Secondly, it is by participating in any IMO contest that young mathematicians of all countries can foster friendly 24.
答案：(C) relations
foster friendly relations（建立友好關係）為固定搭配，表示各國年輕數學家透過競賽培養友誼；behaviors／messages／guests 皆不符合此處語意。
四個選項都是名詞，文法上都放得進去，只能靠語意判斷。答對率五成。
空格前面是 foster friendly（培養友好的……），要問的是「培養友好的什麼」。foster friendly relations（建立友好關係）是常考的字詞搭配，同一組的還有 maintain friendly relations。同句就選得出答案；下一句「因此鼓勵並建立更多國際交流」可以再驗算一次，方向完全吻合。
behaviors（行為）：friendly behavior 本身說得通，但「培養友好的舉止」講的是個人的舉止，與下一句的國際交流接不上。messages（訊息）：訊息是傳遞的，不是培養的。guests（客人）：與 foster 完全搭不起來，這一段講的是國與國之間的往來，不是招待客人。
這一句的架構是 it is by participating in any IMO contest that ...，這是強調句型（分裂句，cleft sentence，劍橋 English Grammar Today 的 Cleft sentences 條目）。它把一個訊息拆成兩個子句：接在 It is 後面的是要強調的部分，that 後面裝的是已經知道的資訊。還原成一般語序就是 Young mathematicians of all countries can foster friendly relations by participating in any IMO contest.，被搬到 It is 後面的是 by participating in any IMO contest（透過參加 IMO 競賽）這個介系詞片語，強調的是「靠什麼方式」。公式是 It is ＋ 要強調的成分 ＋ that ＋ 句子的其餘部分——英文一句話本來先把主詞和動詞這個骨幹交代出去，強調句型就是把你要強調的成分搬到骨幹的位置。要強調的成分是人的時候，that 可以換成 who。句子的主要動詞不能單獨搬進那個位置，要強調動作得改用另一型 What he did was ...；但像本題的 by participating（透過參加）這種被介系詞帶著的動名詞，整組是介系詞片語，進得去。同一份考卷的第三篇有兩處同型，強調的都是主詞：it is the recording industry that wants to fight piracy（第 27 題所在句）、It is the fans that support the kingdoms（第 29 題所在句）。三處對照就知道，被強調的成分可以是主詞，也可以是介系詞片語。
maintain friendly relations（維持友好關係）、establish relations with（與……建立關係）、It is ＋ 強調的成分 ＋ that ...（強調句型）、international exchange（國際交流）、based upon（根據……）、by V-ing（藉由做……）。
There are six international science Olympiads in the world. They are all organized with a simple intention—to 21 global understanding and mutual appreciation among young scientists in all countries. Each of the six science Olympiads 22 its specific aims.
The aims of the International Mathematical Olympiad (IMO), for example, are three-fold. With arduous but interesting math problems, the first aim of the IMO is to discover, to encourage and, most important of all, to challenge 23 gifted young people all over the world. Secondly, it is by participating in any IMO contest that young mathematicians of all countries can foster friendly 24.
Based upon its second aim, more international exchanges are encouraged and established. Any IMO contest brings not only young mathematicians together but also their instructors; 25, the IMO has its final aim to create opportunities for the exchange of information on math schedules and practice throughout the world.