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The Greek mathematician Archimedes is most famous for

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The Greek mathematician Archimedes is most famous for

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The Greek mathematician Archimedes is most famous for discovering that the quantities of water displaced by an immersed object have the same volume as the object itself.

A. discovering that the quantities of water displaced by an immersed object have
B. his discovery that by immersing objects in water, they displace quantities of
C. discovering that the quantities of water displaced by an immersed object has
D. discovering the quantities of water displaced by an immersed object of
E. his discovery of the fact that an object displaces water quantities, when immersed, of

OA A

Source: Economist Gmat

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It should be noted that Water is neither singular nor plural; it is uncountable. The author must have overlooked the usage of "quantities" with water, but this is however grammatically wrong. Anyways, let's picture the solution from another angle of "Quantities" which mean "much" a plural and must be used with a plural verb "HAVE" to make a meaningful sentence construction.

OPTION A - CORRECT
From a logical viewpoint, the combined usage of the plural "HAVE" with "QUANTITIES" makes the underlined phrase correct.

OPTION B - INCORRECT
The plural "objects" and "they" in the underlined portion do not match with the singular "object" in the non-underlined portion. Additionally, the pronoun 'they' has no antecedent. This thus gives the sentence a different meaning.

OPTION C - INCORRECT
"Has" must be "Have". Also, "quantities" violate the subject-verb agreement.

OPTION D - INCORRECT
There is a change in meaning here. Emphasis given to the "quantities" is to be considered instead of those quantities of water displaced.

OPTION E - INCORRECT
Wordy and not crisp in meaning. Therefore, the valid direct object of the verb "replaces" is "quantities"... It's not logical.

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