1)+(2) As from (2) x>0 then \frac{1}{x}<\frac{1}{y} to hold true, y must also be positive (left hand side, \frac{1}{x} is positive and right hand side, \frac{1}{y}, to be greater than that, must also be positive). So x and y have the same sign, they are both positive: xy>0. Therefore the answer to the question is NO. Sufficient.

Answer: C.

Hope it helps.
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Re: Need solution ! [#permalink] New post 04 Aug 2010, 23:06
Thanks Bunuel ! This question was a hard trap. Thanks for the awesome explanation.
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Re: Is xy < 0 ? [#permalink] New post 22 Feb 2014, 12:09
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Re: Is xy < 0 ? [#permalink] New post 01 Mar 2014, 11:11
Hey Bunuel,
Can you please let me know where I'm going wrong in the following method:
Statement1:
1/x < 1/y
Subtract 1/y from both sides: we get (y-x)/xy <0.
Therefore, either xy<0 or (y-x)<0.
If xy<0 then the answer to our question is YES both are opposite signs.
If y-x<0 -> y<x, then both can have same sign or opposite signs (ie.., y<x<0 OR y<0<x OR 0<y<x)
Therefore, Statement1 is INSUFFICIENT.
Statement2: 0<x so x is Positive but no information about y, So statement 2 is INSUFFICIENT.
(1) and (2) together:
We still have y<0<x or 0<y<x
Therefore, Both statements together are INSUFFICIENT. So E.
Thanks for your help! :)
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Re: Is xy < 0 ? [#permalink] New post 02 Mar 2014, 03:55
Expert's post
prsnt11 wrote:
Hey Bunuel,
Can you please let me know where I'm going wrong in the following method:
Statement1:
1/x < 1/y
Subtract 1/y from both sides: we get (y-x)/xy <0.
Therefore, either xy<0 or (y-x)<0.
If xy<0 then the answer to our question is YES both are opposite signs.
If y-x<0 -> y<x, then both can have same sign or opposite signs (ie.., y<x<0 OR y<0<x OR 0<y<x)

Therefore, Statement1 is INSUFFICIENT.
Statement2: 0<x so x is Positive but no information about y, So statement 2 is INSUFFICIENT.
(1) and (2) together:
We still have y<0<x or 0<y<x
Therefore, Both statements together are INSUFFICIENT. So E.
Thanks for your help! :)


\frac{y-x}{xy} <0 means that y-x and xy have the opposite sign: +- or -+.

When combined we know that x is positive. Now, if y were negative, then xy<0, thus y-x must be positive, but in this case y-x=negative-positive=negative, thus this case is not possible, y is NOT negative --> y is positive --> xy=positive.

Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is xy < 0 ? [#permalink] New post 02 Mar 2014, 17:08
Thanks Bunuel for this great explanation!
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Re: Is xy < 0 ? [#permalink] New post 02 Mar 2014, 22:42
nusmavrik wrote:
Is xy < 0 ?

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


Statement I is insufficient:

x = 2, y = 1 (1/2 < 1/1) (xy > 0) (NO)
x = -1, y = 2 (1/-2 < 1/2) (xy <0) (YES)

Statement II is insufficient:
y can be negative or positive

Combining is sufficient:

(1/x) < (1/y)
If 1/x is positive then 1/y is also positive which means y is also positive. Hence xy is greater than zero
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Re: Is xy < 0 ?   [#permalink] 02 Mar 2014, 22:42
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