First, scarcity is a major determinant. 21 a coin is, the more it is worth.
答案：(D) The rarer
【句型】the + 比較級..., the + 比較級... 固定句型「越……就越……」，表示「一枚硬幣越稀有，它就越值錢」；Rare as（不合這個句型結構）、The rare（原級無比較級變化，不合the...the...句型）、Rarest（最高級，這個句型需要比較級不是最高級）都不合。
Rare as 看起來很誘人，因為你學過 Rare as it is（雖然它很稀有）這種形容詞放句首的說法，形狀很像。也可能一看到前一句的 scarcity（稀少）就直覺挑最高級 Rarest。
關鍵全在句子後半：the more it is worth。這裡已經擺明是「the 加比較級」的形狀，而這個句型一定成對出現——「the 加比較級 ..., the 加比較級 ...」，意思是「越…就越…」。前半看到後半的 the more，就知道空格必須也是 the 加比較級，四選一瞬間變成一選一。還原成完整子句驗算：The rarer a coin is, the more it is worth. 等於 If a coin is rarer, it is worth more.（一枚硬幣越稀有，就越值錢）。這個句型你國中看過最短的版本：The more, the better.（越多越好）。語意也對得上：前一句說 scarcity is a major determinant（稀少是主要決定因素），本句正是把這個因素展開來講。
Rare as：這是讓步的說法，形容詞提到句首，Rare as it is 等於 Although it is rare（雖然它很稀有）。語意變成讓步，與後半的 the more it is worth 湊不成對，句型也接不起來。The rare：the 加原級形容詞，構不成這個句型；the rare 若當名詞用是指「稀有的人事物」，整句會散掉。Rarest：最高級。這個句型要的是比較級，不是最高級，也無法與後面的 the more 成對。
the more..., the more...（越…就越…）、the sooner, the better（越快越好）、be worth（值…、值得）、a major determinant（主要決定因素）、determine the value of（決定…的價值）、scarcity value（稀有價值）。
For coin collectors who invest money in coins, the value of a coin is determined by various factors. First, scarcity is a major determinant. 21 a coin is, the more it is worth. Note, however, that rarity has little to do with the 22 of a coin. Many thousand-year-old coins often sell for no more than a few dollars because there are a lot of them around, 23 a 1913 Liberty Head Nickel may sell for over one million US dollars because there are only five in existence.
Furthermore, the demand for a particular coin will also 24 influence coin values. Some coins may command higher prices because they are more popular with collectors. For example, a 1798 dime is much rarer than a 1916 dime, but the 25 sells for significantly more, simply because many more people collect early 20th century dimes than dimes from the 1700s.