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moneyman
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PostPosted: Tue May 06, 2008 4:49 am    Post subject: Ratios Reply with quote
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.


Ans D
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PostPosted: Thu May 08, 2008 1:00 am    Post subject: Re: Ratios Reply with quote
moneyman 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.


Ans D


why two question marks? is it to give the problem an extra sense of urgency? just wondering.

here's a fact that you should know. i can furnish a proof if you reallyreallyreally want me to, but it should be clear:
if a data set can be split into two groups, both of which have at least the ratio a:b for some 2 characteristics, then the entire data set has at least the ratio a:b for those 2 characteristics.
in other words, if the ratio of FT to PT employees is at least, say, 3:1 in both divisions, then the overall ratio of FT to PT employees must also be 3:1.

here's a corollary:
if a data set can be split into two groups, and one of the groups has a ratio HIGHER than the overall ratio for some 2 characteristics, then the other group has a ratio LOWER than the overall ratio for those 2 characteristics - and vice versa.
this follows logically from the above statement, because it violates the first result (and common sense) if both divisions' ratios are somehow higher (or both lower) than the overall ratio.

--

statement (1)
this statement must be true, because if div. y has a lower ratio, then div. x must have a higher ratio to balance things out (see the corollary above).

so, sufficient.

if you want actual inequalities to prove this, i would be glad to provide them, but you should be able to conceptualize this result so that you have a fighting chance of completing the problem within the allotted time.

--

statement (2)
because FT and PT are mutually exclusive, this statement implies that div. x has more FT employees, but fewer PT employees, than does div. y.

therefore, the ratios are (higher / lower) for div. x and (lower / higher) for div. y, so the overall ratio must be higher for div. x.

sufficient

answer = d
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moneyman
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PostPosted: Thu May 08, 2008 4:48 am    Post subject: Reply with quote
Wonderful explanation Ron..Oh and the two question marks is just a habit though it does conatin some frustruation for not having understood the problem Smile
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PostPosted: Thu Oct 30, 2008 4:45 pm    Post subject: Reply with quote
Great explanation, lunarpower
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PostPosted: Thu Oct 30, 2008 7:49 pm    Post subject: Reply with quote
As usual Ron's post is awesome!!

Hey,
If u want the proof refer to
http://www.beatthegmat.com/questions-from-og-cat-t21470.html#90653

I did it by using the inequalities given.
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