In 1997, despite an economy that marked its sixth full year of uninterrupted expansion with the lowest jobless rate in a quarter century, the number of United States citizens
declaring themselves bankrupt has jumped by almost 20 percent, at 1.34 million.
Option Elimination -
(A) declaring themselves bankrupt has jumped by almost 20 percent, at - "has jumped" is wrong. We have a time marker. This happened in 1997.
(B) declaring themselves bankrupt jumped by almost 20 percent, to - As GMATNinja also explained, declaring ....is better than who declared as we aren't concerned about everyone who declared bankruptcy (bit ambiguous if it's just 1997 or even before) but the ones declaring in 1997 is better as ING modifier doesn't talk about the time when it happened. So we look at "in 1997" for the when, and it's clear that they were declaring bankruptcy in 1997. Also, Jumped TO is right in this context. "jumped at" conveys the sense of eagerness to seize an opportunity, E.g., When she heard about the job promotion, she jumped at the chance to apply. In the same context, "jumped to" can be used to mean an impulsive response to a situation, E.g., He jumped to the conclusion that she was guilty without any evidence.
(C) who declared themselves bankrupt has jumped by almost 20 percent, to - "has jumped" is wrong. We have a time marker. This happened in 1997.
(D) who declared themselves bankrupt jumped almost by 20 percent, at - ING is better to limit to just 1997. And Jumped to is better here.
(E) to declare themselves bankrupt jumped almost by 20 percent, at - "to declare" is wrong - they are not about to declare now; this event already happened in the past.