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by naveen451 » Thu Aug 04, 2011 3:19 am
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 full-time employees to the number of part-time employees greater for Division X than for Company Z?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.
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Source: — Data Sufficiency |
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by Ozlemg » Thu Aug 04, 2011 4:13 am
naveen451 wrote: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 full-time employees to the number of part-time employees greater for Division X than for Company Z?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.
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Last edited by Ozlemg on Thu Aug 04, 2011 4:17 am, edited 1 time in total.
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by Anurag@Gurome » Thu Aug 04, 2011 4:16 am
naveen451 wrote: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 full-time employees to the number of part-time employees greater for Division X than for Company Z?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.
Let us assume number of full-time employees for division X = Xf
Number of part-time employees for division X = Xp
Number of full-time employees for division Y = Yf
Number of part-time employees for division Y = Yp

Then question is: Is Xf/Xp > (Xf + Yf)/(Xp + Yp)? or is XfXp + XfYp > XpXf + XpYf? or is XfYp > XpYf?

(1) (Xf + Yf)/(Xp + Yp) > Yf/Yp
or XfYp + YfYp > XpYf + YpYf
or XfYp > XpYf, which answers the required question; SUFFICIENT.

(2) (Xf + Yf)/2 < Xf and (Xp + Yp)/2 < Yp
Yf < Xf and Xp < Yp, which implies XpYf < XfYp, which again answers the required question; SUFFICIENT.

The correct answer is D.
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by gmatboost » Thu Aug 04, 2011 7:38 am
We can also try to approach this using logic rather than algebra:

In order for the ratio of FT:PT to be greater for X than for Z, it has to be greater for X than for Y, since Z is made up of X and Y.

Statement 1 says that the ratio of FT:PT is less for Y than for Z. The only way for this is possible is if the ratio of FT:PT is greater for X than for Z. Sufficient.

Statement 2 basically says that X has more than half of the FT and less than half of the PT. So,it has a relatively large ratio of FT:PT. On the other hand, Y has less than half of the FT and more than half of the PT. So, it has a relatively small ratio of FT:PT. So, the FT:PT ratio is larger in X. Sufficient.

I know that's a lot of words, but I encourage you think through the steps above and see if it's helpful for you, because if applied correctly it might save some time.
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by AN24 » Wed Aug 17, 2011 7:44 am
D
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