you can't have increase and rise in the same sentence ---> one is redundant

down to A and E

It can't be A so E.

Can it be B?

Look closely at the sentence structure of B. The main verb is absent. What we have is the subject and its modifiers. B has other errors as well. Use of participle is incorrect. Use of rising is redundant.

E resolves the errors best. What doubt do you have in E?

After decreasing steadily in the mid-1990's, the percentage of students in the United States finishing high school or having earned equivalency diplomas increased in the last three years of the decade, up to 86.5 percent in 2000 from 85.9 percent in 1999 and 84.8 percent in 1998.

(A) finishing high school or having earned equivalency diplomas increased in the last three years of the decade, up to 86.5 percent in 2000 from 85.9 percent in 1999 and
(B) finishing high school or earning equivalency diplomas, increasing in the last three years of the decade, rising to 86.5 percent in 2000 from 85.9 percent in 1999 and from
(C) having finished high school or earning an equivalency diploma increased in the last three years of the decade, and rose to 86.5 percent in 2000 from 85.9 percent in 1999 and from
(D) who either finished high school or they earned an equivalency diploma, increasing in the last three years of the decade, rose to 86.5 percent in 2000 from 85.9 percent in 1999 and
(E) who finished high school or earned equivalency diplomas increased in the last three years of the decade, to 86.5 percent in 2000 from 85.9 percent in 1999 and

The issues:

Noun + Present participle:

NOUN + Present participle--> NOUN + Verbing

In this case the Verbing modifies the NOUN adjacent to it.

Example:

The man working in a saw mill has risk of accident.

--> Working modifies the man.

So, in the "United States + finishing/having", Verbing modifies USA.

==> Then the meaning becomes "USA is finishing/having high school". It changes the meaning of the sentence.

This kills the options A, B, and C.

2. NO Comma + Who:

Noun + Preposition + Noun + Who

--> In this situation who will refer to the eligible noun. Eligible noun will meet the following two conditions:

2.1. It agrees with the verb after who.
2.2. It makes the sentence meaningful.
2.3. Who cannot refer to things. Who refers to person(s).

Example:

The students in high school who have scored high will be awarded.

--> So, in D and E, who refers to the percentage of students

3. Either X or Y:

--> X and Y MUST be parallel.

In the option D, "either finished high school or they earned" does not maintain the parallelism.

It should be either finished or earned

--> This kills D.

Answer is E.

Thanks gmat1011,niksworth & gmat_perfect.

I think checking on redundency makes it simpler for POE, Although it is easy to miss this checkpoint.

@gmat_perfect : I suspect the reasons for removing A. Of course, the verbing modifier should modify the noun immediately preceding it, logic and necessity can force it todeviate from the above.

Thjat said, let's figure out other errors in these incorrect answer choices.

I feel some sort of missing parallelism, but want to see it clearly.

One reason I suspect it is wrong : the percentage of students .. finishing high school - > It is students who are finishing highscholll not percentage. But would like to confirm.

Second : finishing high school and having earned equivalency diplomas dop not look parallel. want to confirm though.

Third : up to 86.5 percent in 2000 can better be written as to 86.5 percent in 2000 - but need confirmation.

Expert help please .