13.8和13.11哪个大？

近日，最新一期《歌手》排名中，孙楠与香缇·莫分数差距微弱。于是，有网友就13.8和13.11哪个大吵了起来……

今天你练听力了吗？

🤔️别看文章，先做两道数学题：

1. What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n+3   B. 6n

C. 6n-1    D. 6n-3

A. 680 degrees  B. 600 degrees

C. 540 degrees  D. 420 degrees

无注释原文：

Are You Smarter Than an 8th Grader?

From: The New York Times, April 25, 2015

I AM afraid you're eligible to read this column only if you can answer this question faced by eighth graders around the world:

What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n+3

B. 6n

C. 6n-1

D. 6n-3

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

We know Johnny can't read; it appears that Johnny is even worse at counting.

The Educational Testing Service released a global report finding that young adults from the United States rank poorly in reading but are even worse in math — the worst of all countries tested. This is the generation that will be in the labor force for the next half-century, struggling to compete with citizens of other countries.

It's not just that American results are dragged down by poverty. Even American millennials with graduate degrees score near the bottom of international ranks in numeracy.

We interrupt this column for another problem:

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

A. 680 degrees

B. 600 degrees

C. 540 degrees

D. 420 degrees

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.

In a recent column, I offered a paean to the humanities. But it's also true, as a professor notes in a letter to the editor, that science majors do take humanities courses. In contrast, humanities majors often desperately avoid any semblance of math or science (except for classes like “Physics for Poets”).

Numeracy isn't a sign of geekiness, but a basic requirement for intelligent discussions of public policy. Without it, politicians routinely get away with using statistics, as Mark Twain supposedly observed, the way a drunk uses a lamppost: for support rather than illumination.

(I believe American high schools and colleges overemphasize calculus and don't sufficiently teach statistics. Statistical literacy should be part of every citizen's tool kit.)

Public debates often dance around basic statistical concepts, like standard deviation, because too few Americans understand them. And people assume far too much of “averages.”

After all, American adults have, on average, one ovary and one testicle. But try finding such an “average person.”

Another pop quiz:

A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

I know many readers will grumblingly protest that they're just not good at math! True, there are math prodigies who are different from you and me. When the great mathematician Carl Gauss was a young boy, his teacher is said to have asked his class to calculate the sum of all the numbers from 1 to 100. Gauss supposedly supplied the answer almost instantly: 5,050.

The teacher, flabbergasted, asked how he knew. Gauss explained that he had added 1 and 100, 2 and 99, and realized that there would be 50 such pairs each summing 101. So 50 times 101 equals 5,050.

So I agree: Let's resent the Gausses of the world for being annoyingly smart. But let's not use that as an excuse to hide from the rigor of numbers. Countries like Singapore manage to impart extraordinary math skills in ordinary children because they work at it.

Numeracy isn't just about numbers, of course. It's also about logic. Let me leave you with a logical puzzle — a family favorite, one that I first heard as a little kid — that isn't mathematical at all. Yet people with math training seem better at thinking it through and solving it:

You're in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don't know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don't know whether you'll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape? 

It's not a trick question. When you hear the answer, you'll see it's straightforward.

Give up? You ask either of them: “If I asked the other person which door is the one to escape, which would he point to?” Then you take the other door.

- ◆ -

注：完整题目见本文开头；中文文本为纽约时报官方译文，仅供参考

含注释全文：

Are You Smarter Than an 8th Grader?

From: The New York Times, April 25, 2015

I AM afraid you're eligible to read this column only if you can answer this question faced by eighth graders around the world:

下面这个题是用来考世界各地八年级学生的，如果你答不上来，恐怕就不适合阅读这篇专栏了：

eligible /ˈel.ɪ.dʒə.bəl/ 1）表示“有资格的；合格的；具备条件的”，英文解释为“a person who is eligible for sth or to do sth, is able to have or do it because they have the right qualifications, are the right age, etc.”举个🌰：Only those over 70 are eligible for the special payment. 只有70岁以上的人才有资格领取这项专款。

2）还有一个好玩的意思，表示“（指结婚对象）令人中意的；合意的，合适的”，英文解释为“An eligible man or woman is not yet married and is thought by many people to be a suitable partner.”举个🌰：He's the most eligible bachelor in Japan. 他是日本最令人中意的单身汉。

🎬电影《我要当警察》（Observe And Report）中的台词提到：There are several tests to complete in order to be eligible for police academy 想要进警校 得通过几项测试。

column /ˈkɒl.əm/ 1）表示“（报纸、杂志上的）栏目，专栏”，英文解释为“a piece of writing in a newspaper or magazine, usually on a particular subject, that is always written by the same person and appears regularly”举个🌰：She writes a weekly fashion/gossip column. 她每周都在时尚/漫谈专栏中发表文章。

2）表示“（词或数字的）纵列”，英文解释为“any vertical block of words or numbers”举个🌰：Add the column of figures and divide the sum by three. 把这列数字相加，再将总数除以3。

What is the sum of the three consecutive whole numbers with 2n as the middle number?

