🎯 能力诊断测试 · 精准版

在竖式计算 45×7 时，个位 5×7=35，应该怎么写？When doing column multiplication for 45×7, 5×7=35 in the ones place, how should it be written?

老师买了60支铅笔，分给第一组15支，分给第二组25支，剩下的分给第三组。第三组分到多少支？A teacher bought 60 pencils. She gave 15 to Group 1 and 25 to Group 2. The rest were given to Group 3. How many pencils did Group 3 get?

小美有 3 件上衣（红上衣、黄上衣、蓝上衣）和 2 条裙子（长裙、短裙）。她按「先固定一件上衣，再依次配两条裙子」的顺序，想把所有穿法不重复、不遗漏地列出来。她已经写出：红上衣配长裙、红上衣配短裙、黄上衣配长裙、黄上衣配短裙、蓝上衣配长裙，然后就停笔了，以为已经列完。其实她漏掉了哪一种穿法？May has 3 tops (a red one, a yellow one, and a blue one) and 2 skirts (a long one and a short one). She wants to list every outfit with no repeats and no misses, fixing one top at a time and then matching it with each skirt in turn. She writes: red top with long skirt, red top with short skirt, yellow top with long skirt, yellow top with short skirt, blue top with long skirt—then she stops, thinking she has finished. Which outfit did she leave out?

弟弟有8张贴纸，姐姐的贴纸张数是弟弟的3倍。姐姐比弟弟多多少张贴纸？Ben has 8 stickers. His sister Kate has 3 times as many stickers as Ben. How many more stickers does Kate have than Ben?

一串彩灯按照“红、红、黄、蓝”的顺序重复排列。如果这串灯共有 33 盏，其中红灯有多少盏？A string of lights repeats in the order "Red, Red, Yellow, Blue". If there are 33 lights in total, how many are red?

在加法竖式 $\square 7 + 2 \square = 83$ 中，方框代表不同的数字。第一个方框（十位）里的数字是多少？In the addition vertical form $\square 7 + 2 \square = 83$, the squares represent different digits. What is the digit in the first square (tens place)?

一个班级有36名学生，其中1/3是男生，男生中有1/4戴眼镜。戴眼镜的男生有多少人？There are 36 students in a class. 1/3 of them are boys, and 1/4 of the boys wear glasses. How many boys wear glasses?

2台机器3小时一共装配了54个零件。照这样计算，4台机器6小时一共能装配多少个零件？2 machines assemble 54 parts in 3 hours. At this rate, how many parts can 4 machines assemble in 6 hours?

妈妈把一袋糖果分给几个小朋友。如果每人分 2 颗，会多出 6 颗；如果每人分 3 颗，就会少 4 颗。这袋糖果一共有多少颗？Mom is sharing a bag of candies among some children. If each child gets 2 candies, 6 candies will be left over. If each child gets 3 candies, she will be 4 candies short. How many candies are in the bag?

在分母是 10、分子小于 10 的分数中，比 1/2 大的最小分数是多少？先想一想：1/2 相当于十分之几。Among all the fractions whose denominator is 10 and whose numerator is smaller than 10, what is the smallest fraction that is greater than 1/2? (Think: 1/2 is equal to how many tenths?)

鸡兔同笼，共有15个头。小晴懒得数腿，她直接用假设法：假设15只全是鸡，这样算出的腿数比实际少18条。笼中的兔有______只。Chickens and rabbits are in a cage with 15 heads in all. Mia didn't bother counting the legs — she used the assumption method directly: assuming all 15 animals are chickens, the leg count would be 18 fewer than the actual number. There are ______ rabbits in the cage.

老师把 13 枚棋子放进 4 个盒子里。无论怎么放，一定有一个盒子里至少有多少枚棋子？A teacher puts 13 game pieces into 4 boxes. No matter how they are placed, at least one box must contain at least how many pieces?

如果 x = 5，那么 3x + 2 的值是多少？If x = 5, what is the value of 3x + 2?

一根绳子原来长 x 米。剪去 28 米后，还剩 55 米。这根绳子原来长 ____ 米。A rope was originally x meters long. After 28 meters were cut off, 55 meters were left. The rope was originally ____ meters long.

哥哥收集的卡片张数是弟弟的 4 倍，哥哥比弟弟多收集 36 张。两人一共收集了____张卡片。Alex has collected 4 times as many cards as Ben. Alex has collected 36 more cards than Ben. In total, the two boys have collected ____ cards.

天平的左盘放着一个重 x 克的物体和一个 5 克的砝码，右盘放着一个 12 克的砝码，此时天平正好平衡。如果从左盘取走那个 5 克的砝码，要使天平仍然保持平衡，右盘应该（　）。On a balance scale, the left pan holds an x-gram object and a 5-gram weight, and the right pan holds a 12-gram weight. The scale is balanced. If the 5-gram weight is removed from the left pan, what should be done to the right pan to keep the scale balanced?

