By providing such services as mortgages, home improvement loans,

What is problem with D? Consider a simpler example:

By eating healthy and sleeping plenty, I improved my health.

Is the preposition by required before the second gerund as well?

To answer this question, let us recollect the Once in twice out rule:

The parallel structure here is X and Y: If we consider the preposition by inside the parallel structure, we must use by two times. In such case by should be used both in X and in Y.

However we could also consider that the preposition by is outside the parallel structure. In such case we would use by only once. It would cover both X and Y.

This ambiguity often occurs with AND structure because we cannot determine where the parallelism starts, whether the preposition is inside or outside. However, for two-part structures such as NOT ONLY.... BUT ALSO, it is easy to determine whether the preposition is outside or inside and such ambiguity does not occur.

The correct option gives us the following sentence:

By providing such services as (mortgages, home improvement loans, automobile loans, and financial advice) and by staying within the metropolitan areas, Acme Bank has become one of the most profitable savings banks in the nation.

You're right in saying that the second by is not necessary, but it helps show that we are looking at the second item of the main list. Otherwise, the reader could read the sentence like this:
By providing such services as X and Y... (where X is a list of 4 items)

You'll face this problem in any long sentence, or in any sentence in which there are elements that could confuse the reader. You should err on the side of caution and prefer any option that clarifies what the parallel elements are.

AjiteshArun

If we use "by" again, is this not another interpretation -
By providing such services as X and By Y, Acme Bank....

shouldn't option(E) has a comma before "and by staying" since the statement forms an independent clause?

shouldn't option(E) has a comma before "and by staying" since the statement forms an independent clause?

I struck between D and E. whether GMAT tests for punctuation?
Because (D) "and financial advice, and staying" comma separates sentence but in (E) "and financial advice and by staying" after "financial advice" immediately comes "and".

By providing such services as mortgages, home improvement loans, automobile loans, financial advice and staying within the metropolitan areas, Acme Bank has become one of the most profitable savings banks in the nation.

(A) financial advice and staying
(B) financial advice and by staying
(C) and financial advice, staying
(D) and financial advice, and staying
(E) and financial advice and by staying

By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, in 1797-1798 Henry Cavendish's apparatus enabled him to arrive at an astonishingly accurate figure for the weight of the earth.

(A) By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, in 1797-1798 Henry Cavendish's apparatus enabled him

(B) In 1797-1798, by devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, Henry Cavendish's apparatus enabled him

(C) Henry Cavendish devised an instrument made from a rod, wire, and lead balls, and employed uncommonly precise measurements, and in 1797-1798 was able

(D) Having devised an instrument from a rod, wire, and lead balls, and employment of uncommonly precise measurements, Henry Cavendish in 1797-1798 was able

(E) By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, Henry Cavendish was able in 1797-1798

Why is by providing and by staying necessary. For e.g
People never have and never will vote in favor of the referendum. ( In this sentence we would read as people never have have and people never will, there is no need for us to write people twice) Thus why is it necessary to write "by" twice ?

and financial Services -----last one in the list ------> eliminate A,B
by providing..............and by staying............ --------> Parallel
IMO E