2022年数量关系解题技巧—数学运算 .pdf

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1、数量关系解题技巧数学运算（Mathematical skills for solving quantitative relations）I carefully collated documents, documents from the network I only collect and sort out If there is any mistake Please check it yourself! Mathematical skills for solving quantitative relations The second type of question in quantity

2、relation is mathematical operation These questions are usually short Its knowledge content and principles are generally relatively simple But because of the time limit So its quick and accurate We should pay attention to the following 4 aspects: first, master some commonly used mathematical skills,

3、methods and laws Use simple algorithms as many as possible Two is to accurately understand and analyze the text 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 32 页Correctly grasp the meaning of the questions Three is familiar with a certain type of questions and problem-solving methods Four is

4、 to strengthen training Increase sensitivity to numbers And memorize some basic numbers Here are some of the more typical questions Its very helpful to improve the performance First, the question type is solved by using the method of rounding and rounding Example: the value of 5.2+13.6+3.8+6.4 is A.

5、29 B.28 C.30 D.29.2 The answer is A Rounding method is the most commonly used method in simple calculation The method is based on the commutative law and the associative law 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 32 页Make numbers into integers Calculate again Its much easier Two. Using

6、 the mantissa estimation method to solve the question type Example: the value of 425+683+544+828 is A.2488 B.2486 C.2484 D.2480 The answer is D If the numbers are larger There seems to be no law to follow You can first examine whether the mantissa of a number of answers is unique If it is Then you c

7、an use the number of digits to calculate the mantissa And then find the only corresponding item The above questions Adding the number of each bit =5348=20 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 32 页The mantissa is 0 So you can quickly pick the right answer for D Three, using the benchm

8、ark number method to solve the problem type Example: 1997+1998+1999+2000+2001 A.9993 B.9994 C.9995 D.9996 The answer is C When more than two numbers are added together And when their values are close You can find an intermediate number as a benchmark Then add each addend and benchmark difference So

9、as to get their sums In this question Select 2000 as the base number Other numbers are 3 less than 2000 2 less 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 32 页1 less And more than 1 Therefore, the sum of five numbers is 9995 This method can also be used to find the arithmetic mean of severa

10、l similar numbers 1. proportional distribution problem Example: the total number of students in grade one or two and grade three in a school is 450 The proportion of students in three grades is 2:3:4 How many students are there in the most number of classes? A.100 B.150 C.200 D.250 The answer is C A

11、nswer this question You can count the total as 234=9 The largest number of them is definitely the three grade of 4/9 So the answer is 200 people 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 32 页2. mile problem Example: someone walking from one place to another After the whole journey of 2/5

12、Its 2.5 kilometers from the midpoint How many kilometers is the distance between a and B? A.15 B.25 C.35 D.45 The answer is B The midpoint of the whole journey is 2.5/5 of the whole course The distance from 2/5 is 0.5/5 This road is 2.5 kilometers So you can quickly calculate the entire length of 25

13、 kilometers 3. engineering problems Example: a project A team do it alone 15 days to finish; B team do it alone 10 days to complete 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 6 页，共 32 页Two teams cooperation How many days is it going to be done? A.5 days, B.6 days, C.7.5 days, D.8 days The answer

14、 is B This question is an engineering problem The general quantitative relation and structure of engineering problems are: Total work _ = working time Work efficiency We can think of the whole project as 1 Work to complete the work efficiency for 1/n n that day, the two groups together to complete t

15、he work efficiency for 1/n11/n2, according to this formula can quickly get the answer for 6 days in addition There are many variations in engineering problems 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 7 页，共 32 页Such as pond irrigation problems and so on You can use this kind of thinking to solv

16、e problems 4. planting trees Example: if you plant a tree at a distance of one meter How many trees are planted on the 345 meter road? A.343 B.344 C.345 D.346 The answer is D This topic should pay attention to more analysis of the actual situation As the starting point and end point to consider two

17、to plant trees So the answer is 346 1, 8754896 x 48933= (D) A.428303315966 B.428403225876 C.428430329557 D.428403325968 Solving problem: multiplying two product factors into one digit number The number of digits should be 8 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 8 页，共 32 页Excluding A, B, C 2

18、, 3543278 x 2221515= (D) A.7871445226160 B.7861445226180 C.7571445226150 D.7871445226170 Solving problem: multiplying the ten numbers of two product factors The product should be 70 Excluding A, B, C 3, 36542 x 42312= (D) A.1309623104 B.1409623104 C.1809623104 D. No solution is given: multiplying th

