Line testing skills: Use "comparative" thinking to solve problems skillfully

Let's start with an example question:

A company held a year-end dinner, each table arranged 7 ordinary employees and 3 managers, to the last 2 tables, because the management has been arranged, all the ordinary employees were arranged, the result is still a difference of 2 people just sat full, known that the number of ordinary employees of the company is 3 times that of the management personnel, then the company has how many managers:

A、24 B、27 C、33 D、36

Zhonggong analysis: For ease of understanding, suppose there are (n+2) tables. If there are 3 managers and 7 ordinary employees at each table, there are still 18 employees left; It is also known that the ordinary employees are 3 times that of the management personnel, if the front n tables are arranged with 3 managers and 9 ordinary employees, it is equivalent to 2 more employees sitting at each table, then a total of 18 more employees are seated. i.e. 2n=18, n=9. The number of managers is 3n = 27. So the correct answer is B.

The above problem cleverly uses comparative thinking, comparing the similarities and differences between the two schemes, so as to find an equal relationship and achieve the purpose of rapid problem solving. Next, the chinese public education experts took everyone to learn more about this "comparative" thinking.

First, the method introduction

There are two or more different distribution schemes for the same thing. We compare the similarities and differences between the schemes, establish the connections between the schemes, and thus construct the relational formula. This method, we also become the "comparative construct method".

Second, the steps to solve the problem

1. List various schemes according to the meaning of the topic;

2. Differences and linkages between ICP programmes;

3. Construct relational formulas;

4. Solve according to the requirements of the question and the question method.

3. Intensive lectures on example topics

Example 1. Students A and B check in their luggage. The consignment fee is 6 yuan / kg for less than 10 kg, and the per kg charge for the part exceeding 10 kg is slightly lower. It is known that the check-in fees for A and B are 109.5 yuan and 78 yuan respectively, and it is known that A's luggage is 50% heavier than B. So how much lower is the per kilogram charge for the part exceeding 10 kilograms than the part within 10 kilograms?

A、1.5 B、2 C、2.5 D、3

Zhonggong analysis: Suppose the weight of B baggage is (10 +a) kg, the first 10 kg is charged 6 yuan / kg, the back a kg price is assumed to be x yuan / kg, and the checked baggage fee of B is 60 + ax = 78 yuan. The weight of A baggage is (15 + 1.5a), if the front 15 kg charges 6 yuan / kg, the back 1.5a kg charges x yuan / kg, then the A baggage check-in fee is 90 + 1.5ax = 78 * 1.5 = 117 yuan, which is 7.5 yuan more than the actual 109.5 yuan. The extra 7.5 yuan is exactly the 5 kg of the previous 15 kg, so there are 6-x = 7.5 / 5 = 1.5. The request is 1.5 yuan, so the correct answer is A.

Example 2: Xiao Wu went to the store to buy cloth. There are two kinds of cloth that are equally long, Xiao Wu bought the first kind of cloth for 25 meters and the second kind of cloth for 12 meters. After Xiao Wu finished buying, the remaining length of the first kind of cloth was half of the remaining length of the second kind of cloth. So how many meters did these two kinds of cloth originally have:

A、26 B、38 C、72 D、76

Zhonggong analysis: According to the meaning of the topic, two schemes can be constructed: first, the first kind of cloth buys 25 meters, the second kind of cloth buys 12 meters, then the ratio of the remaining length of the two kinds of cloth is 1:2; Second, if the first kind of cloth buys 12 meters and the second kind of cloth buys 12 meters, the ratio of the remaining length of the two kinds of cloth is 2:2 (that is, 1:1, equal relationship). The first kind of cloth in scheme two was bought 13 meters less than in scheme I, while the remaining length of the first kind of cloth was 2 parts and 1 part, respectively, a difference of one part, and the actual difference was 13 meters. There are 3 copies of the plan left, that is, 39 meters. The two kinds of cloth originally had a total of 39 + 25 + 12 = 76 meters. So the correct answer is D.

Example 3: A project is completed by two people, A and B. A and B take 8 days to complete together. Now A and B worked together, and on the way A left for 3 days, and it took 10 days to complete the project. How many days does it take to do it alone?

A、15 B、12 C、10 D、18

Zhonggong Analysis: The title gives two schemes for this project. First, work A for 8 days, and work B for 8 days to complete this project. Second, A worked for 7 days, and B worked for 10 days to complete this project. Comparing the similarities and differences between the schemes, we conclude that the workload of one day is equal to the workload of two days of B. If the efficiency of A is 2, the efficiency of B is 1, and the total amount of work of this project is 8 * (2 + 1) = 24. The time for A to complete this project alone is 24/2 = 12 days. So the correct answer is B.