During my teaching sessions, I have often compared GMAT Sentence Correction to Algebra since after a point the application of the rules becomes absolutely algebraic. One of the rules that brings this algebraic nature of GMAT Sentence Correction to the forefront is the EITHER-OR rule.

We know that EITHER should always be followed by OR but what about other words that are thrown into the picture such as ON or BY or THROUGH or any other word that its used in the sentence?

The simple rule that one should stick to – When using the format EITHER X or Y, X & Y have to be in the same structure.

• EITHER on X should be followed by OR on Y
• EITHER through X should be followed by OR through Y
• EITHER by X should be followed by OR by Y

So

• on EITHER X OR on Y is incorrect since there is no on immediately preceding X, it should be on EITHER X OR Y

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SENTENCE 1
Most efforts to combat such mosquito-borne diseases like malaria and dengue have focused either on the vaccination of humans or on exterminating mosquitoes with pesticides.

(A) like malaria and dengue have focused either on the vaccination of humans or on exterminating
(B) like malaria and dengue have focused either on vaccinating of humans or on the extermination of
(C) as malaria and dengue have focused on either vaccinating humans or on exterminating
(D) as malaria and dengue have focused on eithervaccinating of humans or on extermination of
(E) as malaria and dengue have focused on either vaccinating humans or exterminating

The first rule to apply is that both VACCINATE and EXTERMINATE should be in the same form -TION or -ING.

Both the words are in the same form only on options C and E.

C is incorrect as on EITHER vaccinating (X) is followed by OR on exterminating (Y), it should on EITHER vaccinating (X) OR exterminating (Y) since X is not immediately preceded by on, making option E is the only choice standing.

As you would have noticed the 3/2 spilt between LIKE and AS becomes irrelevant. This is an important thing to keep in mind — the choice between LIKE and AS is not tested, it is usually the choice between LIKE and SUCH AS that is tested.

A few more GMAT Sentence Correction examples of the EITHER-OR rule.

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SENTENCE 2
Many of the earliest known images of Hindu deities in India date from the time of the Kushan Empire, fashioned either from the spotted sandstone of Mathura or Gandharan grey schist.

(A)  Empire, fashioned either from the spotted sandstone of Mathura or
(B)  Empire, fashioned from either the spotted sandstone of Mathura or from
(C)  Empire, either fashioned from the spotted sandstone of Mathura or
(D)  Empire and either fashioned from the spotted sandstone of Mathura or from
(E)  Empire and were fashioned either from the spotted sandstone of Mathura or from

The usage should be one of the three

• fashioned from EITHER x OR y
• fashioned EITHER from x OR from y 
• EITHER fashioned from x OR fashioned (or any other verb) from y

The only option that that follows the correct structure is option E

It goes without saying that what applies to EITHER-OR applies to NEITHER-NOR as well.

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SENTENCE 3
Despite its covering the entire planet, Earth has a crust that is not seamless or stationary, rather it is fragmented into mobile semirigid plates.

(A) Despite its covering the entire planet, Earth has a crust that is not seamless or stationary, rather it is
(B) Despite the fact that it covers the entire planet, Earth’s crust is neither seamless nor is it stationary, but is
(C) Despite covering the entire planet, Earth’s crust is neither seamless nor is it stationary, but rather
(D) Although it covers the entire planet, Earth’s crust is neither seamless nor stationary, but rather
(E) Although covering the entire planet, Earth has a crust that is not seamless or stationary, but

The original sentence does not use the NEITHER-NOR, which is the best usage for this sentence. All other options, except E, have a NEITHER-NOR usage, making it the main error that is tested on this question.

In B and C the usage of NEITHER-NOR is incorrect. It should used in one of the two formats

• NEITHER is it x NOR is it y
• is NEITHER x NOR y

Only Option D, the correct answer uses the right structure.

The trick on such questions is to treat them and read them like algebraic equations. If you are playing it by the ear then more than one option will seem correct since our ears are used to spoken English and not written English.