19、e first two digits of two product factors (36 x 42) The product should be 1512 There is no 15 in the first two digits of each option therefore Theres no right answer 4, 50 x 62 x 70 x 82= (D) 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 9 页，共 32 页A.12722410 B.12822340 C.17892520 D.17794000 Solutio

20、n Thinking: from 50 x 70 to know that the mantissa has two zeros Excluding A, B, C D 5, 125 x 618 x 32 x 25= (D) A.61708000 B.61680000 C.63670000 D.61800000 Solutions: 125 x 618 x 32 x 25= (125 x 8) x (4 x 25) x 618=61800000 6, 86 x 84= (D) A.7134 B.7214 C.7304 D.7224 Solution Thinking: 86 x 84= (8+

21、1) 800+ (4 x 6) =7224 7, 99 x 101= (D) A.9099 B.9089 C.9189 D.9999 Solution Thinking: 99 x 101= (100-1) (100+1) =1002-1=9999 8, two trucks total load of 500 tons The first one is 50 tons more than second vehicles 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 10 页，共 32 页The first and the second are

22、D tons respectively A. (265 235) B. (245) 295) C. (285) 215) D. (275) 225) Solution: dont use (500+50), 2 for the first car loading algorithm According to the problem and quickly find out as long as consistent with the difference of the number of persons 9, the store sold two goods for 3000 yuan eac

23、h The profit and loss were both 20% Then the shop should be (D) A. earn 500 yuan, B. deficit 300 yuan, C. flat, D. deficit 250 yuan Solution Thinking: quickly calculate the cost of making 20% of goods should be 2500 yuan And 20% of the cost of goods is certainly not more than 2500 精选学习资料 - - - - - -

24、 - - - 名师归纳总结 - - - - - - -第 11 页，共 32 页yuan A and C were excluded immediately And then converted from the loss of two, the cost is 3750 yuan thus 750 yuan -500 yuan is 250 yuan 10, today is Tuesday 55 x 50 days later (A) A. Monday, Tuesday, C., Wednesday, D., Thursday, B. Problem solving: from 55 t

25、o 7 multiples, minus 1,50 is 7 multiples plus 1 Quick launch for less than 1 days If you use 55 x 50 / 7=396 6 The answer is also available But it takes more time 11, 20 bakers bake 200 loaves of bread in 2 hours At this rate 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 12 页，共 32 页2 bakers can bak

26、e 100 loaves of bread in D hours A.20 B.15 C.12 D.10 Problem solving: first, ask 20 masters to bake 100 loaves of bread in 1 hours 10 times from 20 masters, 10 times of 2 masters, and 10 times of 1 hours, that is, two hours 12, the examination paper on the judgment to do 1 points Wrong deduction 1 p

27、oints Zhang got 6 points on the judgment question He should have done B in 10 subjects A.1 B.2 C.3 D.4 Problem solving thinking: 10 questions answered 10 points Not only did not score wrong points, but deducted 1 points Two questions should be done wrong 13, 48 and 108 of the greatest common divisor

28、 is (D) A.6 B.8 C.24 D.12 Solution: dreams 48=2 x 2 x 3 x 4 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 13 页，共 32 页108=2 x 2 x 3 x 3 x 3 * (48, 108) =2 x 2 x 3=12 14, if 5,7=74 4,6=52 3,5=34 Then 0,4= (D) A.53 B.51 C.26 D.16 The solution of the problem is that the number of the inner solitary num

29、bers decreases successively And vice versa A, B and C can be excluded immediately in addition Can be the answer (and) that the brackets two numbers are square 15, the provisions of a company Where the purchase of more than 1000 yuan of goods 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 14 页，共 32 页

30、You can enjoy 30 percent off privileges There are 4200 yuan to purchase Can buy the original price of (B) yuan of goods A.7000 B.6000 C.5500 D.5400 Problem solving idea: the decomposition of 4200 yuan into 6 700 yuan can be launched 6000 yuan 16. Divide the 10 apples into three piles Each heap conta

31、ins at least 1 Proper (A) seed classification A.8 B.9 C.10 D.11 Solving problems: list by enumeration method Quickly remove duplicates 17, the annual interest rate of bank deposits is 2.5% Interest tax payable 20% Original 10 thousand yuan 1 years period The actual interest is no longer 250 yuan 精选学

32、习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 15 页，共 32 页In order to maintain this interest income The same period deposits should be increased to (C) yuan A.15000 B.20000 C.12500 D.30000 18, the annual interest rate of bank deposits is 2.5% Interest tax payable 20% Original 10 thousand yuan 1 years p

33、eriod The actual interest is no longer 250 yuan In order to maintain this interest income The same period deposits should be increased to (C) yuan A.15000 B.20000 C.12500 D.30000 Solution Thinking: compensation of 20% of interest tax should increase 25% deposit So it should be added to: 10000+2500=1

