Great question, j_shreyans! My response is below:

For all their usefulness in facilitating comparisons between cities of different sizes, per-capita statistics, especially crime rates, often shine an unfairly harsh light on small towns, in which a single incident can cause such figures to skyrocket.

The sentence makes sense: For all their usefulness... is an idiom that conveys the same meaning as "despite their usefulness..." or "even though they are useful...." So, the sentence is saying that though per-person statistics are useful in comparing different-sized cities, they can also make small towns look worse than they actually are.

A) For all their usefulness in facilitating comparisons between cities of different sizes, per-capita statistics, especially crime rates, often

The original sentence is correct.

B) Despite they are useful in facilitating comparisons between differently sized cities, per-capita statistics, and especially crime rates, often

Incorrect: The sentence is not grammatical. Despite is followed by a noun or noun equivalent, not by an independent clause (they are useful). "Despite their usefulness..." would work.

C) Because they are quite useful in facilitating comparisons between different sized cities, per-capita statistics, especially crime rates, can often

Incorrect: This changes the meaning of the sentence from contrast ("Even though [A]..., ...") to cause and effect. The unfair portrayal of small towns is in contrast to, not because of, the overall usefulness of the statistics.

D) Quite useful when facilitating comparisons between differently sized cities, per-capita statistics, and especially crime rates, which frequently

Incorrect: This is not a complete sentence as the subject (per-capita statistics) has no corresponding verb. The sentence also loses the necessary contrast.

E) For their usefulness in facilitating comparisons between different sized cities, per-capita statistics, especially crime rates, frequently

Incorrect: For all... conveys the sense of "despite," but a simple For... means "due to" or "for the purpose of," which again is not the correct meaning of the sentence.

Let me know if you have any other questions!

Hi Spencer ,

Thanks for your reply , can you please explain more Option D

Hi Spencer ,

Thanks for your reply , can you please explain more Option D .

Option D does not have a corresponding verb for the subject "per-capita statistics". The use of "which" makes this sentence incorrect. Also the part bfore the first comma "Quite useful...cities" and the part after "especially crime rates" should be in contrast and not support. Here the contrast is missing.

Thanks for the follow-up question, j_shreyans, and thanks for the good answer, prachi18oct.

Here is (D) in the context of the sentence:

Quite useful when facilitating comparisons between differently sized cities, per-capita statistics, and especially crime rates, which frequently shine an unfairly harsh light on small towns, in which a single incident can cause such figures to skyrocket.

The biggest problem is that other than the subject, we only have modifiers in this sentence:

Quite useful when facilitating comparisons between differently sized cities... (modifier)
per-capita statistics, and especially crime rates... (compound subject)
which frequently shine an unfairly harsh light on small towns... (modifier)
in which a single incident can cause such figures to skyrocket. (modifies small towns)

It's like writing "My cat, which likes to chase mice, and which I adopted off the street last winter."
To correct this, we need to make sure my cat has a verb: "My cat, which likes to chase mice, was adopted off the street last winter."

The second problem is that the sentence says two things about per-capita statistics, one positive (quite useful) and the other negative (frequently shines an unfair light). Using a transition word to signal the contrast greatly improves the sentence. For example:

The essay, terribly difficult to read, made for excellent afternoon reading.
The essay, though terribly difficult to read, made for excellent afternoon reading.

So, to fix answer choice (D), we could remove which so that the subject has a verb (shine), and add the contrast word though:
Though quite useful when facilitating comparisons between differently sized cities, per-capita statistics, and especially crime rates, frequently shine an unfairly harsh light on small towns, in which a single incident can cause such figures to skyrocket.

Hope that helps clarify what's going on in answer choice (D). Please feel free to respond with any more questions!

pls, help
in A, I do not understand meaning between the first phrase, "for..." and the main clause.

I do not understand the meaning of "for " inhere.

For all their usefulness... is an idiom that conveys the same meaning as "despite their usefulness," "even though they are useful," "even given their usefulness," or "even taking into account their usefulness," etc.

Spencer@Prep4GMAT wrote:For all their usefulness... is an idiom that conveys the same meaning as "despite their usefulness," "even though they are useful," "even given their usefulness," or "even taking into account their usefulness," etc.

where can I see this phrase ? in dictionary?

pls, advise me. thank you

Try this: https://www.yourdictionary.com/for-all