Gmat Prep 2

[maribelsalazar02]

Hi, I can't see how the following Gmat Prep Test 2 data suffic. problem is solved. Please explain..

If zy < xy < 0, is |x-z| + |x| = |z|?

1) z< x
2) y > 0

Official Answer is D

Thanks!

[atul.prasad]

It is given that

zy < xy < 0

consider zy < xy
If we could ascertain that y was > 0 , we could have divided both sides of inequality by y without changing the sign of inequality (note y cant be 0 here since it is given they are < 0)

Statement 1 tells us exactly that:
since z < x , and we have zy < xy y must be +ve

also since zy < 0 and xy < 0 , hence x and z must be negative.

So |x-z| + |x| = x - z + (-x) ( since x > z and |x| = -x because x < 0)
= -z = |z| since we evaluated above that z < 0

So 1 is sufficient

Statement 2 gives us exactly what we needed to know:
since y > 0, z < x and both x and z are -ve , as evaluated above.

So 2 is also sufficient

Hence D is the correct answer

[jnelson0612]

atul, again, excellent work! I have nothing to add to your outstanding explanation.

maribel, please post again if you are still confused.

Thank you,