在備戰(zhàn)新GRE數學考試的過程中,，考生們常常會遇到一些具有挑戰(zhàn)性的題目。為了幫助大家更好地應對這些難題,，我們整理了歷年來的一些典型問題及其解答,。希望通過這些題目的分析,，能夠助力大家在考試中取得優(yōu)異成績。

新GRE數學考試常見難題22-42題

22. A group {8,9,10,11,12} and B group {25,26,27,28}. How many unique sums can be formed by selecting one number from each group? Answer: 8

23. Consider a two-digit number n, where the tens digit is U and the units digit is 5. Given the expression E = (n2 - 25)/100, express E in terms of U. Key: Knowing n = 10*U + 5 simplifies the problem.

24. Three circles with radius 1 intersect at points A, B, and C. Calculate the sum of the lengths of the arcs AB, BC, and CA (the longer segments). Answer: 3

25. For a quadrilateral with sides 4, 5, 12, and x (in clockwise order), find the range of values for x. Answer: 3

26. From positive integers less than 100, if two numbers a and b are chosen, compare the probabilities that both are even versus that a + b is even. Note: The latter is larger since both can be odd.

27. M and R are two individuals among n people arranged in a circle. If one person is selected as the winner, compare the probability that R is immediately to the right of M with the probability that R wins. Answer: (1/n-1) vs (1/n)

28. An item originally priced at $20 is discounted by 30%, followed by an additional 20% off the new price. What is the final price? Calculation: 20 * 0.7 * 0.8 = 11.2

29. When flipping a coin six times, compare the number of outcomes to the number 18. Analysis needed.

30. Given the surface area of a cube, find its perimeter. Note: Surface area = 6a2, where a is the length of a side.

31. In a triangle defined by three lines with given coordinates, determine the angles formed and verify if it is a right triangle. Conclusion: It is a right triangle.

32. Compare the area of a triangle with a side length of 3 to other geometric shapes. Analysis needed.

33. For a four-digit password consisting of three 'x's and one 'k', compare the number of possible passwords to those formed with three digits 'p', 'e', 's'. Result: Fewer combinations.

34. From a set of 4 blue balls and 2 red balls, what is the probability that the second ball drawn is red? Calculation: (4/6)*(2/5) + (2/6)*(1/5) = 1/3

35. For N > 4, compare N2 - 6N + 8 with N2 - 6N + 9. Conclusion: The former is smaller.

36. Given P1, P2, P3,... where P1 = 1 and P(n) = 24P(n-1) for n ≥ 2, compare P(66)/6 with 4. Method: Transform into a geometric series.

37. Compare (5/24)^(1/2)*5 with (5 + 5/24)^(1/2). Conclusion: They are equal.

38. Convert a shopping area of 5*10^9 square feet into a square shape and find the side length in miles, knowing 1 mile = 5280 feet. Calculation needed.

39. For three circles with a radius of 10 that are tangent to each other, compare the perimeter of the area outside the tangents with 50π. Conclusion: They are equal.

40. How many integer pairs (x, y) satisfy the condition x2 + y2 ≤ 100? Answer: 317

41. If N is a positive number, identify which prime numbers cannot exist between N and N + 6: 0, 1, 2, 3, 4, 6. Answer: 0

42. In a class of 52 students with an average score of 45, if two students are removed and the new average is 40, what is the average score of these two students? Calculation needed.

希望以上整理的題目和解答能夠為GRE考生們提供有效的復習參考,，幫助大家在考試中輕松應對各種數學難題,，爭取獲取高分！

Preparing for the GRE Math Section: Essential Tips ??

The GRE math section can be a significant hurdle for many test-takers. However, with the right strategies and preparation, you can improve your performance. Here are some effective tips to help you prepare for the GRE math section successfully.

1. Understand the Format of the Test ??

Before diving into study materials, familiarize yourself with the GRE math section format. It consists of two main parts: Quantitative Reasoning and Analytical Writing. The Quantitative Reasoning section includes questions on arithmetic, algebra, geometry, and data analysis. Knowing the types of questions you will encounter is crucial for effective preparation.

2. Review Fundamental Concepts ??

Ensure you have a solid grasp of basic mathematical concepts. Focus on key areas such as:

• Arithmetic: Operations, percentages, ratios, and proportions.
• Algebra: Solving equations, inequalities, and understanding functions.
• Geometry: Properties of shapes, area, volume, and coordinate geometry.
• Data Analysis: Interpreting graphs, statistics, and probability.

