Is xy |x + y| (2) |x+3|

Question

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

RaghavKhanna · Answer

St. 1:

If |x| + |y| > |x+y|
=> Either x < 0 or y <0

=> xy < 0

=> St. 1 is true

St. 2:

|x+3| < |y-3| < 2

|y-3| < 2
=> y - 3 < 2; y >=3
=> y < 5
=> y = 3 or 4

Or,

3 - y < 2; y< 3
=> y > 1
=> y = 2

=> y = {2, 3, 4}

|x + 3| < 2
=> x + 3 < 2; x >= -3
=> x < -1
=> x = -3,-2

Or,
-x - 3 < 2; x < -3
=> x > -5
=> x = -4

=> x = {-4, -3, -2}

=> x is always negative and y is always positive.
=> xy <0

=> St. 2 is sufficient

=> ANSWER: D

nick1816 · Answer

Statement 1-

Sum of distance of x from 0 and distance of y from 0 is greater than distance between x and -y. It's only possible when x and -y are on the same side of the number line with respect to 0. Hence, x and y are on the opposite side.

Sufficient

Statement 2-

Distance of y from 3 is less than 2. Hence, 0<1<y<5

Distance of x from -3 is less than 2. hence, -5<y<-1 <0

Sufficient

Kinshook · Answer

Asked: Is xy < 0? (1) |x| +|y| > |x + y| x & y have opposite signs xy < 0 SUFFICIENT (2) |x+3| < |y – 3| < 2 |x + 3| < 2 -2 < x + 3 < 2 -5 < x < -1 |y-3| < 2 -2 < y-3 < 2 1 < y < 5 x< 0 ; y>0 xy < 0 SUFFICIENT IMO D

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

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