三个连续整数，中间一个是2n，它们的总和是多少？

A. 6n+3

B. 6n

C. 6n-1

D. 6n-3

consecutive /kənˈsek.jə.tɪv/ 表示“连续的，连贯的，不间断的”，英文解释为“Consecutive events, numbers, etc. follow one after another without an interruption.”举个🌰：This is the fifth consecutive weekend that I've spent working. 这是我连续第五个周末加班。

📍《经济学人》（The Economist）一篇讲述绿色风投的文章中提到：Last year taxpayer-funded green-energy R&D around the world rose for the third consecutive year, to a record $25.4bn, accroding to the IEA. 根据国际能源署的数据，去年全球受政府资助的绿色能源研发连续第三年增长，达到创纪录的254亿美元。

whole number /ˌhəʊl ˈnʌm.bər/ 表示“整数”，英文解释为“a number, such as 2, 8, or 3447, that has no fractions and no digits after the decimal point”

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

超过四分之三的韩国孩子回答正确（答案是B）。美国孩子只有37%答对，落后于伊朗、印度尼西亚和加纳的同龄人。

lag /læɡ/ 表示“缓慢移动；掉队，滞后”，英文解释为“to move or make progress so slowly that you are behind other people or things”举个🌰：He's lagging behind - I think we'd better wait for him to catch us up. 他有点掉队了——我看我们最好等他赶上来。

lag behind 表示“落后”，英文解释为“If one thing or person lags behind another thing or person, their progress is slower than that of the other thing or person.”举个🌰：The restructuring of the pattern of consumption also lagged behind. 消费结构的调整也落后了。

peer /pɪər/ 作动词，表示“仔细看，端详；费力地看”，英文解释为“to look carefully or with difficulty”举个🌰：When no one answered the door, she peered through the window to see if anyone was there. 没有人开门，她就费力地透过窗户朝里望去，看是否有人在。

作名词，表示“同龄人；同辈；同等社会地位（或能力）的人”，英文解释为“a person who is the same age or has the same social position or the same abilities as other people in a group”举个🌰：Do you think it's true that teenage girls are less self-confident than their male peers? 你是否认为十几岁的女孩子不如同年龄的男孩子自信？

We know Johnny can't read; it appears that Johnny is even worse at counting.

我们知道美国小孩的阅读能力不行；看来他们的算术能力更糟糕。

在这个句子中，“Johnny”是一个常用的泛指名字，用来代表所有普通的美国孩子。它并不是指特定的某个人，而是用来泛指一类人。

The Educational Testing Service released a global report finding that young adults from the United States rank poorly in reading but are even worse in math — the worst of all countries tested. This is the generation that will be in the labor force for the next half-century, struggling to compete with citizens of other countries.

美国教育考试服务中心（Educational Testing Service，简称ETS）发布的一份全球报告称，美国年轻人的阅读能力排名不佳，但数学能力排名更糟——是所有参加测试的国家中最低的。这代人将在今后半个世纪成为劳动者，他们难与其他国家的公民竞争。

It's not just that American results are dragged down by poverty. Even American millennials with graduate degrees score near the bottom of international ranks in numeracy.

这不仅仅是说美国人的测试结果受到了贫困的拖累。即使有研究生学位的美国千禧一代，在算术上的得分也在国际排名中接近垫底。

millennial /mɪˈlen.i.əl/ 表示“一千年的，千禧年的；与2000年有关的”，英文解释为“relating to a millennium or to the year 2000”如：millennial celebrations 千禧年庆祝活动。

作名词，通常复数，表示“千禧世代”，英文解释为“a person who was born around the time of the millennium”举个🌰：Millennials have grown up with the internet and can't imagine a world without it. 千禧世代在互联网环境中长大，无法想象没有互联网的世界会是什么样的。

📍千禧世代一般是指出生于20世纪且20世纪时未成年，在跨入21世纪（即2000年）以后达到成年年龄的一代人。这代人的成长时期几乎同时和互联网/计算机科学的形成与高速发展时期相吻合。有时会使人误以为指新千年（即2000年）之后出生的人。

numeracy /ˈnjuː.mə.rə.si/ 表示“基本计算能力，识数”，英文解释为“ability to do basic mathematics”如：statistics on the literacy and numeracy of twelve-year-olds 关于12岁孩子读写和计算能力的统计数据。

