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as mean : in capacity of
such as means: for example
like means : similar to

all 3 words are used before a noun, each with its meaning.

so

only like is correct in this sentence.

above analysis is meaning analysis, which is center of gmat sc. in other words, gmat test us this analysis.

between a and b
without understand of meaning, without using meaning analysis, we can choose the choice in which the word after "both" and "and" are the same. this process is not meaing analysis. it is mechanical process of apply grammar rule without understand meaning

it is clear there are 2 processes, the first the focus of gmat sc, the second easy
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Explanation from GMAT FREE

Creating a filter: the words "such" and "like" do not operate together as they have been combined in the original sentence. The proper idiom is "such as." So (A) is out and we'll for a solution such as the phrase "such as."

Applying the filter: we are left with choices (C) through (E). Within those choices, there is variation in the placement of "both." It can be "both on X and on Y." Or it can be "on both X and Y." Choice (C) has an invalid treatment of "both." So does (D). The correct answer is (E).
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the source is actually from gmat-prep.
the question is just a part of a real gmat question b/c this question only tests one specific grammar concept in gmat. Also, the sentence does not look so complex.
Therefore, test takers can do this question for fun only.
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The brightness on Earth of such celestial bodies like stars invariably depends both on the radius of the luminescent object and its temperature.
This question requires understanding of multiple concepts such as:
1. Use of like Vs as( like can't be used to show examples whereas 'as'/such as is used for giving examples.
2. Parallelism. (Use of word pair i.e not only- but also with parallel structure)

A. like stars invariably depends both on the radius of the luminescent object and its temperature// can't use like for giving examples//

B. like stars invariably depends both on the radius of the luminescent object and on its temperature//same as A//

C. as stars invariably depends on both the radius of the luminescent object and on its temperature// Follow rule 1 but violates rule 2 because it is not parallel. It would be correct if 'on both X and Y' and not 'on both X and on Y'

D. as stars invariably depends both on the radius of the luminescent object and its temperature//same as C//

E. as stars invariably depends both on the radius of the luminescent object and on its temperature//correct because parallel and use of such as for giving examples//
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The brightness on Earth of such celestial bodies like stars invariably depends both on the radius of the luminescent object and its temperature.


A. like stars invariably depends both on the radius of the luminescent object and its temperature (Such as is the correct idiom)

B. like stars invariably depends both on the radius of the luminescent object and on its temperature (Same as A)

C. as stars invariably depends on both the radius of the luminescent object and on its temperature (Idiom Both x and y Should be parallel)

D. as stars invariably depends both on the radius of the luminescent object and its temperature (Same as C)

E. as stars invariably depends both on the radius of the luminescent object and on its temperature (Correct)
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The brightness on Earth of such celestial bodies like stars invariably depends both on the radius of the luminescent object and its temperature.

A. like stars invariably depends both on the radius of the luminescent object and its temperature
B. like stars invariably depends both on the radius of the luminescent object and on its temperature
C. as stars invariably depends on both the radius of the luminescent object and on its temperature
D. as stars invariably depends both on the radius of the luminescent object and its temperature
E. as stars invariably depends both on the radius of the luminescent object and on its temperature

Source GMAT FREE

The sentence tests idiomatic usage and parallelism.

- Idiomatic usage such as is correct while like as is not. Eliminate choices (A) and (B).

- Eliminate (C) due to change in meaning: 'both the radius of the luminescent object' should include another noun phrase to justify the use of the word 'both' before introducing 'and on its temperature' + parallelism issue.

- Between (D) and (E), (E) is the better choice as the use of parallelism is appropriately illustrated here ('both on the radius of the luminescent object and on its temperature').

Hence, the answer is choice (E).
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