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Each employee of Company Z is an employee of either Division [#permalink]
31 Aug 2007, 09:28
Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of FT employees to the number of PT employees greatre for Division X than for Company Z?
1) The ratio of the number of FT employees to the number of PT employees is less for Division Y than for Company Z
2) More than half of the FT employees of Company Z are employees of Division X and more than half of the PT employees of Company Z are employees of Division Y
- Division X: more (must be higher to balance out the division Y ratio)
- Division Y: less (given)
2) No specific information about the actual number of FT and PT employees, there could be an extreme difference in the number of FT versus PT employees in the company, one way or the other, that can throw the ratios anywhere.
Company Z = Division X + Division Y = (FTx + PTx) + (FTy + PTy)
FTx=Full Time Employee of Div X
PTx=Part Time Employee of Div Y
FTy=Full Time Div Y
PTy=Part Time Div Y
We're looking to find if FTx/PTx is > or < (FTx+FTy)/(PTx+PTy)
1) FTy/PTy < (FTx+FTy)/(PTx+PTy)
This tells us nothing about the number or ratio of part time/full time workers in X. It could be that Y has fewer total works than X or that Y has many more part time workers than X.
2) 1/2(FTx + FTy)< are in Div X and 1/2(PTx + PTy)< are in Div Y
This tells us that the FTx/PTx is at least greater than 1 and that (PTx + PTy) > than PTx. Therefore FTx/PTx has to be greater than (FTx + FTy)/(PTx + PTy) b/c the numerator of FTx/PTx is at least 2(FTx + FTy) while the denominator of FTx/PTx is at least 1/2(PTx+PTy)