Odd number (also called odd number): a number that is not divisible by 2;

Prime number (also called prime number): a number with only 1 and its own two factors;

Composite number: Besides 1 and itself, there are other factors.

1. Composite number of prime numbers

For the examination of the composite number of prime numbers, the first is the examination of its definition. Under the premise of understanding the topic, it is usually accompanied by various operations, especially the candidates need to remember the prime numbers within 20. Therefore, when answering this kind of question, we must understand the meaning of the question and clarify the concept.

For example, some topics will involve the understanding of absolute value, so the review of elementary mathematics must be comprehensive and thorough. For example, the exams of 20 15, 1, 20 1,1involve the examination of absolute values; The examination questions in 20 10 and1June are related to real life to examine prime numbers.

Let 20 15.05438+0 be a prime number less than, and * * * that meets the conditions has ().

Groups 2, 3, 4, 5 and 6

The prime number less than analytically is: Therefore, there are four groups that meet the conditions. It should also be noted that the elements are out of order.

Answer c

Let 20 1 1.0 1 be three different prime numbers (prime numbers) less than, and then ()

By analyzing different prime numbers less than 12, we can know that the selection range is 2, 3, 5, 7, 1 1. By trying, it can be quickly concluded that 3, 5 and 7 meet the requirements in the question. Or this question can be set, by removing the absolute value sign, and finally get. So among the prime numbers within 12, we can find two groups of prime numbers with a difference of 4, namely 7 and 3, 1 1 and 7. According to the requirements of the topic, we can know that the qualified prime numbers are 3, 5 and 7, and then we can know 15.

Answer d

20 10.0 1 One of the three children is a preschool child (under 6 years old). Their ages are all prime numbers (prime numbers), with a difference of 6 years in turn. The sum of their ages is ().

According to the meaning of the question, one of the children may be 2, 3 or 5 years old, and the other two children may be 8 years old and 14 years old (both are not prime numbers, omitted); 9 years old, 15 years old (both are not prime numbers, so they are discarded); 1 1 years old and 17 years old (meet the requirements), so the total age of the three children is 5+11+17 = 33.

Answer c

In the examination of composite numbers of prime numbers, the second is the examination of factorization of prime factors. First of all, we must figure out what a prime factor is. Secondly, it should be clear that the factorization of prime factors can often be carried out by short division, and it should be noted that the final factorization factor must be a prime number. Often this part of the topic will not be directly examined, and candidates need to be clear about the need to decompose prime factors. For example, this part of knowledge was examined in the examination questions in June of 20 14.

20 14.0 1 If the product of several prime numbers (prime numbers) is, their sum is ().

Analysis decomposes prime factors, so the sum of these prime factors is.

answer

2. Odd and even numbers

The examination of odd and even numbers is often the examination of their definitions, which is usually judged by the sufficiency of conditions. For this kind of problem, we can often judge quickly by giving counterexamples. For some problems that can't be solved by counterexamples, we can often make judgments through simple reasoning. Here, candidates need to accurately judge the parity of integers, especially the parity performance of odd and even numbers.

Here is a detailed introduction to the odd-even judgment topics involved in the real questions in the past five years.

20 14. 10 is a multiple of 4.

(1), all even (2), all odd.

The analysis of this question belongs to the topic of conditional adequacy judgment, and two points need to be paid attention to: first, the directionality of judgment, that is, the problem is deduced from conditions; The second is the understanding of sufficiency, that is, all the values that meet the conditions meet the problem. For condition (1) and condition (2), it is found that no counterexample can be found, and reasoning judgment is made respectively. First, the stem is processed to determine whether it is a multiple of 4, that is, whether it is a multiple of 4. The requirements in the condition (1) are all even numbers, and they are all even numbers, that is, they are all multiples of 2, so it is enough for the condition (1) to be multiplied by multiples of 4. The requirements in condition (2) are all odd numbers, and the knowable ones are all even numbers, that is, all multiples of 2, so the multiplication is a multiple of 4, and condition (2) is enough.

answer

20 13. 10 is divisible by 2.

(1) is odd, and (2) is odd.

Analyzing this problem belongs to the topic of conditional adequacy judgment. For the condition (1), we can give a counterexample. For example, if it is not divisible by 2, then the condition (1) is not sufficient; For condition (2), the same counterexample can be given, for example, it is not divisible by 2, so condition (2) is not sufficient; At this time, judging by combining condition (1) and condition (2), it is found that there is no counterexample at this time, and reasoning verification is needed. Both are odd numbers, which is known and odd, so they must be even numbers, which shows that the combination of the two conditions is sufficient.

Answer c

20 12.05438+0, all positive integers, all even numbers.

(1) is even; (2) is an even number.

Analyzing this problem belongs to the topic of conditional adequacy judgment. Through reasoning, we can quickly judge that the condition (1) tells us that it must be even, so we can know that it is even, the stem is established, and the condition (1) is sufficient; Judging from the condition (2), it must be even, so we can know that it is even, the stem is established, and the condition (2) is sufficient.

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