Data Sufficiency

Please explain the approach to this problem, any shortcuts it took me a while to get to this one. OA later. Would appreciate detailed discussion

Its D , solving ratios u get easily ..will post explanation later as leaving for office now

Coming to explanation now..

Cosider very simple eqns..

Lets fx be the full time employee of X division , and fy be full time for Y and fz be fulltime for company Z

fz = fx + fy --eqn (1)

Similaryly let px be partime employe of divsion x and pz be of Y division and pz of Z company as a whole.. so

pz = px + py --eqn(2)

From Statemnent 1 of the question , you get fy/py < fz/pz
Now this ratio can be rewitten as pz/py < fz/fy
Subsitue the value of fz and pz from above eqns..
You get 1 + (px/py) < 1 + (fx/fy)
===> px/py < fx/fy..reoraginse this ratio as fy/fx < py/px..whxich again be written as 1 + fy/fx < 1 + py/px ==> (fy + fx)/fx < (py + px)/px
.===> fz/fx < pz/px ==> fz/pz < fx/px---------> Sufficient

From statement (2) you know fx > fy and px < py...
fx/px > fy/px ----> as fx > fy ...
Now fy/px > fy/py --- as px < py (Numerator remaing same if u increase the ratio it becomes less)
So this further implies fx/px > fy/py ---> Following same logic as for statement 1 you can re-organise this ratio as below

py/px > fy/fx ==> (pz - px)/px > (fz - fx)/fx==> pz/px - 1 > fz/fx - 1
==> fz/pz <fx/px--------Sufficient.

Choose D

Dont u have a shorter or easier explanation, that strikes u in the 2min time limit??? I mean what should be approach to get the answer in the GMAT conditions and quick!

For me it was 50 secs to be true.. to expplain u how i formed ratios it took me time to type

i just formulated ratios instantly , its very easy if u put in paper.. Yiu got be comfortable with ratios to get intutive ..what i showed i could have just made use of 1 ratio and directly would have arrived at answer but then uou might have got confused with how exactly i got , etc...

But if u read carefully all i did is ratio manipulations and nothing else..and its very simple if u juggle with ratios

Basically only u need to care if fz = fx + fy and pz = py + px and make use of the statements.. Moment you make use of these you will see answer coming to u ..