Statement [1]
Consider z= 2 and x =3,
then |x-z| + |x| = |3-2| + |3| = 1 + 3 = 4
and |z| = |2| = 2
Hence |x-z| + |x| is not equal to |z|
Consider another example
z = -4, x = -2
then |X-z| +|x| = | -2 + 4| + |-2| = 2 + 2 = 4
and |z| = |-4| = 4
Hence |x-z| + |x| = |z|
So statement [1] alone is not sufficient.
From statement [2]
as y > 0 and using zy < xy, we get z < x
And as proved earlier, this is not sufficient.
So statement [1] and [2] together are not sufficent.
Whats the OA?
Thanks
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Source: Beat The GMAT — Data Sufficiency |
OA is d...
For 2nd Statement : since y > 0 we can very well say that z < x < 0 hence ur example
z = -4, x = -2
then |X-z| +|x| = | -2 + 4| + |-2| = 2 + 2 = 4
and |z| = |-4| = 4
Hence |x-z| + |x| = |z|
tells that statement [2] is sufficient
For 1st condition : i feel to satisfy zy < xy < 0
y has to be greater than 0
hence condition same as specified in [2]
So [1] must also be sufficient
For 2nd Statement : since y > 0 we can very well say that z < x < 0 hence ur example
z = -4, x = -2
then |X-z| +|x| = | -2 + 4| + |-2| = 2 + 2 = 4
and |z| = |-4| = 4
Hence |x-z| + |x| = |z|
tells that statement [2] is sufficient
For 1st condition : i feel to satisfy zy < xy < 0
y has to be greater than 0
hence condition same as specified in [2]
So [1] must also be sufficient
