(A) Incorrect
Modifier / Meaning: The original sentence is not correct, though it may sound just fine! Here’s an example of correct usage for the noun modifier that: The cat that I own is very friendly. The expression the cat that I own can be turned around in this way: I own the cat. In other words, the subject and verb of the modifying clause, I own, become the main subject and verb of the “turned-around” sentence, and the noun being modified, cat, becomes the object of that turned-around sentence. (The modifier marker, that, is dropped.)
But look what happens when you try that same trick on the given problem: They met the day. Except…they didn’t meet the day. They met each other, and they met on that day.
(B) Incorrect
Meaning or Idiom: The modifier where is inappropriate because the day is not a location.
(C) Incorrect
Meaning or Idiom: Of when is not an acceptable idiom in English; if you know that, you can eliminate this choice. Alternatively, it is redundant to say the day when they met, as the word day already conveys a timeframe. You could say simply the day they met.
(D) Incorrect
Modifier / meaning: While is not a noun modifier marker; it’s an adverbial modifier marker. In other words, it is modifying more than just a plain noun. In this case, it would need to modify the action describe the day, so the sentence is saying that the description occurs at the time of their first meeting. While they meet for the first time, they describe that day / that meeting. This is illogical, since the sentence refers to a long-married couple whose memories have changed over time.
(E) CORRECTFew people use the construction on which (or by which or for whom or etc) in casual speech, but it is the proper construction here. If you haven’t read the explanation for answer (A) yet, take a look at it now, then come back here. Try that same trick with this choice (this time, keep the of but still drop the modifier marker, which) : They met on the day. Yes! This is exactly what the sentence is trying to say: the couple met on the day.
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