🎯 能力诊断测试 · 精准版

比较下列两个数的大小：256 和 321Compare the following two numbers: 256 and 321

甲篮有15个苹果，乙篮有7个苹果。从甲篮拿几个苹果放入乙篮，两篮的苹果就一样多？Basket A has 15 apples and Basket B has 7 apples. How many apples must be moved from Basket A to Basket B so that both baskets have the same number of apples?

联欢会上有 5 个小朋友，每两个人之间握一次手（握过一次的两个人不再重复握）。按顺序有序地数：第 1 个小朋友和其余 4 人各握一次，共 4 次；第 2 个小朋友和还没握过手的 3 人各握一次，共 3 次；照这样依次往下数。这 5 个小朋友一共要握多少次手？At a party there are 5 children. Every two children shake hands exactly once (the same two children never shake hands twice). Counting in order: the first child shakes hands with the other 4 children, so that is 4 handshakes; the second child then shakes 3 more hands with the children not greeted yet; the third and fourth children keep counting in the same way. How many handshakes are there in all?

图书角原来有50本图书，借出一些后，又新买回18本，现在图书角一共有45本。借出了多少本图书？A classroom library had 50 books. Some books were borrowed out, and then 18 new books were added. Now the library has 45 books in all. How many books were borrowed out?

甲、乙两个盒子共有 20 个球。如果从甲盒拿出 2 个放入乙盒，两个盒子里的球就一样多。原来甲盒有多少个球？Boxes A and B have a total of 20 balls. If 2 balls are moved from Box A to Box B, the two boxes will have the same number of balls. How many balls were in Box A originally?

在 20 米长的跑道一侧插旗子，两端各插一面，一共插了 6 面旗子。相邻两面旗子之间相隔多少米？Flags are placed along one side of a 20-meter track, with one at each end. A total of 6 flags are placed. How many meters are between two adjacent flags?

一个农场有鸡和兔子共40只，鸡有2只翅膀，兔子有4条腿。如果农场里鸡的数量是兔子的3倍，问农场里有多少只兔子？A farm has 40 chickens and rabbits in total. Chickens have 2 wings and rabbits have 4 legs. If the number of chickens is 3 times the number of rabbits, how many rabbits are there on the farm?

阿姨今年 30 岁，小美今年 6 岁。下面哪句话是正确的？Aunt Grace is 30 years old, and Mia is 6 years old. Which of the following statements is true?

修路队要修一条长108米的路，每名工人每天修6米，要求6天正好修完。一共需要多少名工人？A road crew must pave a road 108 meters long. Each worker paves 6 meters per day, and the job must be finished in exactly 6 days. How many workers are needed in all?

4 名同学排成一排照相，一共有多少种不同的站队方法？Four students stand in a row for a photo. How many different ways can they line up?

甲、乙、丙三个数的和是 96。乙是甲的 2 倍，丙比乙多 6。甲是多少？The numbers A, B, and C add up to 96. B is twice A, and C is 6 more than B. What is A?

两个自然数的和是 12（两个数可以相同）。先把各种组合一一列举出来试一试：这两个数的乘积最大是多少？Two whole numbers add up to 12 (they may be the same). Try listing all the possible pairs first: what is the greatest possible product of the two numbers?

计算：1/3 + 1/6 = ?Calculate: 1/3 + 1/6 = ?

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.

一张边长 10 厘米的正方形纸，正中间剪去一个正方形洞，洞的每条边离纸最近的边缘都是 2 厘米。这张纸剩下部分的面积是多少平方厘米？A square sheet of paper has a side length of 10 cm. A square hole is cut out from the center, and each side of the hole is 2 cm from the nearest edge of the sheet. What is the area of the paper that remains, in square centimeters?

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.

甲、乙两人有一些贴纸。如果甲给乙 9 张，两人的贴纸张数就一样多；如果乙给甲 9 张，甲的贴纸张数就是乙的 5 倍。甲原来有多少张贴纸？Two children have some stickers. If A gives 9 stickers to B, they will have the same number of stickers. If B gives 9 stickers to A, then A will have 5 times as many stickers as B. How many stickers did A have at first?