We interrupt this column for another problem:

下面再试试另一个问题：

interrupt /ˌɪn.təˈrʌpt/ 1）表示“打断（其他人说话）”，英文解释为“to stop a person from speaking for a short period by something you say or do”举个🌰：She tried to explain what had happened but he kept interrupting her. 她试图解释所发生的事情，但他不停地打断她。

2）表示“使暂停；使中断”，英文解释为“to stop sth for a short time”举个🌰：The game was interrupted several times by rain.比赛因下雨中断了几次。

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

从早上6:20到同一天的8点，时钟的分针旋转了多少度？

A. 680 degrees

B. 600 degrees

C. 540 degrees

D. 420 degrees

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.

只有22%的美国八年级学生给出了正确回答B，落后于巴勒斯坦人、土耳其人和亚美尼亚人。

In a recent column, I offered a paean to the humanities. But it's also true, as a professor notes in a letter to the editor, that science majors do take humanities courses. In contrast, humanities majors often desperately avoid any semblance of math or science (except for classes like “Physics for Poets”).

在最近的专栏中，我为人文学科奉上了一曲赞歌。但是正如一位教授在给编辑的信中指出的，科学专业的学生事实上有在学习人文课程。相形之下，人文专业的学生往往拼命逃避任何和数学或科学沾边的东西（除了“诗人物理学”这样的课程）。

paean /ˈpiː.ən/ 表示“赞歌；以颂扬为主题的影片（或短文）；颂赞”，英文解释为“a song, film, or piece of writing that praises someone or something very enthusiastically”

(the) humanities 表示“人文学科（如文学、语言、历史、哲学等）”，英文解释为“the study of subjects such as literature, language, history, and philosophy”举个🌰：I've always been more interested in the humanities than the sciences. 我一直对人文学科比对自然科学更感兴趣。

semblance /ˈsɛmbləns/表示“近似；相似；表象；假象；外观；外貌”，英文解释为“a situation in which sth seems to exist although this may not, in fact, be the case”举个🌰：The ceasefire brought about a semblance of peace. 停火协定带来了表面的和平。

Numeracy isn't a sign of geekiness, but a basic requirement for intelligent discussions of public policy. Without it, politicians routinely get away with using statistics, as Mark Twain supposedly observed, the way a drunk uses a lamppost: for support rather than illumination.

会算术不是怪咖的标志，而是对公共政策进行理性讨论的基本要求。路灯在醉鬼的眼里是用来支撑身体而不是照明的——据说语出马克·吐温(Mark Twain)，如果没有算术，政客三天两头像醉鬼利用路灯一样去利用统计数据，也不会被发现。

表示“统计数据；统计资料”，英文解释为“information based on a study of the number of times something happens or is present, or other numerical facts”举个🌰：Statistics show/suggest that women live longer than men. 统计资料显示女性比男性寿命长。

lamppost /ˈlæmp.pəʊst/ 表示“路灯柱；灯杆”，英文解释为“a tall post with a light at the side of roads and in other public places”

illumination /ɪˌluː.mɪˈneɪ.ʃən/ 表示“光，照明”，英文解释为“light”举个🌰：The only illumination was from a skylight. 唯一的光亮来自天窗。

(I believe American high schools and colleges overemphasize calculus and don't sufficiently teach statistics. Statistical literacy should be part of every citizen's tool kit.)

（我相信美国高中和大学过分强调了微积分，而在统计方面教得比较少。统计应该是每一个公民应有的基本素养。）

calculus /ˈkæl.kjə.ləs/ 表示“微积分”，英文解释为“an area of advanced mathematics in which continuously changing values are studied”

literacy /ˈlɪt.ər.ə.si/ 1）表示“识字；读写能力”，英文解释为“Literacy is the ability to read and write.”举个🌰：Many adults have problems with literacy and numeracy. 很多成年人有读写和计算的困难。

反义词：

📍illiteracy表示“文盲”（Illiteracy is the state of not knowing how to read or write.）

2）表示“（某领域或某方面的）知识，能力”，英文解释为“knowledge of a particular subject, or a particular type of knowledge”举个🌰：Computer literacy is becoming as essential as the ability to drive a car. 会用计算机与会开车一样将成为一种必备的技能。

表示“工具包”，英文解释为“A tool kit is a special set of tools that are kept together and that are often used for a particular purpose.”

