外国语学校小升初入学考试中英文奥数题库.doc

1、- 1 -外国语学校小升初英语奥数训练题第一部分1、三个素数的倒数之和是 ，则这三个素数中最大的是多少？206151. The sum of the reciprocals of three prime numbers is , so what is the greatest 20615one among the three prime numbers?2、有一个分数，它的分子加 2，可以约简为 ；它的分母减 2，可以约简为74。这个分数是多少？5142. There is a fraction. If its numerator adds 2, it can be reduced to be

2、 ; if its 74denominator subtracts 2, it can be reduced to be . So what is this fraction? 25143、一个数分别除以 ， ， ，所得的商都是自然数。这个数最小是多少？142093. A number is divided by , and respectively and the quotients are all 420natural numbers. So what is the minimum value of this number? 4、一片竹林，去年不开花的竹子比开花的 2 倍还多 55 棵，今

3、年又多了 100 棵开花，这时开花的竹子恰好是不开花的 4 倍，这片竹林有多少棵竹子？4. There is a bamboo forest. Last year, the non-blooming bamboos were two times and 55 more than the blooming bamboos. With another 100 bamboos blooming this year, the blooming bamboos are four times as many as the non-blooming bamboos. So, how many bamboos

4、 are there in this forest? （红色的地方我有点不确定，葛老师您看看应该怎么翻）5、从 中去掉两个分数，余下的分数之和为 1。这两个分12086412- 2 -数是哪两个分数？5. Take out two fractions from to make the sum of remaining 12086412fractions to be 1. So what are these two fractions? 6、一个整数与它的倒数的和等于 20.05，这个整数是多少？它的倒数是多少？6. The sum of an integer and its reciproca

5、l is 20.05, so what is this integer and what is its reciprocal? 7、四个非零自然数的和为 38，这四个自然数的乘积的是小值是多少？最大值是多少？7. The sum of four nonzero natural numbers is 38, so what can the minimum product of these four natural numbers be? And what can the maximum product be?8、已知 a 是质数， b 是偶数，且 a2+b=2008，则 a+b+1 结果是多少？

6、8. It is known that a is a prime number and b is an even number and that a2+b=2008, so what is the result of a+b+1? 9、一个质数 p，使得 p+2，p+4 同时都是质数。则 的结果是多4121p少？9. There is a prime number p, which can make p+2 and p+4 to be prime numbers as well. So what is the result of ? 4121p10、 彼此不等且大于 0 的偶数 a，b，c ，

7、d 满足 a+b+c+d=20，这样的偶数组（a，b，c ，d）共有多少组？10. There are four different even numbers a, b, c and d, which are all greater than 0. If they should satisfy the equation of a+b+c+d=20, how many groups of such even numbers (a, b, c, d) are there?- 3 -11、 在一个两位数的中间加上一个 0，得到的新数比原来大 8 倍，原来的两位数是多少？11. Add a “0” t

8、o the middle place of a double-digit number, so that the new three-digit number is 8 times more than the original number. So what is the original double-digit number?12、 如图，从 A 到 B 有多少条不同的路线？（只能向上或向左走）BA12. As shown in the picture, how many different ways are there to go from A to B? (One can only w

9、alk up or towards left) 13、 小马虎在考试中做一道计算题时，将一个数乘 9 错算成除以 9，接着又将加上 30 错算成减去 30，结果得 18，如果按正确的运算顺序，所得的结果是多少？13. When doing a calculation in an exam, a careless student made some mistakes. Rather than multiplying a number by 9 and then adding 30, he divided the number by 9 and then subtracted 30, so tha

10、t the result was 18. If he did the calculation correctly, what would the result be? 14、 袋里有若干个球，其中红球占 ，后来又往袋里放了 6 个红球，这时125红球占总数的 。现在袋里有多少个球？21- 4 -14. There are some balls in a bag and the red balls account for of the total amount. 125After adding another 6 red balls into the bag, the red balls acc

