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by Akansha » Mon May 23, 2011 9:29 pm
Each employee of company Z is employed in 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 number of part-time employees greater for Division X
than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for
division Y than for company Z
b. More than ½ of full-time employees of company Z are employees of div
X, and more than ½ of part-time employees of company Z are employees
of div Y

OA is D
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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon May 23, 2011 10:50 pm
Akansha wrote:Each employee of company Z is employed in 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 number of part-time employees greater for Division X
than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for
division Y than for company Z
b. More than ½ of full-time employees of company Z are employees of div
X, and more than ½ of part-time employees of company Z are employees
of div Y

OA is D
Let the no. of full time employees in Division X and Y be Fx and Fy respectively.
Also let the no. of part time employees in Division X and Y be Px and Py respectively.
Then the question is: Is Fx : Px > (Fx + Fy) : (Px + Py) or is FxPy > PxFy?

(1) Fy: Py < (Fx + Fy) : (Px + Py) or FyPx < PyFx or FxPy > PxFy.
So, (1) is SUFFICIENT.

(2) (Fx + Fy)/2 < Fx and (Px + Py)/2 < Py
Fx/Fy > 1 and Py/Px > 1 implies FxPy > PxFy
So, (2) is SUFFICIENT.

The correct answer is D.
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by Frankenstein » Mon May 23, 2011 10:56 pm
Hi,
From(1):
Let the no. of full-time and part-time employees of Division X be a and b respectively
Let the no. of full-time and part-time employees of Division Y be c and d respectively
c/d < (a+c)/(b+d) => (bc+cd-ad-cd)/d.(b+d) < 0 => bc-ad/d.(b+d)<0 => bc -ad <0 =>bc<ad
Adding ab on both sides we get bc+ab < ad+ab =>b(a+c) < a(b+d) => b(a+c)/b.(b+d) < a.(b+d)/b.(b+d)
=>(a+c)/(b+d) < a/b
So, the ratio of the number of full-time employees to number of part-time employees is greater for Division X than for Company Z
Sufficient

From(2): a > (a+c)/2 and d > (b+d/2) => 2a>a+c and 2d > b+d => a>c and d>b. So, ad > bc.
From this, we can proceed in the way we did for case(1)
Sufficient

Hence, the answer is D. As of now, I can't give a simpler solution. I will try to make it simple and post it if at all I get any.

Cheers!
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