Do the following sentences mean the same?
1. Most students usually study hard to enter a university.
2. Most students usually study hard to enter universities.
One does not enter two (or more) universities at once. This sentence would not be phrased like this, with 'universities' in the plural.
3. Most students usually study hard to go to university.
(1) and (3) are both general statements about what is necessary academically to go on to tertiary education. (1) is slightly more formal - one speaks more of 'going to high school', but universities are grander, and formally, one 'enters a university', one 'is admitted into the School of Medicine'.
4. Most students usually study hard to go to the university.
To say this, a previous sentence must have mentioned a specific university which you are now referring to - 'the'/'this' university
5. Most students usually study hard to go to universities.
Same as (2),
6. Most students usually work very hard studying at (the-only if a specific university has been mentioned previously) university.
7. Most students usually work very hard to study at universities.
(2) and (6) apply here.
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