is x negative?

Question

GMATBusters’ Quant Quiz 2.0 Question -1 
 For questions from previous quizzes click   here

is x negative? 
(1) x + y = -12 
(2) y < x-12

freedom128 · Answer

1) (x,y) can be (-12,0),(0,-12), etc. x can be any number.
NOT SUFFICIENT

2) x-y>12
(x,y) can be (13,0),(0,-13),(-1,-12), etc. x can be any number.
NOT SUFFICIENT

1)+2)
x-y>12 --> x-(-12-x)>12 --> 2x>0 --> x>0
X is not negative. 
SUFFICIENT.

FINAL ANSWER IS (C)

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rvarora · Answer

Only Option C gives a confirmed No
Here is Why

willacethis · Answer

Statement 1 is clearly insufficient since there are multiple values that satisfy the equation (ex. x can be -10 if y = -2 or x can be 1 if y = -22)

Statement 2 is insufficient since all we know is that y + 12<x. Now, x can have both positive and negative values (for ex. x can be -9 if y = -22 or x can be 13 if y = 1)

If we combine both the equations, y+12<x<12-y. Again, x can have both, positive and negative values (ex. x can be 3 if y= -10 or x can be -1 if y= -14)

Hence, answer is E.

numb007 · Answer

ANS: C
i)x+y=12
 Insufficient Info
ii)y-x<-12
 or -x+y>12
 Insufficient Info
Adding i and ii
 2y>0
Hence y>0
Hence ANS: C

pk123 · Answer

is x negative?
(1) x + y = -12
(2) y < x-12

Option 1: x+y=-12 
this is insufficient since if x=-5, y can be -7 or if x=5 y can be -17 
There are no limitations on x or y, so x can be either positive or negative

Option 2: y<x-12
In this case either x can be positive or negative as well
lets say x=-5 , y can be <-17 while if x=5 y can be y<-7
so x can be either positive or negative

Lets combine
y<x-12
From previous example if x =-5, y <-17 so could be -17.01 or if x=5, y will be <-7 ..so it could be 07.01
with this in mind if y<x-12, y can be though of =outcome of (x-12) -0.01 ...i.e y=x-12.01
Using this value in option 1
x+x-12.01=-12
x becomes positive

Hence both option combined gives x as positive and is sufficient to answer 
Option C

globaldesi · Answer

is x negative?
(1) x + y = -12
(2) y < x-12
1) x + y = -12 x can be positive or negative both
x = 3 and y = -15
or x = -15 and y 3
not sufficient

2) y < x-12
again x can be both + or -

combine
given y< x-12
or y+12 <x
and x + y = -12
x+x-12 <-12
or 2x <0
thus x <0
thus sufficient
C

fauji · Answer

Approach

S1: x + y = -12
- Take a simple case: if x = 2, y= -14 ....x is positive.
- Take another case: if x = -2, y= -12 .... x is negative.
- So overall no final answer we are getting as multiple values(+,-) are possible....Insufficient

S2: y < x-12
Rearrange: x > y+12
- Take a simple case: if y= 1 then x= 13 ....x is positive.
- Take another case: if y= -24 then x= -12 .... x is negative.
- Two different values of x, no final answer..... Insufficient

Combine S1 and S2
- Put Equation: y= -12-x from (S1) in (S2) y < x -12
= -12-x < x-12 => x>0 , Hence x is non-negative. we get the final answer, hence Sufficient

Option C

QuantMadeEasy · Answer

is x negative?
(1) x + y = -12
(2) y < x-12

(1) x can be negative or positive. Insufficient

(2) x - y >12; sign of x is unknown. Insufficient

(1)+(2); y = -12-x
substituting in (2)
x + 12 + x > 12
x > 0
Sufficient

IMO C

lacktutor · Answer

--> is x negative?

(Statement1): x + y = -12
--> x could be either negative or positive:
if y=4, then x will be equal to -16 (YES)
if x=4, then y will be equal to -16 (NO)
Insufficient

(Statement2): y < x-12
Clearly insufficient
--> x could be either positive or negative

Taken together 1&2,
y= -x-12
--> -x-12 < x-12
-2x < 0
x >0 (Always NO)
Sufficient

The answer is C.