=1290 After sorting, 5×X+45×27=1290 determines that [Example 2]: A set of natural numbers that satisfies the equation 1983=1982x-1981y is: A.x=12785.

(1) Odd and even numbers:

A number that is not divisible by 2 is called an odd number; a number that is divisible by 2 is called an even number.

Two-number operations: Sum and difference - Same, odd and even; Product: Even if even, all odd and odd

Multi-digit operations: Sum and difference - Look at the number of odd numbers Product: Even if even, all odd and odd

Special tips : A+B and A-B have the same parity

Number parity characteristics

Investigation of odd and even numbers:

[Bring in verification, lock the answer, quick kill]

[Example 1]: The labor department of a certain place rents two A and B Classrooms provide training for rural practical talents. Both classrooms have 5 rows of seats. Classroom A can seat 10 people in each row, and Classroom B can seat 9 people in each row. A total of 27 training sessions were held in the two classrooms that month, and each training session was packed with seats. A total of 1,290 people were trained that month. Question: How many times did classroom A hold this training in total that month?

A. 8 b. 10C. 12D. 15

Analysis: According to the meaning of the question, classroom A can seat 50 people for each training, while classroom B can seat 45 people for each training. 50X+45×(27-X)=1290 After sorting, 5×X+45×27=1290. It is determined that X is an odd number. Combined with the option verification, only option D matches the answer.

[Bring in verification, narrow the scope, and verify the answer]

[Example 2]: A set of natural numbers that satisfy the equation 1983=1982x-1981y is:

A.x=12785, y=12768 B.x=12784, y=12770 C.x= 11888, y=11893 D.x=1947, y=1945

Analysis: Since 1983 is an odd number and 1982x is an even number, then 1981y must be an odd number, that is, y must be an odd number. Exclude A and B, and then substitute C. The mantissa method verifies that C conforms to the title

[Narrow the scope of enumeration and solve indefinite equations]

[Example 3]: A certain country implements the following tax rate scheme for residents’ income; the portion that does not exceed US$3,000 per person per month is levied at a 1% tax rate, and the amount exceeding US$3,000 does not exceed US$6,000. The portion exceeding USD 6,000 is taxed at the rate of Y% (X and Y are integers). Assume that a resident of this country has a monthly income of $6,500 and pays $120 in income tax. What is Y?

A.6 B.3 C.5 D.4

analysis: 3000×1%+3000×x%+500×y%=120, then 6x+y=18, x and y are both integers, 6x must be an even number, It can be obtained that y is an even number, excluding B and C; since x and y are integers, y=6 satisfies the condition and selects A.

[Examination questions]

[Example 4]: Some students in a certain class participated in a mathematics competition. Each test paper had 50 questions. The scoring criteria are: 3 points for each correct answer, 1 point for each unanswered question, and 1 point deducted for each incorrect answer. Let me ask: Is the sum of the scores of these students an odd number or an even number?

A. Odd number B. Even number C. All possible D. Unable to judge

Analysis: It is impossible to get the total score of these students in this question, so we should start with the analysis of each person's score. Because each question has an odd number regardless of whether it is answered correctly, not answered, or incorrectly. There are 50 questions in total. If the 50 odd numbers are added and subtracted, the result is an even number, so everyone's score is an even number. Because the sum of any even numbers is an even number, the total score of this group of students must be an even number

[Example 5]: (2016 Guangzhou) Municipal Federation of Trade Unions held a trade union knowledge competition. Each contestant answered 25 questions, and each correct answer was awarded 3 points. , 1 point is awarded for no answer, 1 point is deducted for wrong answer. A certain unit sent 7 players to participate. Four scorers counted the total scores of the players in the unit. The results were 539 points, 490 points, 469 points, and 434 points respectively. After verification, one scorer's statistical result is correct, then the average score of the 7 players in the unit is ( ) points.

A.77 B.70 C.67 D.62

Analysis: There are 25 questions in total. The score of each question is an odd number. After summing, it is still an odd number. Everyone's score is an odd number. When the seven odd numbers are added, the total The score is still an odd number, odd number/7=average score, and the average score must be an odd number. Since the full score is 25×3=75, the only qualified answer is option C.

[Basic sum, difference, product and quotient operations of numbers]

[Example 6]: The difference between two numbers, big and small, is 2345, where the big number is 8 times the decimal. Find the sum of the two numbers.

A. 3015 B.3126 C. 3178 D.3224

Analysis: The difference between the two numbers is an odd number, and the sum of the two numbers must be an odd number, so the answer is A. If there are two odd numbers, consider the sum of the two numbers to be a multiple of 9

[Example 7]: (2009-Joint Entrance Examination) A person went to a bookstore and bought a book and a magazine. When paying, he priced the book The numbers in the ones place and the tens place are reversed, so I'm going to pay 21 yuan to pick up the goods. The salesperson said: "You should pay 39 yuan." How much more is the book more expensive than the magazine?

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

Analysis: The sum of the book and the magazine is 39. According to the sum of the two numbers and the difference between the two numbers are both odd and even, the answer must be an odd number. After substituting C, the book value is 31, the magazine value is 8, and the book price is 13 after being reversed. 13+8=21 yuan, which is completely consistent with the meaning of the question, so the answer is C.