given d:nd = 2/3

first thing first... we have no idea abt the actual doctorates or non - doctorates from the given data...

now..

statement 1)
here they are talking abt actual number of people hired... and the new ratio will differ since we dont know the original number of people...
lets say for eg..
assume that there are actually 2 doc and 3 non docs...
d: nd = 2/3

now again lets say if there is 1 non doc who was hired, so keeping the first statement in mind... we will be adding 2 doc

new ratio = (2 + 2) / ( 3+ 1) = 4/ 4 = 1

now lets assume originally there are 4 docs and 6 non docs... keeping the ratio 2:3

so new ratio = (4 +2) / (6 + 1) = 6/7

so as u can see the ratio will not remain constant...

i have demonstrated will actual numbers... but u dont need to do all this...
rem u can add actual numbers to ratio to get new ratio... it will always depends on the actual number of people originally...

this insufficient...
statement2)

again the statement is insufficient, since it deals with actual numbers...

together... no help... still we dont know original...

Pick E

> I'm looking for a thorough answer to this including concepts behind it and how to approach such a question.

>> Perfect! That´s how I teach my students in more than 10 years, and this is the only way I believe one should be really prepared to go over the scaled score of 48 in Math...

Let us start with the question stem!
Let D and N be the numbers (in the past) of Doctorates and Non-Doctorates (respectively), therefore we know that
D = 2k and N = 3k , where k is a positive integer. (That´s the nice way of dealing with proportions...)

Now let DH and NH be the number of Doct. and Non-Doct. hired in the 5-year period.

Our focus is then to the ratio: (D+DH)/(N+NH)

Let us start with statement (2), because it seems to me that it is the easier to begin with!

(2) Not enough:

Given that DH = 50, we look for (2k+50)/(3k+NH) and to guarantee that there is not a single value possible,

> TAKE NH = 0 and k = 1 to obtain the particular answer 52/3 = 14
> TAKE NH = 0 and k =2 to obtain the particular answer 54/6 = 9

This is enough to guarantee that statement (2) is insufficient to answer the question asked.

(1) Please consider DH = 2w and NH = w, where w is a positive integer (perhaps even w=0 could be considered...)

Then we are looking for the ratio (2k+2w)/(3k+w) and again it is easy to BIFURCATE (I created this word to mean "find a bifurcation, that is, two possible answers/"roads" satisfying all the conditions imposed at that moment"):

> Take k = w = 1 to obtain 4/4 = 1
> Take k = 2 and w = 1 to obtain 6/7

This is enough to guarantee that statement (1) is insufficient, too.

(1+2) From the fact that DH = 2w = 50, we know that w = 25 and we are looking for the ratio (2k+50)/(3k+25) but we are still with answers depending on the k variable! Observe this:

> Take k =1 to obtain 13/7
> Take k =2 to obtain 54/31 (different from 13/7)

From the fact that we were able to BIFURCATE (1+2), the answer is "E" without any doubt.

I hope you like that !

Obs.: this takes much less time that it seems by the length of my solution. It´s just a matter of practice this tool till you start to bifurcate and structurate without writing that much!

That's great, thanks for the explanation!

I´m really glad you like it!

All the best in your GMAT prep,
Fábio.