An 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 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.

Statement (1) says - (F.T in Y)/(P.T in Y) < (F.T in Z)/(P.T in Z). We do not know the distribution of employees within the X & Y, also there is no information about the distribution of Full time and part time employees in Z. Hence insufficient

Statement (2) gives information about the employee distribution between X & Y, in terms of full time and part time employees. To realize the information lets assume: -

Total employees in Z = 50, Total Full Time = 30, Total Part Time = 20 Ratio in Z = 30/20 = 3/2

So, No. of Full time employees in X > 15(more thn half) lets assume 18,

Also No. of part time employees in Y > 10(more thn half). lets assume 12

So the no. of part time employees in X =8 Hence ratio in X = 18/8 = 9/4 >2

Similarly ratio in Y = 12/12 = 1

So Ratio in X > Ratio in Z > Ratio in Y

But we don't know the distribution of Full time Vs Part time employees in Z, X& Y
So lets flip to the no of F.T in Z = 20 and P.T = 30 Now Ratio in Z = 20/30 = 2/3

So No. F.T in X > 10 (Assume 12) so F.T in Y = 8

and P.T in Y > 15 (Assume 18) so P.T in X = 12

Ratio in X = 12/12 = 1
Ratio in Y = 8/18 = 4/9
Ratio in X = 2/3

Ratio in X > Ratio in Z> Ratio in Y

Hence it is sufficient. Answer is (B)

I did something similar and came up with the same answer. But as per GMATPrep the answer is (D).

You are right on about statement (2). As for (1), watch out for ratio problems like this...the important take-away is that ratios are often more powerful than they look. You may have more information than you think because, by definition, ratios have a relationship between variables embedded in them. Here's the approach I used for (1).

Set up a chart with X, Y, and Z (the total of X + Y) in columns, and PT and FT in rows. We'll call the number of PT employees Px, Py, and Pz for X, Y, and Z, respectively. Remember that Px, Py and Pz are all greater than 0. Similarly, we'll call the number of FT employees Fx, Fy, and Fz for X, Y, and Z, respectively.

The question asks: Is Fx/Px > Fz/Pz?

(1) SUFFICIENT: We are told that Fy/Py < Fz/Pz.

Note that (Fx + Fy = Fz) and (Px + Py = Pz) so we can write the division Y quantities in terms of the Z and X quantities, rephrasing the statement this way:

Fy/Py < Fz/Pz
(Fz - Fx)/(Pz - Px) < Fz/Pz
Pz(Fz - Fx) < Fz(Pz - Px) <--We don't have to flip the sign here; the question told us that all P values are positive.
PzFz - PzFx < FzPz - FzPx
- PzFx < - FzPx
PzFx > FzPx <--Flip the sign here; we multiplied by -1.
Fx/Px > Fz/Pz <--We don't have to flip the sign here; the question told us that all P values are positive.

This answers the question with a definite "yes."

So, the correct answer is D.

Thanks for the explanation Emily. To be honest with you, I went to this route but fumbled because it was taking lot of time. Any suggestions?

GMAT 2007

I chose answer B the first time.

But then I got it.

2 gives fy/py < (fx + fy/px + py)

fy(px + py) < py(fx + fy)

fyPx + fypy < pyfx + pyfy

fypx < pyfx

fy/py < fx/px - SUFFICIENT

Biggest thing, GMAT 2007? Recognize that this is going to happen to you on the test, too, so think about how you're going to make an educated guess when necessary.

The essential shortcut for (1) here is to understand thoroughly what information a ratio does (and does not) tell you, and how multiple related ratios work. If you understand them thoroughly, then you'll realize that, from statement 1, if the overall company's ratio is greater than that for division y, then division x's ratio must be greater than that for the overall company, because the two ratios come together, or combine, to provide the overall company ratio.

If you don't know the material well enough to see that intuitively, or if you just miss it in the stress of the test (which will also definitely happen), then it's going to be a lot tougher to get this in two minutes. That's when you move to educated guessing.

On DS, always start with whichever statement you think is easier. Even if you can only get through that one, you've narrowed down to 2 or 3 answers, so you have a much better shot if you have to pull the plug, guess, and move on. If you can do a little more beyond that, then you might be able to get a feel for which answer to choose (from among the remaining answers), but at the least you've eliminated at least 2 choices just by working through one statement.

Division X Division Y
Part Time a b
Full Time c d

We need to find if, c/a > (c+d)/(a+b) , or ac+bc > ac+ad , or bc > ad. So bc > ad is what we need to prove.

1.. tells us d/b < (c+d)/(a+b) , or ad+ab < bc + bd , which is not sufficient to prove bc > ad.

2.. tells us 2 things. First c> (c+d)/2 , or c > d. Second b > (a+b)/2 or b > a. Both of these together imply bc > ad. Hence sufficient.

1.. gives us ad+bd < bc+bd
sp bc > ad