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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.
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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
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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
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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
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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
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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
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--> 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.
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Solution :

Is X negative ?

Statement 1

x+y = -12

X = -12-y

-12-Y CAN BE POSITIVE OR NEGATIVE AS PER THE VALUE GAINED BY Y

INSUFFICIENT


Statement 2

y<x-12

x>y+12

again x can take positive and negative values.

INSUFFICIENT


Combining both the conditions [PLOTTING ON THE GRAPH DIRECTLY]

No common solution

1st statement will be plotted as a "LINE"
2nd statment will be plotted as a region


They don't have any points in Common.

Hence, E
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Ans should be C

As from statement 1 X can be both positive and Negative ( X = 18, Y = -30 OR , X = -6 , Y = -6)
From statement 2 we can conclude that X-Y >12 ( X = -12 , Y = 30 OR X= 20 , Y = 2)

Combining Both statements we can conclusively say that is x is not negative
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#1
x + y = -12
value of x & y can be either both -ve or either of them can be + and -
isufficient
#2
y < x-12
again y and x can be either both -ve such that y< x & x can be both +ve or -ve
insufficient
from 1 &2
we can say y has to be -ve and x has to be +ve
IMO C sufficient

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

Is x<0?
1) x + y = -12--------(i)
If x = -1, then y= -11, So, x<0, Yes
If x = 0, then y = -12, So, x<0, No
Insufficient.
2) y < x-12
x-y>12-----------(ii)
If x = 0 and y = -13, 13>12. So, x<0, No
If x = -1 and Y= -14, 13>12, So x<0, Yes
Insufficient.
1) + 2)
By solving equation (summation) i and ii
x+y = -12
x-y > 12
----------
2x ≥ 0
So, x≥ 0, which can never be negative.

Hence, Ans. is C.
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Answer is C

St-1: not sufficient as value of x can be positive, zero or negative depending on the value of y

St-2: not sufficient as value of x can be positive, zero or negative depending on the value of y

Using both statement 1 and 2
y<x-12
--> x-y>12-----(1)

from 1 we have x+y=-12
y=-12-x
-->substituting value in (1)
x+12+x>12
2x>0
x>0

therefore both statements combined are sufficient
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C is the answer to the above question substitute the value
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is x negative?
(1) x + y = -12
(2) y < x-12


Answer: C
Solution:
x <0?
(1) x + y = -12
so if x = 0, y =-12: answer is no
so if x = -1, y = -11: answer is yes
so (1) is insufficient
(2) y< x-12
so if x = 0 & y =-13: answer is no
so if x = -1, y = -14: answer is yes
so (2) is insufficient
combining (1)+(2): replacing y = -12-x from (1) into (2)
-12-x < x-12
2x>0
x> 0
so the answer is no
so (1)+(2) is sufficient
Answer: C
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Answer: C

1. x+y=-12
There are various possibilities of values of x and y for which x+y=-12
Not sufficient

2. y-x<-12
Different value of x and y are possible (both positive and negative) which can satisfy this equation. Not sufficient

3. Consider both the statements
From equation 1, x+y=-12 which implies x=-y-12 ..............(A)
Substituting (A) in equation 2,
y-x<-12
y-(-y-12)<-12
2y<-24
y<-12

Now, since y<-12 and from equation 1, x+y=-12, x must be positive to satisfy the given equation.
So the answer is No, x is not negative.
Sufficient
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1) Insufficient.
No information about x is given. For example, x can take on the value 0, -2, etc. There's no restriction.
2) Insufficient.
No information about x is given. For example, x can take on the value 0, -2, etc. There's no restriction.
1)+2) Suffcient
y<x-12. Adding x to both terms
y+x<x+x-12
x+y<2x-12
From 1) we know that x+y=-12, then
x+y=-12<2x-12
Clearly -12+12<2x. Therefore x>0 (answer the question)
Answer: C
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Hi All,

I have a doubt: when we combine the statements, by inserting St-2 into St-1, we have that
x+y=-12 --> (St-1)
x+(x-12) <-12 --> (since St-2 is y<x-12)

Solving this gives x<0, which I understand is incorrect. When I insert St-1 into St-2, I get x>0 however, I really want to know why the above produces a wrong answer.

Bunuel GMATBusters ScottTargetTestPrep

Thank you
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