34、2500 (element) 19, there are 80 documents A, B, C 3 people participated in the treatment 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 16 页，共 32 页B than 8 copies But its just a 3/5 of the number of copies The ratio of the number of documents they dealt with was (D) A.2:4:6 B.2:4:5 C.2:5:8 D.2:3:5 S

35、olution: since the files are processed individually, they are integers Then, if the sum of the three ratios cannot be divided into 80, the fraction will be eliminated It should be ruled out 20, someone with a 15% off discount to buy a bicycle, save 60 yuan He paid (D) yuan A.350 B.380 C.400 D.340 Th

36、inking: to obtain the original price by 60, 15/100 Deduct 60 yuan again It can also be worked out quickly from C-D=60 21, the number of boys in a school is 15 less than the number 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 17 页，共 32 页of students in the whole school 5/9 The number of girls is 15

37、more than the total number of 4/9 in the school The total number of students in this school should be (D) A.600 B.610 C.620 D.630 Problem solving idea: what can be divisible by 9 is that Because people can only be integers A and B 2 people meet from 12 noon to 1 oclock meeting And agreed that the fi

38、rst person arrived, you can wait for two people after 15 minutes, no one to come, you can leave. Suppose they all come to the meeting place at their own time What is the probability that the 2 of them can see the above? A.1/16; B.1/4; C.3/8; D. above, three are not correct Answer: B 15/60=1/4 Sales

39、promotion in a store Where you buy more than 200 yuan worth of goods, you can discount 20% So with 300 yuan of money in the shop can buy value - Lianshan 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 18 页，共 32 页yuan goods A.350 yuan b.384 yuan C.400 yuan d.420 yuan According to the November 22, 200

40、0 peoples Daily reported The year January to October, Jilin Province industrial profits of 7 billion 640 million yuan Nearly 6 times higher than the same period last year The state-owned enterprise losses 1 billion 500 million yuan A reduction of 42.2% and a profit of 6 billion 740 million yuan An i

41、ncrease of 8 times These two indicators are ranked in the forefront of the country So we know According to the statistics from January to October of the year A. state-owned enterprises in Jilin province have achieved overall profitability B. Jilin state owned enterprises have not yet achieved overal

42、l profitability 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 19 页，共 32 页C. Jilins industrial growth rate is among the best in the country D. Jilin has made remarkable progress in establishing a modern enterprise system At some point the clock is between 10 and 11 At this moment 6 minutes after the

43、 minute and this time 3 minutes before the hour is in the opposite direction and in a straight line Then this moment is A.10 points 15 points, B.10 points 19 points C.10 points 20 points, d.10 points 25 points A, B, two people from the 400 meters of the ring track of a point a back at the same time

44、8 minutes later, the two met third times It is known that every second is more than 0.1 meters per second that The shortest distance between the two meeting place and the a point along the runway is third A.166 m b.176 m c.224 m d.234 M. 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 20 页，共 32 页Ther

45、e are two trains with a and B trains A car is 72 meters long Driving 860 meters per minute; B 84 meters long It runs 700 meters per minute How many minutes does it take for the two trains to meet and leave? The train of thought should be like this: (72+84) / (860+700) =? The answer is 1/10 minutes,

46、six seconds A worker walking speed of 5 kilometers per hour, if he goes to work on foot from 1/10, then take the car speed of 25 kilometers per hour, then walk 1 miles just to the factory, then he can take two hours to walk to work than to the factory. Ask him how many kilometers away to A? A 15 B 1

47、6 C 14 D12 The distance between cars is x, and the total distance is y X/5-x/25=2 X=12.5 12.5+1=9/10y, y=15 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 21 页，共 32 页According to the November 22, 2000 peoples Daily reported In the 1-10 months of the year, the profits of Jilins industry reached 76 40

48、0 million yuan Nearly 6 times higher than the same period last year The state-owned enterprise losses 1 billion 500 million yuan The minus pair reached 42 2%; realize profit 67 400 million yuan Increased by 8 times These two indicators are ranked in the forefront of the country accordingly We know A

49、ccording to the statistics of 1-10 months ( A The state-owned enterprises in Jilin province have realized the overall profitability 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 22 页，共 32 页B Jilin state owned enterprises have not yet achieved overall profitability C Jilins industrial growth rate ra

50、nks first in the whole country D Remarkable progress has been made in the construction of modern enterprise system in Jilin Province The answer is A, I believe that the title was about 1 billion 500 million losses X lost in 1999 2000 young loss point For X-15 So why is it profitable? Do not understa