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The question presents a sentence, part of which or all of which is underlined. Beneath the sentences, you will find four ways of phrasing the underlined part. Select whichever is most suitable. If it is correct, select "No Change". The administration discussed whether the number of students studying European languages was likely to decline when the senior lecturer retired.
A)no change
B)whether the number of students studying European languages were likely
C)if the students studying European languages were likely
D)if the number of European language students were likely

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Answer
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Hint: Whether is a conjunction that conveys a doubt or a choice. Was is the verb used for singular nouns.

Complete step-by-step answer:

From the hint given to us, we know that ‘whether’ is a conjunction that conveys a doubt or a choice. ‘Was’ is the verb used for singular nouns. Upon observing the underlined phrase, we understand that it conveys the uncertainty of the number of students to decrease. Thus, ‘whether’ is the appropriate conjunction used. ‘If’ conveys the possibility of something. Possibility and uncertainty are not the same. Possibility means when it is expected that something will happen, whereas, uncertainty is not being sure about what will happen.
The noun phrase ‘the number of’ requires a singular verb to form an agreement, that is, it does not form an agreement with a verb that is for plural nouns. From the hint given to us we know that ‘was’ is the verb used for singular nouns. Hence, was is correctly placed in the underlined phrase.
Hence, we can conclude that option ‘a’ is the correct answer. All the other options use the verb ‘were’ which is wrong.

Note: The noun phrase ‘a number of’ uses the plural form of the verb, whereas, ‘the number of’ uses the singular form of the verb.