Is x + y negative? (1) x is positive. (2) y is negative.

X = 1, Y = +2

X = 2 Y = -1

Answer - E

x+y<0 if both x & Y are - or x is - and y is + with |x|>|y| or x is + and y is - with |y| > |x|.

Even with the combinaion, since we only know the sign not the magnitude, it is insuff.

1. Not sufficient

x>0
if y>0 then x+y is not less than 0
if y<0 x+y may or may not be less than 0

2. Not sufficient

y<0
if x<0 then x+y<0
if x>0 x+y may or may not be less than 0


together
x>0 y<0

x y
1 -1 => x+y is not less than 0

1 -2 =>x+y <0

Hence not sufficient.

Answer is E.

Target question: Is x + y negative?

Statement 1: x is positive
Since we have no information about y, there's no way to determine whether x + y is negative.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is negative
Since we have no information about x, there's no way to determine whether x + y is negative.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 1 and y = -3. In this case, x + y = 1 + (-3) = -2. So, the answer to the target question is YES, x+y IS negative
Case b: x = 2 and y = -1. In this case, x + y = 2 + (-1) = 1. So, the answer to the target question is NO, x+y is NOT negative
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

To make x+y<0
We have to prove 3 things together
1. The sign of x
2. The sign of y
2. Check if x<-y

From statement 1, we only know the sign of x
From statement 2, we only know the sign of y
From both 1 and 2, we know sign of both x and y. Still we dont know whether x<-y

Go with concepts. It will take much lesser time