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# Each employee of Company Z is an employee of either division

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Intern
Joined: 14 Jan 2006
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Each employee of Company Z is an employee of either division [#permalink]

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27 May 2006, 13:37
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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 employee 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.

please explain.

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Manager
Joined: 25 Apr 2006
Posts: 50

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27 May 2006, 17:22
Ans: B

(1) ratio of FT to PT emp of Comp. Z and Div Y doesnt tell us anything about the ratio relation between comp Z and Div X. Not Sufficient

(2) Increase in FT emp of Div X and decrease in PT emp of Div X (since it is more in Div Y) increases the the ratio for Div X while the ration remains the same for Comp. Z. Suff.

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Intern
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28 May 2006, 03:43
nope. its not correct according to gmat prep.

Anyone else wants to try ?

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VP
Joined: 21 Sep 2003
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Location: USA

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28 May 2006, 09:06
Initially got A , but it should be D.

Let:
x = number of FT employees in div X
y = number of FT employees in div X

p = number of FT employees in div Y
q = number of FT employees in div Y

What is asked?
Is x/y > (x+p)/(y+q)
=> Is x/y > p/q?

1. Given, p/q < (x+p)/(y+q)
=> p/q < x/y Hence SUFF.

2. 1/2(x+p) < x and 1/2(y+q) < q
or

x/(x+p) > 1/2 & q/(y+q) > 1/2

Add these 2:

x/(x+p) + q/(y+q) > 1
xy+xq+xq+pq > xy+xq+py+pq
=> x/y > p/q

Hence D.
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Intern
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28 May 2006, 15:57
OA is 'D'

good work giddi. i couldn't solve the problem. thanks for the explanation.

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28 May 2006, 15:57
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# Each employee of Company Z is an employee of either division

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