DS Power prep

[Suresh]

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 employees to the number of part-time employees greater for Div 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 Div Y than for Company Z.
(2) More than half of the full-time employees of Company Z are employees of Div X, and more than half of the part-time employees of Company Z are employees of Div Y

OA is D. Someone please explain. Thank you!

[RonPurewal]

(1)
remember that ratios are the same as fractions in this sort of context.
this statement means that the FT employees are a smaller fraction of division Y than of the company as a whole. this means that they must be a bigger fraction of division X than of the company as a whole, because the fraction of the whole company that's employed FT must be between the two divisions' fractions.
sufficient.

(analogy: if i mix two powders together to make a shake that's 5% fat, and the first powder is 3% fat, then the second powder must be more than 5% fat)

--

(2)
the first part means that (FT in div. X) > (FT in div. Y), and the second part means that (PT in div. X) < (PT in div. Y).
therefore, considering the ratio of FT : PT for each division, we have that FT/PT for div. X must be greater than FT/PT for div. Y. (this is the case because of either the numerator or the denominator: the numerator of X is greater, and the denominator is smaller.)
since the FT/PT fraction is bigger for div. X than for div. Y, it must be bigger for div. X than for the company as a whole (see the reasoning above under statement (1) for why this is true).
sufficient.

[Suresh]

I think I was overwhelmed during the exam with the length of the question. After seeing your explanation I don't understand why I couldn't solve it.
Many thanks!!!

[700+]

(1)
remember that ratios are the same as fractions in this sort of context.
this statement means that the FT employees are a smaller fraction of division Y than of the company as a whole. this means that they must be a bigger fraction of division X than of the company as a whole, because the fraction of the whole company that's employed FT must be between the two divisions' fractions.
sufficient.

(analogy: if i mix two powders together to make a shake that's 5% fat, and the first powder is 3% fat, then the second powder must be more than 5% fat)

I'm not able to clearly understand this part. Could you please explain with a much more elaborate example.

[RonPurewal]

I'm not able to clearly understand this part. Could you please explain with a much more elaborate example.

1/
for us to help you, you'll have to specify what you didn't understand.

2/
what do you mean by "much more elaborate"?
i'll assume you don't actually mean elaborate, because an example that's actually elaborate, by definition, will be harder to understand than an example that's simple.

[namnam123]

pick number to do this fast

100=30-fx+10-fy+20-px+40-py

30= number full time of x division.

finish in 1 minutes.

[RonPurewal]

pick number to do this fast

100=30-fx+10-fy+20-px+40-py

30= number full time of x division.

finish in 1 minutes.

whoa, that doesn't work. you can't pick ONE VALUE for a data sufficiency problem, and then think you're done!
if you do that, you'll think that every statement is always sufficient.

it is possible to use number plugging on data sufficiency, but you have to plug in MULTIPLE possible values.
if you keep getting the same answer with all of your plug-ins, then the statement is sufficient.
if two of your different plug-ins give two different answers -- clearly something that can never happen with one plug-in -- then the statement is insufficient.

[prashant.ranjan]

I know that if we solve this question algebraically, it's going to take a little more time......but still following is the algebraic approach....

The question is asking If
Fx/Px > (Fx + Fy) / (Px + Py)
We can solve this further ...
Is Fx/Px > Fy/Py

(1) says
Fy / Py < (Fx + Fy) / (Px + Py)
Cross multiplying we get
Fy Px < Fx Py
=> Fx/Px > Fy/Py
Sufficient.

(2) says (As Ron has said above....) Fx> Fy and Py > Px
Finding the ration we get Fx/Px > Fy/Py
Hence Sufficient and (D) as the answer

Thanks and Regards
Prashant

[tim]

thanks!

[rkafc81]

Hi

I have some questions about this question :)

* How do I do this question by the process of discovery and generating numbers etc.?

* What does Ron mean by this?
(1)
remember that ratios are the same as fractions in this sort of context.

* I got mixed up understanding what signifiies a greater ratio... Is a ratio of 2:1 greater than 4:1 ? or less than 4:1?

thanks

[RonPurewal]

* How do I do this question by the process of discovery and generating numbers etc.?

try making up some numbers that satisfy the statements. then, find the requisite ratio from those numbers.

remember that your goal, when you pick your own numbers, is to prove insufficiency.
on this problem, you get "insufficient" if you can get ...
... an instance in which the desired ratio is greater for X than for Z;
and
... an instance in which it isn't.
if you can't get both of these cases -- i.e., if you get the same one of these cases every single time -- then you pick "sufficient".

it's not very hard to come up with numbers that satisfy these statements. the only possible challenge is the presence of lots of different quantities, but that's something you can handle with a good organizational chart.
for each statement, you should find that the answer to the question is always "yes" no matter which numbers you pick.

* What does Ron mean by this?
(1)
remember that ratios are the same as fractions in this sort of context.

since it's a sufficiency problem, the idea is that having a ratio is the same as having a fraction.

let's say you're talking about boys and girls in a class.
then, "the fraction of the class consisting of boys = 2/5" is the same as "the ratio of boys to girls = 2:3".
"the fraction of the class consisting of boys = 1/2" is the same as "the ratio of boys to girls = 1:1".
etc.
also, the bigger the fraction gets, the bigger the ratio gets, too. therefore, phrasing a question like this one in terms of fractions isn't different from phrasing it in terms of ratios.

* I got mixed up understanding what signifiies a greater ratio... Is a ratio of 2:1 greater than 4:1 ? or less than 4:1?

remember that ratios themselves are, algebraically, like fractions. (they aren't equivalent to the fractions discussed above.)
so, because the fraction 2/1 is less than the fraction 4/1, it follows that 2:1 is a smaller ratio than 4:1.

[supratim7]

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

...............Div X........Div Y
Full T..........a.............b.........a+b
Part T.........c.............d..........c+d
................a+c.........b+d.......a+b+c+d

(a, b, c, d are all positive all integers)

is the ratio of the number of full-time employees to the number of part-time employees greater for Div X than for Company Z?

Rephrase: a/c > b/d? or ad > bc?

(1) The ratio of the number of full-time employees to the number of part-time employees is less for Div Y than for Company Z.

b/d < a/c (Sufficient: AD)

(2) More than half of the full-time employees of Company Z are employees of Div X, and more than half of the part-time employees of Company Z are employees of Div Y

a > (a+b)/2
a > b
a = GT b

d > (c+d)/2
d > c
c = LT d

a/c > b/d?
GT b/LT d > b/d? Yes. (Sufficient: D)

Is the process fine??

Many thanks | Supratim

[jlucero]

All of this looks good except one tiny detail. The original question should actually be stated not as Rephrase: a/c > b/d but as a/c > (a+b)/(c+d). Ultimately, this would be rephrased as what you have (which might be what you implied here), so you are 100% correct with your answer.

[supratim7]

All of this looks good except one tiny detail. The original question should actually be stated not as Rephrase: a/c > b/d but as a/c > (a+b)/(c+d). Ultimately, this would be rephrased as what you have (which might be what you implied here), so you are 100% correct with your answer.

my bad.. missed it.

Statement (1) also needs similar correction..

"The ratio of the number of full-time employees to the number of part-time employees is less for Div Y than for Company Z.
b/d < (a+b)/(c+d)
bc + bd < ad + bd
bc < ad (Sufficient: AD)"

Thank you for the correction Joe. Appreciate it.

[jnelson0612]

Thanks, Joe and supratim! And yes, I was just reading the thread and thinking that your interpretation of statement 1 needed to be fixed. Glad that you caught it. :-)