Are you sure about the answer? Thanks
with 1) you know that y and z have the same sign, but you don't know anything about x

Firstly dont think A is the answer ..let's look at it
statement 1 :
y & z are either both negative or both positive
don't know anything about x . hence statement 1 insufficient

statement 2 :
x & y are either both negative or both positive
don't know anything about z . hence statement 2 insufficient

taking both the statement together
if from statement 1 , we say y,z are negative , then x is also negative which we can derive from statement 2 because x,y are of the same sign
in this case x(y+z) > 0

if from statement 1 , we say y,z are positive , then x is also positive which we can derive from statement 2 because x,y are of the same sign
in this case x(y+z) > 0

So , I will go with option C

jainrahul1985 wrote:If xyz ≠ 0, is x (y + z) ≥ 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|
OA A

xyz ≠ 0 or x,y or z ≠ 0
1) |y + z| = |y| + |z| so y & z have the same sign
but no info about the sign of x
so x(y+z) may be +ve or -ve Insuff
2) |x + y| = |x| + |y| so x & y have same sign
but no info about the sign of z Insuff
Combining x,y & z have same sign
xy + xz > 0 but ≠ 0
so either C or E

kstv wrote:

jainrahul1985 wrote:If xyz ≠ 0, is x (y + z) ≥ 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|
OA A

xyz ≠ 0 or x,y or z ≠ 0
1) |y + z| = |y| + |z| so y & z have the same sign
but no info about the sign of x
so x(y+z) may be +ve or -ve Insuff
2) |x + y| = |x| + |y| so x & y have same sign
but no info about the sign of z Insuff
Combining x,y & z have same sign
xy + xz > 0 but ≠ 0
so either C or E

St1 doesn't say abt X

St2 doesny say abt Z

Combining we get Inconsistent answers.
Examples :
x= -3,y=-2 z=-1
we have x (y + z)

: -3 *(-2-1) >0

when we have x=-3,y=-2,z=4
x (y + z) <0

Inconsistent ..Rite??

So pick E.

OA pl. ?

jainrahul1985 wrote:If xyz ≠ 0, is x (y + z) ≥ 0?
(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|

OA A

will you pl. cross check the OA again and post again?

debmalya_dutta wrote:Firstly dont think A is the answer ..let's look at it
statement 1 :
y & z are either both negative or both positive
don't know anything about x . hence statement 1 insufficient

statement 2 :
x & y are either both negative or both positive
don't know anything about z . hence statement 2 insufficient

taking both the statement together
if from statement 1 , we say y,z are negative , then x is also negative which we can derive from statement 2 because x,y are of the same sign
in this case x(y+z) > 0

if from statement 1 , we say y,z are positive , then x is also positive which we can derive from statement 2 because x,y are of the same sign
in this case x(y+z) > 0

So , I will go with option C

Perfect solution!

From (1), we know that y and z are the same sign, but know nothing about x.

From (2), we know that x and z are the same sign, but know nothing about y.

Together, we know that all 3 are the same sign.

So, when we multiply out the expression in the question, we're always going to get a non-negative answer: sufficient.

(I say non-negative because we could have x=y=z=0 and a final answer of 0.)