CMB's written test - quantitative relationship

One . Problem solving skills

1. Substitution exclusion

Substitution and exclusion is the first method of quantitative relationship . Substitution exclusion, as the name suggests, is to substitute the answer options into the original question , Options inconsistent with the meaning of the topic can be excluded , Finally get the right answer .

Give priority to the question type of substitution and exclusion ：

（1） Multi digit number problem 、 The problem of remainder 、 Age issues 、 Indefinite equation, etc .

（2） Problems that cannot be dealt with directly , You can consider substituting in and excluding .

Example ：

[1] The age of the four people is an adjacent natural sequence, and the oldest is no more than 30 year , The product of four people's ages can be 2700 Divisible and not divisible by 81 to be divisible by . Then how old is the oldest of the four ？（ ）

A.30 B.29 C.28 D.27

[2] It is known that Mr. Zhang's childhood took up of his age 1/14, Again 1/7 He came of age , It's over again. 1/6 He's married , After marriage 3 His son was born in , son 7 At the age of , The sum of their ages is the square of a prime , Then Mr. Zhang's age at marriage was ：( )

A.38 year B.32 year C.28 year D.42 year

2. Digital characteristic method

Application of digital characteristics , In fact, it is a special kind of substitution and exclusion . Digital features include ： Parity 、 Divisible property 、 Multiple characteristic .

Basic principles of parity ：

【 Basics 】

Odd number ± Odd number = even numbers ; even numbers ± even numbers = even numbers ; Odd number ± even numbers = Odd number ; Odd number × Odd number = Odd number ; Odd number × even numbers = even numbers ; even numbers × even numbers = even numbers

【 inference 】

One 、 And difference ： If the sum of any two numbers is odd （ even numbers ）, So bad is also an odd number （ even numbers ）; If the difference between any two numbers is odd （ even numbers ）, Then sum is also odd （ even numbers ）.

Two 、 Multiply any natural number by an even number , The result must be even .

Parity application characteristics ：

① Know and seek difference 、 Know the difference and sum

② Diploid , average

③ Form like aX+bY=c Class of indefinite equations

Example ：

[1] The single digit and ten digit of mother's current age are adjusted and then reduced 10 Age is the age of a son , In another 3 The age of the mother is the age of the son 2 times , Then the mother's current age is （）.

A.53 B.52 C.43 D.42

[2] A man went to the bookstore to buy a book and a magazine , When paying , He reversed the number of one digit and ten digit in the book pricing , Ready to pay 21 Yuan pickup . The salesman said :“ You should pay 39 Yuan is right .” How much are books more expensive than magazines ？（ ）

A. 20 B. 21 C. 23 D. 24

The basic law of divisional determination

①2,4,8 The rule of division and remainder

A number can be 2( or 5) to be divisible by , If and only if the last digit can be 2( perhaps 5) to be divisible by ;

A number can be 4( perhaps 25) to be divisible by , If and only if the last two digits can be 4( perhaps 25) to be divisible by ;

A number can be 8( perhaps 125) to be divisible by , If and only if the last three digits can be 8( perhaps 125) to be divisible by ;

②3,9 The basic law of divisional determination

A number can be 3 to be divisible by , If and only if the sum of its digits can be 3 to be divisible by ;

A number can be 9 to be divisible by , If and only if the sum of its digits can be 9 to be divisible by ;

③ Use scenarios

Problems appear 2、4、8、3、9 Multiple of equal .

The problem appears multiple 、 fraction 、 percentage 、 The proportion 、 Words such as grouping .

Appear in the title “ The sum of the digits ”

Example ：

[1] A four digit number “□□□□” The difference can be 15、12 and 10 Divide up , And the sum of the three quotients obtained when divided by these three numbers is 1365, Ask four digits “□□□□” What is the sum of the four numbers in ？

A.17 B.16 C.15 D.14

[2] A car drove on its first day 5 Hours , The next day I drove 600 km , Drive less on the third day than on the first 200 km , I drove for three days 18 Hours . It is known that the average speed of the first day is the same as that of the whole three days , How many kilometers did you drive in three days ？

A.800 B.900 C.1000 D.1100

Multiple characteristic

example ： The ratio of male to female in the class is 7:4, So the man / Woman =7/4

The number of boys must be 7 Multiple ; The number of girls must be 4 Multiple ; The total number must be 11 Multiple ; The difference between men and women must be 3 Multiple ; The number of boys is of the total 7/11

if a：b = m：n, or 𝑎/𝑏=𝑚/𝑛 perhaps 𝑎=𝑚/𝑛·𝑏 （m、n Coprime ,m：n Can't continue to make an appointment ）. be a yes m Multiple ;b yes n Multiple ;a + b yes m + n Multiple ;a –b yes m –n Multiple

Example ：

[1] At the year-end party of a company , All employees perform in groups . If the 7 male 5 Female collocation Group , Only 8 Male employees ; If the 9 male 5 Female collocation Group , only 40 Female employees . The total number of employees of the company is ？（ ）

A.446 B.488 C.508 D.576

[2] A triathlon competition is held in a certain place , The whole journey is 51.5 km , swimming 、 Bicycle 、 The distance ratio of long-distance running is 3:80:20. The time ratio of Xiao Chen in these three projects is 3:8:4, The average speed of his long-distance running in the race is 15 km / Hours , And it takes time to change items twice 4 minute , So how long does it take him to finish the race ？

A.2 Hours 14 branch B.2 Hours 24 branch C.2 Hours 34 branch D.2 Hours 44 branch

3. Equation method

Equation method is one of the most important methods of quantitative relationship .