此处指的是一个人应该具备的一套基本技能或知识，英文解释为“skills and knowledge that are useful for a particular purpose or activity, considered together”

Public debates often dance around basic statistical concepts, like standard deviation, because too few Americans understand them. And people assume far too much of “averages.”

公开辩论常常避开基本的统计概念，比如标准差，因为了解它们的美国人太少了。而人们对“平均数”有太多一厢情愿的理解。

表示“避开；回避”，英文解释为“To avoid or evade talking about some issue or topic directly or at all.”

standard deviation /ˌstæn.dəd ˌdiː.viˈeɪ.ʃən/ 表示“标准偏差”，英文解释为“a number that shows the amount by which members of a group are different from the mean (= average) value for the group”

assume /əˈsjuːm/ 1）表示“假定；假设；认为”，英文解释为“to think or accept that sth is true but without having proof of it”举个🌰：It is generally assumed that stress is caused by too much work. 普遍认为，紧张是工作过重所致。

2）表示“承担，担任；僭取，夺取；呈现，具有”，英文解释为“to take or begin to have responsibility or control, sometimes without the right to do so, or to begin to have a characteristic”举个🌰：The new president assumes office at midnight tonight. 新总统在今晚午夜就职。

After all, American adults have, on average, one ovary and one testicle. But try finding such an “average person.”

美国成年人平均每人有一个卵巢和一个睾丸。但你找到一个这样的“一般人”试试。

ovary /ˈəʊ.vər.i/ 表示“卵巢；子房”，英文解释为“either of the pair of organs in a woman's body that produce eggs, or the part of any female animal or plant that produces eggs or seeds”

testicle /ˈtes.tɪ.kəl/ 表示“睾丸”，英文解释为“either of the two round male sex organs that produce sperm and are contained in the scrotum (= bag of skin) below and behind the penis”

Another pop quiz:

再来一个临时小测验：

pop quiz /ˈpɒp ˌkwɪz/ 表示“（没有提前通知的）突击测验，突击考试”，英文解释为“a short, informal test that is given without any warning”

A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

一块木头有40厘米长。它被切成3段。以厘米为单位，三段木头长度分别是2x-5、x+7和x+6。最长的那段有多长？

美式 centimeter 英式 centimetre /ˈsen.tɪˌmiː.tər/ 表示“厘米，公分”，英文解释为“a unit of length equal to 0.01 of a metre”

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

只有7%的美国八年级学生回答正确（答案是15厘米）。相比之下，新加坡八年级学生中有53%回答正确。

I know many readers will grumblingly protest that they're just not good at math! True, there are math prodigies who are different from you and me. When the great mathematician Carl Gauss was a young boy, his teacher is said to have asked his class to calculate the sum of all the numbers from 1 to 100. Gauss supposedly supplied the answer almost instantly: 5,050.

我知道很多读者会发牢骚说，他们只是不擅长数学而已！诚然，世界上有些数学天才异于你我常人。据说伟大的数学家卡尔·高斯(Carl Gauss)还是一个小男孩时，他的老师在课上要求学生计算从1到100所有数字的总和，高斯几乎瞬间就得出答案：5050。

grumblingly /ˈɡrʌm.bəl.ɪŋ.li/ 表示“发牢骚着；喃喃抱怨着”，英文解释为“in a low voice that shows that you are not pleased or happy”

prodigy /ˈprɒd.ɪ.dʒi/ 表示“奇才，天才”，英文解释为“someone with a very great ability that usually shows itself when that person is a young child”

The teacher, flabbergasted, asked how he knew. Gauss explained that he had added 1 and 100, 2 and 99, and realized that there would be 50 such pairs each summing 101. So 50 times 101 equals 5,050.

老师大吃一惊，问他怎么知道。高斯解释说，他把1和100相加，2和99相加，他意识到这样的对子有50个，每对的和为101。所以，50乘以101等于5050。

flabbergasted /ˈflæb.ə.ɡɑː.stɪd/ 表示“目瞪口呆的，大吃一惊的”，英文解释为“feeling shocked, usually because of something you were not expecting”举个🌰：She is flabbergasted by the whole affair. 整件事使她目瞪口呆。

So I agree: Let's resent the Gausses of the world for being annoyingly smart. But let's not use that as an excuse to hide from the rigor of numbers. Countries like Singapore manage to impart extraordinary math skills in ordinary children because they work at it.