弟弟从家出发去公园，每分钟走 60 米。他出发 4 分钟后，哥哥从家出发，沿同一条路去追弟弟，每分钟走 90 米。哥哥出发多少分钟后追上弟弟？A younger brother leaves home for the park, walking 60 meters per minute. Four minutes after he sets out, his older brother leaves home along the same road to catch up, walking 90 meters per minute. How many minutes after the older brother starts does he catch up?

某公司去年的利润是500万元，今年比去年增长了20%，今年的利润是____万元。A company's profit last year was 5 million yuan. This year's profit increased by 20% compared to last year. This year's profit is ____ million yuan.

老师把 60 颗糖果按 2:3 分给两个人。分到较多糖果的那个人分到了多少颗？A teacher shares 60 candies between two people in the ratio 2:3. How many candies does the person with the larger share receive?

用一个平面去截一个正方体（平面可以任意倾斜），下面的形状中，截面不可能出现的是哪一个？A cube is sliced through by a single plane, which may be tilted at any angle. Which of the following shapes can the cross-section never be?

小明和小丽拥有的故事书本数之比是 5:3，小明比小丽多 24 本。小明有多少本故事书？Ming and Lily own storybooks in the ratio 5:3. Ming has 24 more storybooks than Lily. How many storybooks does Ming have?

甲、乙、丙三人的弹珠数满足 甲:乙 = 3:5，乙:丙 = 2:3，且三人的弹珠数都是整数。三人弹珠总数最少是多少颗？The numbers of marbles Amy, Ben and Carl have satisfy Amy : Ben = 3 : 5 and Ben : Carl = 2 : 3. Each of the three numbers is a whole number. What is the least possible total number of marbles the three children can have?

一根长10厘米的木条，一端固定在点O。木条绕点O旋转了整整 2/5 圈，它扫过区域的面积是多少平方厘米？（π取3.14）A stick 10 cm long is pinned at one end, point O. The stick rotates about O through exactly 2/5 of a full turn. What is the total area swept by the stick, in square centimeters? (Use π = 3.14)

如图所示，正方形ABCD的边长为10厘米。E是AB边的中点，F是BC边的中点，G是CD边的中点，H是DA边的中点。连接EG和FH，求阴影部分的面积是多少平方厘米？In the diagram, square ABCD has a side length of 10 cm. Point E is the midpoint of side AB, point F is the midpoint of side BC, point G is the midpoint of side CD, and point H is the midpoint of side DA. Lines EG and FH are drawn. What is the area of the shaded region in cm²?

一件商品按进价加价 60% 定价。促销时要按定价降价出售，但需保证仍能获得 20% 的利润（按进价计算）。应按定价降价________出售。（用百分数表示）An item is marked at a price 60% above its cost. During a sale, the marked price is to be reduced, but the store must still earn a 20% profit on the cost. By what percent of the marked price should the price be reduced? (Express your answer as a percent.)

一艘小船在静水中的速度是每小时15千米，水流速度是每小时3千米。小船从甲码头顺流而下行驶2小时到达乙码头，随后立即逆流返回甲码头。往返一共用了多少小时？A boat travels at 15 km/h in still water, and the current flows at 3 km/h. The boat goes downstream from Dock A for 2 hours to reach Dock B, then immediately returns upstream to Dock A. How many hours does the whole round trip take?

一盒彩纸，第一次用去总数的 1/3，第二次用去剩下的 1/2，这时还剩 12 张。这盒彩纸原来共有多少张？A box holds some sheets of colored paper. The first time, 1/3 of all the sheets are used. The second time, 1/2 of the sheets that are left are used. Then 12 sheets remain. How many sheets were in the box at first?

10位同学参加聚会：每两人之间都握一次手，共握手m次；散会时每人送给其他每人一张贺卡，共送出n张。m和n分别是多少？At a party of 10 students, every pair of students shakes hands exactly once, giving m handshakes in all. Afterwards, each student gives a card to every other student, giving n cards in all. What are the values of m and n?

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?