Ratios

[moneyman]

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

[lunarpower]

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

[moneyman]

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

[gmattakers]

Great explanation, lunarpower

[cramya]

As usual Ron's post is awesome!!

Hey,
If u want the proof refer to
https://www.beatthegmat.com/questions-fr ... html#90653

I did it by using the inequalities given.

[its time]

Hi Ron,
Thanxs a great explanation and really helps..i m still not very clear with the second part though...can u kindly explain a little more..
when u say that ''the ratios are (higher / lower) for div. x and (lower / higher) for div. y''..how does is it say that ratio of FT/PT for x >FT/PT for z???

Thanx..

[MFaulkner]

I agree, great explanation!

this question had me stumped before this

[maaz_gmat]

Still couldn't crack this.. Ron, Not sure when we are comparing the ratios between x and Y as explained by you, how that relates to the question asked. Ratio of FT to PT greater for Division X than for company Z.

If it were Ratio of FT to PT greater for Div X than for Div Y, it seemed to be a solution. Please help in the understanding of the same.

Thanks.

[abhicoolmax]

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

Great abstraction Ron. Loved your choices of words.

In other words, I think Ron's words can also be translated as (Ron please correct me if I wrong? I used the following in my GMATPrep - I was looking for alternate solution!):
1. If x1/y1 > (x1+x2)/(y1+y2) , then x1/y1 > x2/y2 (For all +ve values of x1,x2,y1,y2)
- this what we need to prove (Question Stem)
2. If (x1+x2)/(y1+y2) > x2/y2 , then x1/y1 > x2/y2 (For all +ve values of x1,x2,y1,y2)
- this is what Stmt-1 says
3. If x1>x2, y2>y1 Then x1/y1 > x2/y2 (For all +ve values of x1,x2,y1,y2)
- this is what Stmt-2 says

NOTE: the choice of x1,x2,y1,y2 has nothing to do with the original question. This is just an abstraction or rather generalization.

[sachindia]

Hi Ron,
I am unable to digest how the following can be true..

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.

Please help..

[lunarpower]

Hi Ron,
I am unable to digest how the following can be true..

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.

Please help..

hi,
please explain exactly what you don't understand. if you just say "i can't digest it", then the best i can do is simply to repeat the concept. that won't help anybody.

in different terms --
if you have a/b and c/d, where a > c and b < d, then a/b is definitely bigger than c/d.
maybe that will help

[sachindia]

Hi Ron,
I was actually unable to understand how 'overall' ratio will be higher for but after thinking about this Question on the lines of weighted average concept, could understand that ratio has to be higher for X when compared to the same of the company Z.