11、ount for of the total amount. So how many balls are there in the bag now? 15、 有 1567 名同学排成一排玩游戏，从排头到排尾按顺序说“我” “最”“棒”3 个字（每人说一个字） ，再从排尾到排头重新按顺序说这 3 个字，其中有多少人两次都说“我”这个字？15. 1567 students stand in a row to play games, speaking “Im” “the” “best” from the head of the row to the end of the row (each stude

12、nt speaks one word at a time) and then speaking these three words from the end of the row to the head of it. So, how many students speak “Im” twice? 第二部分1、一条船顺水航行 48 千米，再逆水航行 16 千米，共用了 5 小时；这条船顺水航行 32 千米，再逆水航行 24 千米，也用了 5 小时。求这条船在静水中的速度。1. It takes a boat 5 hours to sail 48 km downstream and 16 km u

13、pstream. And it also takes the boat 5 hours to sail 32 km downstream and 24 km upstream. So what is the speed of this boat in still water? 2、有一所学校，男生占学生总人数的 ，学生总人数与男生人数都是三位数，53组成这两个三位数的六个数字正好是 1、2、3、4、5、6。问：这所学校有多少学生？2. In a school, boy students account for of all the students. It is known that the

14、number of all the students and the number of boys are both three-digit numbers and the six digits making up these two three-digit numbers are 1, 2, 3, 4, 5 and 6. So how many students are there in this school? 3、六个小朋友在一起做游戏。他们每人想一相整数写在卡片上交给老师，老师用不同的方式把其中 5 人写的数加在一起，得到以下 6 个数：87、92、98、99、104、110。那么卡片

15、上写的数中最接近平均数的是什么- 5 -数？3. Six children play games. Each of them writes down an integer on a card and gives the card to a teacher. The teacher adds up any 5 of the six numbers in different ways and gets the following six numbers: 87, 92, 98, 99, 104 and 110. So what number on the six cards is closest

16、to the average number? 4、现在一副去掉大小王的扑克牌，共 52 张。把它们洗匀后，分成 A、B 两组，各 26 张。请问：在 1000 次洗牌中，A 组中的黑牌数和 B 组中的红牌数，有几次会完全相同？4. There is a set of playing cards, a total of 52 cards, which does not include the big king and the little king. After being shuffled, the cards are divided into A and B groups, 26 cards

17、 in each group. So in 1000 times of shuffle, how many times will the number of black cards in Group A be exactly equal to the number of red cards in Group B? 5、给 10 位学生发铅笔，每人 3 支还剩下一些，每人 4 支又不够。如果剩下的和不够的同样多，那么共有多少支铅笔？5. Divide pencils among 10 students. There will be some pencils left if each studen

18、t is given 3 pencils and it will not be enough to give each student 4 pencils. Given that the number of the pencils left is equal to the number of the insufficient pencils, how many pencils are there totally? 6、甲、乙、丙丁进行象棋比赛，每两人之间要赛一盘。规定胜一盘得 2 分，平一盘各得 1 分，输一盘不得分。甲、乙、丙共得 10 分，丁得多少分？6. A, B, C and D pl

19、ay chess and every two people need to compete once. It is ruled that winning will bring 2 marks, a draw will bring 1 mark and losing will bring no marks. A, B and C altogether get 10 marks, so how many marks does D get? 7、甲、乙两人卖商品，甲的比乙多 10 个，可是全部卖出后的收入都是 15 元。如果甲的商品按乙的价格出售可卖 18 元，那么，甲、乙各有多少个商品？7. A

20、and B sell commodities. A has 10 more commodities than B, but both of them gain a profit of 15 yuan after selling out their commodities. If A sells his commodities according to Bs price, he will get 18 yuan. So how many commodities do A and B have respectively? - 6 -8、有 20 包花生给一只猴子吃，一包只能吃一天，但不能连续两天都

21、吃（即今天吃了，明天就不能吃） ，且间隔的天数彼此不同。那么，这 20 包花生至少要多少天才能吃完？8. 20 bags of peanuts will be used to feed a monkey and one bag of peanuts can only last for one day. The monkey cannot eat peanuts every two continuous days (if it eats peanuts today, it cannot eat them tomorrow) and the interval days should be diff

