tohellandback wrote:If xyz ≠ 0, is x (y + z) ≥ 0?


1) |y + z| = |y| + |z|
2) |x + y| = |x| + |y|

OA later

IMO C coz if we take either statement then both y an z or x and y will have the same sign.. and hence we don't know what could be the sign of x(y + z).

but if we take both the statements then we know that x, y, z should have the same sign and then we know that x(y+z)>0..
hence C..

ketkoag wrote:

tohellandback wrote:If xyz ≠ 0, is x (y + z) ≥ 0?


1) |y + z| = |y| + |z|
2) |x + y| = |x| + |y|

OA later

IMO C coz if we take either statement then both y an z or x and y will have the same sign.. and hence we don't know what could be the sign of x(y + z).

but if we take both the statements then we know that x, y, z should have the same sign and then we know that x(y+z)>0..
hence C..

could you elaborate the statement in bold?

1) |y + z| = |y| + |z| --> this implies that both y and z are positive.
e.g. if y=1 and z=-2 then |(+1) + (-2)| = -1 but |+1| + |-2| = 3 so y and z must both be positive for the eqn to hold. This however, still doesn't tell us about x (it couldn be +ve or -ve, all we know about z form the given info is that is is non-zero.

2) |x + y| = |x| + |y|--> for similar reasons as in 1), x and y must both be positive byt we don't know about z (it can be positive or negative)

1) and 2) together, we know that x, y and z are positive hence x(y+z) must be >0.

life is a test wrote:1) |y + z| = |y| + |z| --> this implies that both y and z are positive.
e.g. if y=1 and z=-2 then |(+1) + (-2)| = -1 but |+1| + |-2| = 3 so y and z must both be positive for the eqn to hold. This however, still doesn't tell us about x (it couldn be +ve or -ve, all we know about z form the given info is that is is non-zero.

2) |x + y| = |x| + |y|--> for similar reasons as in 1), x and y must both be positive byt we don't know about z (it can be positive or negative)

1) and 2) together, we know that x, y and z are positive hence x(y+z) must be >0.

I dont think the equations imply they are both positive.

IMHO C,

for first to be true both y, z has to be same sign, but x could be any sign and magnitude so not suff.

similarily for second to be true both x, y has to be same sign, but z could be any sign and mag so not suff,

combined x, y, z has to be same sign, either all positive or all neg, either way x(y+z)>=0

so C

wots the OA?

OA is C

|y + z| = |y| + |z| --> this implies that both y and z are positive.
e.g. if y=1 and z=-2 then |(+1) + (-2)| = -1 but |+1| + |-2| = 3 so y and z must both be positive for the eqn to hold. This however, still doesn't tell us about x (it couldn be +ve or -ve, all we know about z form the given info is that is is non-zero.


****************************************************
The statement implies that both y and z have same signs: both positive or both negative.

|4+5| = |4| + |5|
|-4-5|= |-4|+|-5|[[/spoiler]