A. Caucasian workers had; by 2013, they were earning almost six dollars less

Caucasian workers had incorrectly conveys that the earnings of the Hispanic workers are being compared to what Caucasian workers earned at some point prior to 2001.

Also, the meaning of they were earning almost six dollars less is ambiguous. Six dollars less than what?

B. Caucasian workers had earned, a figure that was almost six dollars less by 2013

This repeats the tense issue by using had earned, and a figure that was almost six dollars less by 2013 does not clearly convey how exactly the amount was six dollars less. Had the difference decreased by six dollars, or is the intention of the sentence to convey that the difference in earnings went from twelve dollars to six dollars?

C. Caucasian workers did; this figure had decreased to almost six dollars by 2013

In the version, Caucasian workers did correctly conveys that what is being discussed is what the Caucasian workers earned in 2001. Also, this figure had decreased to almost six dollars fairly clearly conveys that the twelve dollar difference had decreased to six dollars by 2013.

D. Caucasian workers, which was almost six dollars less by 2013

In this version, there is no clear antecedent to which. What exactly was almost six dollars less?

E. had Caucasian workers, a figure that had decreased to almost six dollars less by 2013

The past perfect construction, had Caucasian workers, is not parallel to the simple perfect Hispanic workers ... earned, even though the two describe events that occurred in the same time period.

Also, figure that had decreased to almost six dollars less is somewhat awkward and redundant. The figure had decreased to six dollars, not six dollars less.

The correct answer is C.

1. The easiest way to approach this question is through the verbs at the end of the first clause. Options A, B, and E all use the Past Perfect of the verb TO EARN, either in the full form (option B) or simply in the form of the auxiliary verb HAD (options A and E). Nevertheless, there is no reason to use the Past Perfect here: the Past Simple is what is required, since in its first clause the sentence is attempting to compare what Hispanic and Caucasian workers EARNED in 2001. Eliminate these three options.

2. In option D, the antecedent of WHICH is unclear, so you can eliminate this one as well.

3. Option C, which uses DID as the auxiliary verb standing in for EARNED, is therefore the best answer.

(Note, however, that the best answer is defective: it refers to THIS FIGURE and says that it had decreased TO ALMOST SIX DOLLARS BY 2013, but the figure is actually not mentioned. TWELVE DOLLARS A WEEK LESS is not a exactly A FIGURE, and even if it were, it certainly could not decrease TO ALMOST SIX DOLLARS. What the sentence is trying to say is that twelve dollars a week less in 2001 had become, by 2013, six dollars a week less.)

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This seems to be quite a favorite sentence structure in GMAT.

A GMATPrep sentence that comes to mind:

In 1981 children in the United States spent an average of slightly less than two and a half hours a week doing household chores; by 1997 that figure had grown to nearly six hours a week.

There are actually 3 events that this sentence talks about:

(a) Children in the United States spent an average of slightly less than two and a half hours a week doing household chores (1981)

(b) 16 years passing since then (between 1981 and 1997)

(c) But, before those 16 years passed (within those years, as indicated by the words by 1997), that figure (two and a half hours a week doing household chores) went up to 6 hours.

However, while (b) and (c) both happened in the past, (c) happened before (b) and hence, (c) should be in past perfect (in this case: had grown). In fact, this is a classical usage of Past Perfect.

Our book EducationAisle Sentence Correction Nirvana discusses this concept of Past perfect tense, its application and examples in significant detail. In the book, we have provided a similar example:

In 2007, a typical web user spent less than 4 hours a month on Facebook; by 2011, that figure had gone up to 8 hours.

If someone is interested, PM me your email-id, I can mail the corresponding section of the book.