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Each employee of company Z is an employee of Division X

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Each employee of company Z is an employee of Division X

by varun289 » Sun Dec 16, 2012 9:52 am
Each employee of company Z is an employee of Division X or Division Y. 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 of 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 aman88 » Sun Dec 16, 2012 10:15 am
IMO B
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by puneetkhurana2000 » Sun Dec 16, 2012 3:18 pm
This is a good question from 800score.com and I got it right but it took me about 3 minutes, so will post a quicker way to solve this soon.

Thanks

Puneet
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by Anurag@Gurome » Sun Dec 16, 2012 7:49 pm
varun289 wrote:Each employee of company Z is an employee of Division X or Division Y. 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 of 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
XfYp + YfYp > XpYf + YpYf
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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