Range of application ： And the difference ratio problem 、 Chicken and rabbit in the same cage 、 Profit and loss issues 、 Engineering problems 、 Economic profit problem 、 Travel problems, etc .

The principle of setting unknowns ： In the same way , Give priority to the desired quantity and set the intermediate variable 、 Additional copies ( There are scores 、 percentage 、 Proportional multiple feature ) Give priority to the small rather than the large .

Example ：

[1] A restaurant has seats 12 People can sit together 10 There are two kinds of dining tables for people 28 Zhang , It can hold at most 332 Eat at the same time , Ask how many tickets there are in the restaurant 10 Human table ？

A.2 B.4 C.6 D.8

[2] Xiao Ming is responsible for transporting eggs from a farm to the snack bar . In accordance with the relevant provisions , Every delivery 1 Eggs intact , Available freight 0.1 element ; If an egg breaks , Not only can I not get the freight of the egg , Every broken egg must be compensated 0.4 element . Xiao Ming 10 Deliver eggs in January 25000 gold , Get freight 2480 element . that , In transit , The egg is broken ：

A.20 gold B.30 gold C.40 gold D.50 gold

Two . Classic questions

1. Probability problem

1. Basic probability the probability of a situation occurring ＝ The number of conditions met ÷ The total number of cases .

P＝ The number of conditions met / The total number of cases

2. Step by step multiplication

Step by step probability = The product of the probabilities of each step that satisfies the condition

3. Classified additive

Overall probability ＝ The sum of the probabilities of various conditions that meet the conditions

4. Reverse calculate the probability of an event = 1－ Probability that the event will not occur

Example ：

[1] A company will hold a fellowship for seven consecutive days from Monday to Sunday , An employee randomly selects one of them to attend the fraternity for two consecutive days , Then his probability of attending the fraternity for two consecutive days from Friday to Sunday is （）.

A.1/2 B.1/3 C.1/4 D.1/6

[2] Xiao Wang is numbered 1、2、3、4、5 Of 5 Randomly selected from this book 3 Ben , Then the probability that the numbers of these three books are exactly three adjacent integers is ：

A.1/2 B.2/5 C.3/10 D.3/5

2. Economic profit problem

1. Profit discount ：

The total cost = Individual costs × Import volume ; Total selling price ＝ The unit price × Sales volume ;

profits ＝ The price is - cost ; Total profit ＝ Total selling price - The total cost

The profit margin = profits / cost = （ The price is − cost ）/ cost = The price is / cost −1

2. Segmented billing

The problem of subsection charging mainly involves water and electricity 、 postage 、 Commission and other issues are usually billed in segments . The key to solving the problem is to find the segmentation node , Discuss and calculate between partitions .

Example ：

[1] Purchased by a store 400 Same summer clothes .7 Monthly purchase price 1.6 Times to sell , Co sold 200 Pieces of ;8 Monthly purchase price 1.3 Times to sell , Co sold 100 Pieces of ;9 Monthly purchase price 0.7 Times will be the remaining 100 Pieces are all sold , Total profit 15000 element . Ask how much the purchase price of this batch of summer clothes is ？（）

A.125 B.144 C.100 D.120

[2] For a mobile phone, press 2000 Unit price sales , The profit is the selling price 25%. If repricing , Reduce the profit to the new selling price 20%, The new price is （）？A.1900 element B.1875 element C.1840 element D.1835 element

3. Sequence problem

The average

The formula ：𝑎̅=（𝑎1+𝑎2+⋯⋯+𝑎𝑛）/ 𝑛

Example ：

[1] With the opening of Taiwan's free travel , The improvement of rural farmers' quality of life , Farmers in a rural area spontaneously organized several farmers in the same village to travel to Taiwan , Its travel expenses include , Personal handling fees for going to Taiwan , The average fare for traveling in Taiwan is 503 element , The average ticket per person 1998 element , Other expenses average per person 1199 element . It is known that the total cost of this trip is 92000 element , The total average cost is 4600 element . How much is the total number of people going to Taiwan and the handling fee for individuals going to Taiwan ?

A.20 people ,700 element B.21 people ,650 element C.20 people ,900 element D.22 people ,850 element

[2] Teacher Zhong and four teachers participated in the teacher skills competition held by the school . The grades of these four teachers are 78 branch 、81 branch 、82 branch 、79 branch , And teacher Zhong's score is more than the average of five 6 branch . that , Of the five , The second place scores more than the fourth （） branch .

A.2 B.3 C.4 D.5

Reference material ： Liu Wenchao Vin

Thank you for reading ：）

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