两辆汽车同时从相距 480 千米的两地出发，相向而行，4 小时后相遇。已知甲车每小时行 65 千米，乙车每小时行多少千米？Two cars start at the same time from two towns 480 kilometers apart and drive toward each other. They meet 4 hours later. Car A travels at 65 kilometers per hour. How many kilometers per hour does Car B travel?

用数字 5、6、7、8 组成没有重复数字的三位数，其中大于 700 的三位数一共有多少个？Using the digits 5, 6, 7, and 8, how many different three-digit numbers greater than 700 can be formed if no digit may be used more than once?

一件衣服原价300元，降价20%后，又上涨了15%，现在的价格是____元。A piece of clothing originally costs 300 yuan. After a 20% discount, its price increases by 15%. The current price is ____ yuan.

一个长方体长6厘米、宽4厘米、高3厘米，表面积是108平方厘米。把它切成两个完全相同的小长方体（有三种不同的切法），这两个小长方体的表面积之和最少是多少平方厘米？A cuboid measures 6 cm by 4 cm by 3 cm and has a surface area of 108 cm². It is cut into two identical smaller cuboids (there are three different ways to cut). What is the least possible sum of the surface areas of the two smaller cuboids?

一个盒子里装有红、蓝、黄三种颜色的弹珠，红、蓝、黄弹珠的数量比是 3:2:1。蓝色弹珠占弹珠总数的几分之几？A box contains red, blue and yellow marbles in the ratio 3:2:1. What fraction of the total number of marbles are blue?

正方形ABCD的边长是12厘米。E、F、G、H分别是AB、BC、CD、DA四条边的中点。顺次连接E、F、G、H，得到四边形EFGH。四边形EFGH的面积是多少平方厘米？Square ABCD has a side length of 12 cm. Points E, F, G, and H are the midpoints of sides AB, BC, CD, and DA, respectively. Joining E, F, G, and H in order forms quadrilateral EFGH. What is the area of quadrilateral EFGH, in square centimeters?

一个立体图形由一个圆柱和一个圆锥组成：圆柱的底面半径是 3 厘米、高是 4 厘米；圆锥与圆柱等底，高是 3 厘米，正好放在圆柱的正上方。这个立体图形的体积是多少？（结果用含 π 的式子表示）A solid is made of a cylinder with a cone of the same base sitting exactly on top of it. The cylinder has a base radius of 3 cm and a height of 4 cm; the cone has a height of 3 cm. What is the volume of the whole solid? (Express your answer in terms of π.)

把一块棱长 6 厘米的正方体木料削成一个尽可能大的圆柱（圆柱的底面是正方体一个面上所能画出的最大的圆，高与正方体的棱长相等）。削去部分的体积是多少立方厘米？（结果用含 π 的式子表示）A wooden cube has edges of 6 cm. It is carved into the largest possible cylinder: the cylinder's base is the largest circle that fits on a face of the cube, and its height equals the cube's edge. What is the volume of the wood carved away? (Express your answer in terms of π.)

一个整数除以7余3，除以5余2，这个数最小是多少？An integer leaves a remainder of 3 when divided by 7 and a remainder of 2 when divided by 5. What is the smallest such number?

小明、小刚、小红三人收集卡片。小明的卡片数是小刚的 5/6，小红的卡片数是小明的 4/5，小刚比小红多 14 张。小红有多少张卡片？Ming, Gang and Hong collect cards. Ming's number of cards is 5/6 of Gang's, and Hong's number of cards is 4/5 of Ming's. Gang has 14 more cards than Hong. How many cards does Hong have?

一个空水池，单开进水管 4 小时可以注满。这一次从空池开始，把进水管和排水管同时打开，结果用了 12 小时才把水池注满。如果单开排水管，多少小时可以把一满池水排空？An empty pool can be filled by the inlet pipe alone in 4 hours. This time, starting with an empty pool, the inlet and the drain are opened at the same time, and it takes 12 hours to fill the pool. If the drain is opened alone, how many hours would it take to empty a full pool?

一辆汽车从 P 城开往 Q 城，前 3 小时行驶了 195 千米。照这样的速度，剩下的路程正好还要行驶 2 小时。P、Q 两城相距____千米。A car travels from City P to City Q. In the first 3 hours it covers 195 km. Keeping the same speed, the remaining part of the trip takes exactly 2 more hours. The distance between City P and City Q is ____ km.

把 100 克 A 种糖水和 200 克 B 种糖水混合，得到浓度 32% 的糖水；把 200 克 A 种糖水和 100 克 B 种糖水混合，得到浓度 28% 的糖水。A 种糖水的浓度是多少？Mixing 100 g of solution A with 200 g of solution B gives a 32% sugar solution, while mixing 200 g of solution A with 100 g of solution B gives a 28% sugar solution. What is the concentration of solution A?

某班要从全班同学中选出2名值日生（两人的任务完全相同）。已知不同的选法恰好有36种，这个班共有多少名同学？A class must choose 2 students for duty, and the two students have exactly the same task. If there are exactly 36 different ways to choose the pair, how many students are in the class?