22、erent. So how many days at least will it take the monkey to eat up these 20 bags of peanuts? 9、在 1 到 100 这 100 个自然数中，找出 3 个自然数，使它们的倒数和为 1。9. Find out 3 natural numbers among 100 natural numbers from 1 to 100, so that the sum of these three numbers reciprocals is 1. 10、 有一个边长为 1 分米的正方形，甲先划去正方形面积的 ，乙接

23、着划去31剩下面积的 ，然后甲又划去剩下面积的 ，乙再划去剩下面积的 ，2312，依次类推。如果两人分别划了三次，此时这个正方形还剩下多少平方分米没有被划去？10. There is a square whose sides are 1 dm. A first cuts off of the square and B 31cuts off of the remaining area. Then A cuts off of the remaining area and B cuts 21off of the area left,After A and B cut the square in th

24、e same manner for three times, how many square decimeters is the area left? 11、 3 个六面体都是按照相同的规律涂有红、黄、蓝、白、黑、绿 6 种颜色（如图） 。黄色对面是（ ）色，白色对面是（ ）色，红色对面是（ ）色。黑 黄白白绿红 蓝 红黄- 7 -11. As shown below, 3 hexahedrons are painted with 6 colors of red, yellow, blue, white, black and green according to the same rule.

25、So the color opposite yellow is ( ), the color opposite white is ( ) and the color opposite red is ( ). 12、 大毛、二毛、三毛每天早晨都要在运动场上进行长跑训练。一天，他们在 200 米跑道的同一起跑线上同时起跑，当三毛正好跑完一圈时，二毛超过三毛 圈，大毛超过三毛半圈，这天早晨他们共跑了 15 圈。如果他们41始终以各人的速度跑步，那么他们每人各跑了几圈？12. A, B and C took long-distance running training on the playgroun

26、d every morning. One day, they started at the same time from the same starting line of the 200-meter runway. When C finished a circle, B was circle ahead of C and A was half circle 41ahead of C. They altogether ran 15 circles. If they kept running with constant speeds, how many circles did they run

27、respectively? 第三部分16、 一个三位数，如果它的每一位数字都不超过另一个三位数对应数位上的数字，那么就称它被另一个三位数“吃掉” 。又规定“任何数都可以被它相同的数吃掉” 。比如，241 被 342“吃掉” ，123 被 123“吃掉” ，但是 240和 223 互相都不能被“吃掉” 。现请你设计出 6 个三位数，它们中的任何一个都不能被另外 5 个“吃掉” ，并且它们的百位数字只允许取 1，2；十位数字只允许取 1，2，3；个位数字只允许取 1，2，3，4，那么这 6 个三位数之和是多少？There is a three-digit number. If every digi

28、t of it does not exceed its counterpart of another three-digit number, then, we can say that it is eaten by the later three-digit number. It is also the rule that any number can be eaten by itself. For example, 241 is eaten by 342 and 123 is eaten by 123. But 240 and 223 can not be eaten by each oth

29、er. Now please conceive six three-digit numbers and make sure that none of them can be eaten by the other five. In addition, their hundreds digits can only be 1 or 2, their tens digits can only be 1, 2 or 3, and their ones digits can only be chosen from 1, 2, 3 and 4. Then, what is the sum of the si

30、x three-digit numbers?17、 小王骑自行车，小张骑摩托车，他们同时从 A、B 两地相向而行，在距中点 10 千米处相遇。已知小王骑车的速度是小张的 ，求 A、B 两地间的53black yellowwhitewhitegreenred blue redyellow- 8 -距离。Xiao Wang is riding a bike and Xiao Zhang is riding a motorcycle. They move face to face from A and B respectively at the same time. They meet at the

31、 place which is 10 kilometers away from the midpoint. Given that Xiao Wangs speed is three fifths of that of Xiao Zhang. What is the distance between A and B?18、 小刚骑车从 8 路汽车的起点站出发，沿着 8 路车的行驶路线前进。当他骑了 1650 米时，一辆 8 路公共汽车从起点站出发，每分钟行 450 米。这辆汽车在行驶过程中每行 5 分钟停靠一站，停车时间为 1 分钟。已知小刚骑车速度是汽车行驶速度的 ，这辆车出发后多少分钟追上小

