The construction of new apartments in Brewsterville increased the

The last sentence of the question stem highlights this.

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That is the paradox isn't it?
We are supposed to find out the reason for this paradox
The reason apartments were being built was because of increase in the number of people wanting to reside there. So once the apartments are being built, the rent of existing apartments should go down

The new apartments were constructed at the outset of a trend of increasing numbers of people seeking residence... This shows the above point
Increase in the rent of existing apartments still isn't solved through this statement.
Not able to grasp the point

It shows why the rents increased even with new construction. If there is greater demand, then new housing as much of an impact on price. In fact, it still might not be enough housing and thus housing prices go up. Does this make sense?

Then in fact option A makes more sense doesn't it. It says fewer apartments were constructed than planned and hence could not accommodate the increasing trend leading to higher rent of the existing apartments
Does this add up or am I still missing something?

Not quite. (A) is saying fewer were planned. But does this resolve anything? We are making the assumption that demand already outstripped supply and is causing prices to rise.

Are we not assuming that the new construction of apartments will fall short of the increasing trend of people seeking residence in the city?

(A) Fewer new apartments were constructed than originally planned -- For this, we have to assume that demand is increasing (otherwise new apartments will drive the price down). This assumption is what (E) is already stating. So you are making an assumption to make another conclusion when the assumption is stated as an answer choice. We can't do this. You are saying demand is up, so if new apartments are less than expected, then prices go up. You are making too many steps and assumptions when the answer choice is spelled out in (E). We are only told that supply increased and so did prices. WHY? Because of demand, which is the only way to make (A) work as an answer choice. And because we have to make this assumption, it cannot work as an answer choice.

(E) The new apartments were constructed at the outset of a trend of increasing numbers of people seeking residence in Brewesterville

Following Nightblade354 advise to push my CR skills beyond the limits, I'll post an extensive analysis of this questions, explaining the initial thoughts on the stimulus and the reasons why I reject four options and choose one as the winner . I beieve this is one of the best ways to improve in CR. Don't just do questions, but try to extract as much as possible from each of them. I think doing blind review help a lot in doing so (more about blind review here: https://gmatclub.com/forum/mod-nightblade-s-quick-guide-to-cr-proficiency-295316.html)

Here is the stimulus: The construction of new apartments in Brewsterville increased the supply of available housing there. Ordinarily, increasing the supply of available housing leads to lwoer rents for existing apartments. But in Brewsterville, rents for existing apartments rose.

Initial thoughts: This is a discrepancy questions, so I should expect a gap in the stimulus. Let's identify the gap.

1º Premise: +supply of houses
2º Premises: +supply of houses ----> - rent of existing apartment
Counterpremise: + rent of existing apartment

Ok, so generally an increase in housing supply leads to lower rents of existing apartments (in the argument and in real life as well so it is easy to imagine it). But rents in existing apartments increased. Why? It could be that there has been a steep increase in the population of Brewsterville because of different reasons (new industry being generated and therefore more jobs, a new university, etc). Ok, this is my only thought for now. If price stays the same , it is reasonable to think that demand increases with the increase in supply (Law of Supply and Demand)

Options:

(A) Fewer new apartments were constructed than originally planned.

If fewer new apartment were constructed, there is still an increase in supply, although this is lesser than the one expected. If nothing else is said in this option (i.e. demand doesn't change), then rental prices of existing apartment should still go down). Doesn't explain the discrepancy. Incorrect

(B) The new apartments were much more desirable than the existing apartments

Again, this options doesn't say anything about changes in demand. If demand is the same, we can assume that people will move out to the new apartments. Therefore, exsiting apartment should decrease its rent to make them attractive enough to not lose clients. Incorrect

(C) Rents in some areas close to Brewsterville dropped as a result of the construction of the new apartments

This is reasonable. Rent should drop if there is an increase in supply. But how does this option help me explain why in other areas rent went up? No explanation possible under this options. Incorrect

(D) A sizeable number of people moved out of the existing apartments while the new apartments were being constructed

If people moved out because new apartment were being constructed, this means less demand in exisitng apartments and therefore prices should have gone down and not up. Again, this doesn't explain why rent of exisitng apartments went up. Incorrect

(E) The new apartments were constructed at the outset of a trend of increasing numbers of people seeking residence in Brewesterville

Aha! This is my option. For the first time, this option talks about an increasing demand. If this demand is higher that the supply the new apartments will provide, then it makes sense now that existing apartments rental price went up. Correct

OPTION E