所以我同意：大家一起来怨恨高斯这种聪明得让人恼火的人。但我们不能把那当作借口来躲开严谨的数字。像新加坡这样的国家，就成功地让普通孩子掌握了良好的数学技能，因为他们在这方面努了力。

resent /rɪˈzent/ 表示“感到愤恨；不满；憎恶”，英文解释为“to feel angry because you have been forced to accept someone or something that you do not like”举个🌰：He resents having to explain his work to other people. 他讨厌非得向人们解释他的工作。

📍词根“sent”来源于拉丁语“sentire”，意思是“感觉”。前缀“re-”表示“再次”，所以“resent”可以联想为“再次感觉到某事”，通常是不愉快的事情。想象每次他人问你同样的问题，你的怨恨情绪就更加强烈。近义词：dislike（不喜欢），同根词：resentment（怨恨），常用短语：resent someone for something（因某事怨恨某人）。

美式rigor 英式 rigour /ˈrɪɡ.ər/ 1）表示“严厉；严格；苛严”，英文解释为“the fact that people are made to follow rules in a very severe way”举个🌰：They were punished with unusual rigour. 他们遭到了非常严厉的惩罚。

2）表示“严密；缜密；严谨”，英文解释为“the quality of being detailed, careful, and complete”举个🌰：Her arguments lacked intellectual rigour. 她的论点不够理智和严谨。

impart /ɪmˈpɑːt/ 1）表示“传授；告知”，英文解释为“to communicate information to someone”如：to impart the bad news 告知坏消息；

2）表示“赋予，给予”，英文解释为“to give something a particular feeling, quality, or taste”举个🌰：Preservatives can impart colour and flavour to a product. 防腐剂能使产品保持色泽和味道。

Numeracy isn't just about numbers, of course. It's also about logic. Let me leave you with a logical puzzle — a family favorite, one that I first heard as a little kid — that isn't mathematical at all. Yet people with math training seem better at thinking it through and solving it:

算术当然不仅仅是数字。它还涉及逻辑。下面有一个逻辑题——是我家里人最喜欢的一个，我第一次听到它的时候还是一个小孩——完全和数学无关。然而，接受过数学培训的人似乎更善于思考并解决它：

logic /ˈlɒdʒ.ɪk/ 1）表示“逻辑思维，理性思维”，英文解释为“a particular way of thinking, especially one that is reasonable and based on good judgment”举个🌰：I fail to see the logic behind his argument. 我看不出他的论点有什么逻辑依据。

2）表示“逻辑学，逻辑推理”，英文解释为“a formal scientific method of examining or thinking about ideas”如：a treatise on formal logic 关于形式逻辑学的论文。

puzzle /ˈpʌz.əl/ 1）表示“令人费解的情况；难题；谜”，英文解释为“a situation that is difficult to understand”举个🌰：Scientists have been trying to solve this puzzle for years. 多年来科学家们一直试图解开这个谜。

2）表示“测验智力的游戏（或玩具）”，英文解释为“a game or toy in which you have to fit separate pieces together, or a problem or question that you have to answer by using your skill or knowledge”如：a jigsaw puzzle 智力拼图玩具。

You're in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don't know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don't know whether you'll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape? 

你在一个地牢里，地牢有两扇门，其中一扇是逃生门，另一扇是死亡门。地牢里除你之外只有两个人，其中一人总是讲真话，另一个总是说谎。你不知道谁讲真话谁说谎，但他们互相知道。你可以问他们其中一人一个问题，当然，你不知道你问的究竟是老实人还是骗子。那么，这个问题该怎么问，才能知道哪扇是逃生门，哪扇是死亡门，从而死里逃生？

dungeon /ˈdʌn.dʒən/ 表示“（尤指城堡中的）地牢”，英文解释为“an underground prison, especially in a castle”

替execution /ˌek.sɪˈkjuː.ʃən/ 表示“（依法进行的）处决，处死”，英文解释为“the legal punishment of killing someone”举个🌰：Execution is still the penalty in some states for murder. 在一些国家，犯谋杀罪的人仍然被处以死刑。

2）表示“（尤指有计划的）实行，履行，表演”，英文解释为“the act of doing or performing something, especially in a planned way”举个🌰：Although the original idea was good, its execution has been disappointing. 尽管最初的想法很好，但真正做起来却令人失望。

It's not a trick question. When you hear the answer, you'll see it's straightforward.

这不是一个脑筋急转弯。一旦你听到答案，你会觉得它很简单。

trick question /ˌtrɪk ˈkwes.tʃən/ 表示“欺骗性问题；陷阱问题”，英文解释为“a question that makes you believe you should answer it in a particular way, when the real question is hidden or there is no right answer”

Give up? You ask either of them: “If I asked the other person which door is the one to escape, which would he point to?” Then you take the other door.

想不出来了？你可以问他们中的任何一个“如果我问另一个人哪扇门是逃生门，他会指哪扇呢？”然后你走另一扇门就可以了。

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