For the purpose of self-improvement, the Roman emperor Marcus Aurelius

For the purpose of self-improvement, the Roman emperor Marcus Aurelius wrote 12 books, each a collection of notes and personal observations based on stoic philosophy.

(A) each a collection of notes and personal observations
The meaning is clearly conveyed without any grammatical error. "each a collection of notes and personal observations based on stoic philosophy." clearly modifies the 12 books.

(B) each a collection of notes and personal observations that were being
"Being" is a present participle which denotes the ongoing nature of things. It doesn't make sense to say that the personal observations of Marcus Aurelius are still going.

(C) with each being a collection of notes and personal observations
Same error as (B). Also, the use of with conveys a different meaning than what is intended. The collection of notes and personal observations are meant to modify the books, however the use of "with" suggests that the books were simultaneously being a collection of notes and personal observations.

(D) with collections of notes and personal observations to be
The usage of "to be" suggests that the purpose of writing the books was stoic philosophy. However, the purpose was self-improvement.
This answer choice differs from the intended meaning of the sentence.

(E) with collections of notes and personal observations that are
The use of "with" suggests that Marcus Aurelius wrote the books with collections of notes and personal observations that are based on stoic philosophy. However, the collection of notes and the personal observations themselves became the book

Expert's Global Official Explanation:

Meaning + Redundancy/Awkwardness + Pronouns + Tenses

Understanding the intended meaning is key to solving this question; the intended meaning of this sentence is that the Roman emperor Marcus Aurelius wrote 12 books, each of which is a collection of notes and personal observations based on stoic philosophy.

• In a “noun + comma + phrase” construction, the phrase must correctly modify the noun; this is one of the most frequently tested concepts on GMAT sentence correction.
• The simple past tense is used to refer to actions that concluded in the past.
• The simple past continuous tense is used to refer to actions that took place over a period of time in the past.
• The simple future tense is used to refer to actions that will take place in the future.
• The simple present tense is used to indicate actions taking place in the current time frame, indicate habitual actions, state universal truths, and convey information that is permanent in nature.
• “being” is only to be used when it is part of a noun phrase or represents the passive continuous verb tense; the use of passive continuous must be justified in the context.

A. Correct. This answer choice correctly modifies “12 books” with “each a collection of…”, conveying the intended meaning- that each book is itself a collection of notes and personal observations. Further, Option A avoids the tense errors seen in Options B, D, and E, as it correctly uses the past participle (“based” in this sentence) to refer to an action that concluded in the past. Additionally, Option A is free of any awkwardness or redundancy.

B. This answer choice incorrectly uses the simple past continuous tense verb modifier “were being based…” to refer to an action that concluded in the past; please remember, the simple past tense is used to refer to actions that concluded in the past, and the simple past continuous tense is only used to refer to actions that took place over a period of time in the past.

C. This answer choice is needlessly wordy due to the use of the phrase “with each being”; please remember, “being” is only to be used when it is part of a noun phrase or represents the passive continuous verb tense.

D. This answer choice incorrectly modifies “12 books” with “with collections of notes and personal observations”, incorrectly implying that the 12 books contain collections of notes and personal observations; the intended meaning is that each book is itself a collection of notes and personal observations; in a “noun + comma + phrase” construction, the phrase must correctly modify the noun. Further, Option D incorrectly uses the simple future tense verb phrase “to be based” to refer to an action that concluded in the past; please remember, the simple past tense is used to refer to actions that concluded in the past, and the simple future tense is used to refer to actions that will take place in the future.

E. Trap. This answer choice incorrectly modifies “12 books” with “with collections of notes and personal observations”, incorrectly implying that the 12 books contain collections of notes and personal observations; the intended meaning is that each book is itself a collection of notes and personal observations; in a “noun + comma + phrase” construction, the phrase must correctly modify the noun. Further, Option E incorrectly uses the simple present tense verb “are based” to refer to an action that concluded in the past; please remember, the simple past tense is used to refer to actions that concluded in the past, and the simple present tense is used only to indicate actions taking place in the current time frame, indicate habitual actions, state universal truths, and convey information that is permanent in nature.

A is the best answer choice.

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