32、刚？323. Xiao Gang starts from the origin station of No.8 bus by bike and goes along the route of No.8 bus. When he covers 1650 meters, a No.8 bus sets out from the origin station and moves 450 meters per minute. This bus pulls up for one minute at one bus stop every five minutes. Given that Xiao Gang

33、s speed is two thirds of that of the bus, how many minutes will it take the bus to catch up with Xiao Gang after its departure?19、 甲、乙两筐水果重量相等，如果从甲筐取出 6 千克水果放入乙筐，这时，甲筐比乙筐少 ，甲筐原有水果多少千克？414. There are two baskets of fruits, A and B, with the same weight. If one takes out 6 kilograms of fruits from A a

34、nd put them into B, then, the fruits in A is a quarter less than those in B. How many kilograms of fruits are there in A in the first place?20、 下面的每个图形中的数字都存在一定的规律，请找一找，再算出第四个图形中的“？”表示的数是多少？8 13 12 6 22 3 43 512 13 14 ?5 3 4 2 9 5 11 65. There exists a certain regularity of the numbers in the follow

35、ing pictures. Please find the regularity and figure out the number indicated by a question mark in the fourth picture.21、 如果一个整数等于它各个数位上数的和的 3 倍，那么这个数会是多少？6. If an integer is three times as large as the sum of the figures in its digit positions, then, what is the number?22、 有两个大小不同的正方形 A、B，如下图，B 的中心

36、与 A 的一个顶点重合，重叠部分的面积是 A 面积的 ，你能知道正方形 A 的边长是 B 的多少倍91- 9 -ABAB吗？7. Square A and square B are different in size. As is shown in the following picture, the center of B and one of the vertexes of A overlap each other. The area of the overlapped part is one ninth of that of A. Do you know how many times t

37、he side of A is as long as that of B?23、 上题中，如果 A 与 B 以下图的方式重叠时，那么重叠部分面积又是 B面积的几分之几？8. In the above problem, if A and B overlap like the following picture, then, what portion is the area of the overlapped part to that of B in terms of fraction?24、 图 1 中有 8 个面积都是 4 平方厘米的正三角形，依次叠放在同一条直线上，从左到右，每个三角形底边的

38、中点恰好与下一个三角形的一个顶点重合，那么由这 8 个三角形所盖住的面积是多少平方厘米？9. There are eight identical regular triangles in the following picture. Each area is 4 cm2. They overlap one another on the same straight line. From left to right the midpoint of the base line of every triangle overlaps with one of the vertexes of the nex

39、t triangle. What is the area covered by the eight triangles in square centimeters? 25、 下图中有 10 个边长都是 2 厘米的正方形，依次地排在一条直线上，而且正方形的一个顶点，正好是下一个正方形的中心，那么由这 10 个正方形所盖住的面积是多少？- 10 -In the following picture, ten squares with the same side length of 2 cm are arranged on one straight line in order. One of the

40、vertexes of one square is just the center of the next one. What is the area covered by the ten squares?26、 有一个 33 的方格，能否通过若干次操作，使得方格中的所有数变为0？（其中一次操作是指将表中一行的 3 个数或一列的 3 个数同时加上或减去同一个数） ，如果能请给出一种操作方案，如果不能，请说明理由。11. There is a 33 grid. Can you turn all the numbers in the grid into 0 after several operat

41、ions? (The operation is to add or minus the same number to or from the three numbers in one row or in one column at the same time.) If you can, please give one plan, and if not, please give your reason.27、 上题中，其他条件不变，能否通过若干次操作，使得方格中的所有数变为 1 呢？12. In the above problem, if we keep the other conditions

42、 unchanged, can you turn all the numbers in the grid into 1 after several operations?28、 将一张长方形纸片连续对折，对折的次数越多，折痕的条数也就越多，请问对折 8 次后，折痕有多少条？（向同一个方向对折）13. If one folds a piece of rectangular paper continuously, the more times he folds the paper, the more creases there are on the paper. After it has been folded 8 times, how many creases are there on the paper? (Please fold it in the same direction.)1 1 23 7 82 6 7