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Is xy < 0? (1) |x| + |y| > |x + y| (2) |x + 3| < |y – 3| < 2

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Senior Manager
Senior Manager
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P
Joined: 25 Dec 2018
Posts: 307
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Is xy < 0? (1) |x| + |y| > |x + y| (2) |x + 3| < |y – 3| < 2  [#permalink]

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New post Updated on: 07 Apr 2019, 00:01
00:00
A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:44) correct 41% (02:15) wrong based on 22 sessions

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Is xy < 0?

(1) |x| + |y| > |x + y|

(2) |x + 3| < |y – 3| < 2

Originally posted by mangamma on 06 Apr 2019, 05:44.
Last edited by Bunuel on 07 Apr 2019, 00:01, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 10 Oct 2018
Posts: 177
Location: United States
GPA: 4
WE: Human Resources (Human Resources)
Re: Is xy < 0? (1) |x| + |y| > |x + y| (2) |x + 3| < |y – 3| < 2  [#permalink]

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New post 06 Apr 2019, 06:05
It's a Yes/No question. We need to find if xy<0

Statement 1: |x| +|y| > |x + y|
It would be easier if we put numbers to test rather than solving the equation.
If you scrutinize the equation, you'll find x and y can't be both negative or both positive. (Try it!)

So either of them has to be negative. Only then the equation would work.

Let's take simple numbers. Let x=-2 and y=1.
|-2| +|1| > |-2 + 1| => 3>1
So -2*1<0......SUFFICIENT!

Statement 2: |x+3| < |y – 3| < 2
Again try to put in numbers. If you'll scrutinize this equation, it is similar to stat1 as in x and y both can't be positive or negative. It has to be either of them.
|-4+3| < |3 – 3| < 2 => 1<0<2

-4*3<0......SUFFICIENT!

Thus, both the statements are sufficient to answer the question. Hence, option D
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Re: Is xy < 0? (1) |x| + |y| > |x + y| (2) |x + 3| < |y – 3| < 2   [#permalink] 06 Apr 2019, 06:05
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