3. Practice with Real GRE Questions ??

Utilize official GRE practice questions to familiarize yourself with the test's style. Websites like ETS provide free resources that include sample questions and answers. For example, you might encounter a question like:

What is the value of x in the equation 2x + 3 = 11?

Answer: x = 4.

Practicing these types of questions will help you become comfortable with the format and timing of the actual exam.

4. Time Management is Key ?

During the GRE, time management is crucial. Each section has a strict time limit, so practice pacing yourself. A common strategy is to allocate a specific amount of time to each question and stick to it. If you find yourself spending too long on one question, move on and come back if time allows.

5. Use Process of Elimination ?

When faced with multiple-choice questions, use the process of elimination to narrow down your options. Discard answers that are clearly incorrect, which increases your chances of selecting the right answer from the remaining choices. This technique is particularly useful when you're unsure of the correct answer but can identify wrong ones.

6. Take Full-Length Practice Tests ??

Simulating the test environment by taking full-length practice exams is essential. This not only helps you gauge your readiness but also allows you to practice endurance. After completing a practice test, review your answers thoroughly, especially the ones you got wrong. Understanding your mistakes is a vital part of the learning process.

7. Stay Calm and Confident ??

Finally, maintain a positive mindset. Test anxiety can hinder your performance, so practice relaxation techniques such as deep breathing or visualization. Remind yourself that preparation is key, and trust in your abilities. Confidence can significantly impact your performance on test day.

By following these tips and dedicating time to your studies, you can enhance your GRE math skills and approach the test with confidence. Remember, consistent practice and a positive mindset are your best allies in this journey. Good luck! ??

GRE數學高分攻略

對于準備參加GRE考試的考生來說,，數學部分雖然相對較為簡單，但依然需要認真復習和有效的備考策略,。以下是一些實用的建議,，希望能幫助你在GRE數學部分取得高分,！??

1. 熟悉考試格式

了解GRE數學部分的結構是成功的第一步,?？荚嚢▋刹糠郑?span style="color:blue;">Quantitative Reasoning（定量推理）和Quantitative Comparison（定量比較）。確保你熟悉每種題型的要求和解題技巧,，這樣可以提高你的答題效率,。

2. 重點復習基礎知識

GRE數學主要涵蓋以下幾個方面：算術,、代數,、幾何和數據分析,。在復習時,，確保掌握這些領域的基本概念和公式,。比如,，你需要熟悉如何計算比例,、百分比,，以及基本的幾何公式,。??

3. 做大量練習題

通過做練習題來鞏固你的知識?？梢允褂霉俜降腉RE練習材料和其他參考書籍。推薦的題目包括：

• Sample Question: "If x + 5 = 12, what is the value of x?"
• Answer: "x = 7"

定期進行模擬測試也是非常重要的,，這樣可以幫助你適應考試的時間限制和壓力,。

4. 學會分析錯誤

每次練習后,，仔細分析錯誤的題目。理解錯誤的原因是提升能力的關鍵,。記錄下錯誤的類型,，并針對性地進行復習。例如,，如果你發(fā)現(xiàn)自己在幾何題上常常出錯,，那么就需要加強這一部分的練習和理解,。

5. 時間管理

在GRE考試中,，時間是一個重要因素。你需要學會如何合理分配每道題目的時間,。一般來說，每道題目應該控制在1.5到2分鐘之間。通過做模擬測試來提高你的時間管理能力，確保在考試中不會因為時間不足而影響發(fā)揮,。

6. 使用數學工具

GRE允許考生使用計算器,。在備考時，熟悉計算器的使用是非常重要的,。確保你能快速輸入數據并進行基本運算,。??

7. 參加學習小組

與其他考生一起學習可以提供額外的支持和動力,。參與學習小組可以讓你分享資源,、討論難題和互相激勵,。你還可以從其他考生的經驗中獲得新的見解和技巧,。

8. 保持積極心態(tài)

備考過程中,，保持積極的心態(tài)非常重要。遇到困難時,，不要氣餒,。相信自己的能力,，持續(xù)努力,，你一定能取得好成績,！??

希望以上的建議能夠幫助你在GRE數學部分取得高分,！祝你好運,！