Mathematics Exclusion Questions Line test, Mathematics Exclusion Questions

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Question 1: This question will be faster with substitution elimination. It is impossible for both of them to answer more questions incorrectly than B's 5 questions incorrectly, and 5 (1 6) = 30, therefore, the total number of questions must not exceed 30, excluding A and B; Continue to look, "the number of questions answered correctly by both people is 5 more than half of the total number of questions", if it is d, half of 12 is 6, 6 + 5 = 11, only 12-11 = 1 wrong, and B is wrong 5 questions, which does not meet the meaning of the question, and is excluded; So the answer is c.

Question 2: This question tests the principle of tolerance and repulsion, and if you really understand the principle of tolerance and repulsion, this question is not difficult. According to the question, you can first find out the number of people who like at least one movie = 100-16 = 84, let the number of people like Avatar be x, and substitute the data into the two-set formula of the repulsion principle "a b = a + b - a b" to obtain:

84 = 57 + x - 45, solution x = 72, answer c.

A to B pair: 5+x 2

A is wrong B is wrong: x 6

A is true and B is false: 5-x 6

A is wrong and B is right: x 4-x 6

x=(5+x/2)+x/6+(5-x/6)+(x/4-x/6)x=10+7x/12

5x=120

x=24 answer to c!

The answer is C!

You can draw a picture and look at it, and you will understand.

If you need a picture, just wait a minute, the upload is slow.

There is at least one type, 39-7 = 32 species.

I understand this.

If you add up all the items containing A, B, C, and C, then those containing A, B, and C are added 2 times each, and those containing A, B, and C are added 3 times.

Use the sum of A, B, C, and subtract AB, B, C, and A-C.

In this way, those containing both A, B and C were reduced 3 times.

The resulting number is at least one minus all three.

It is: 17 + 18 + 15 - 7 - 6 - 9 = 28 species.

Then all three are: 32-28 = 4 types.

The comprehensive equation is:

32 + 7 + 6 + 9-17-18-15 = 4 types.

As shown in the figure, circle No. 1 contains A, circle No. 2 contains C, circle No. 3 is the part of circle No. 1 and circle No. 2 containing B that intersects area No. 5, the part of circle No. 2 that contains both A and C and circle No. 3 intersects is area No. 6, the part that intersects circle No. 1 and circle No. 3 that contains both B and C is area No. 4, the part that intersects the three circles containing both A and B is area No. 7, and the area of the whole graph containing three components at the same time = 1+2+3-4-5-6+7, because 1+2+3, then (4-7), ( 6-7) and (5-7) were repeated once each, while 7 was repeated twice.

4-5-6, removing the repetition of (4-7), (6-7) and (5-7) above, and 7 is subtracted by one more time, so +7 is required at the end

Now I'm asking for 7

The area of the whole plot and the area of the rest of the areas 1-6 are known, so the area of area 7 = the area of the whole plot + 4 + 5 + 6-1-2-3, that is, 32 + 7 + 6 + 9-17-18-15 = 4

Foods containing one vitamin are counted.

Foods containing two vitamins were counted twice.

Foods containing three vitamins were counted three times.

Foods containing two vitamins were minus once.

Foods containing three vitamins were reduced twice.

It just so happens that each color in the picture is counted again.

That is, foods that contain all three vitamins. There are 32 + 7 + 6 + 9-17-18-15 = 4 types.

The idea should be this: at least one is 32 kinds, to get the one containing three, you need to subtract one and two, in the process of subtraction, the one containing one is only subtracted once, and the one containing two is subtracted twice, then it is subtracted one more, it needs to be added once, and in the end the one containing two is only subtracted once, and the one containing three is subtracted three times, and in the process of adding it is added three more times, offset, and the one containing three is not added or subtracted, so in the end the one containing one and two is exactly subtracted, Only three of them remained.

You can draw pictures, which is more intuitive and helps to understand!

Hope it helps!

You fill in the values into three intersecting circles, and it's easy to figure it out, adding the number that appears twice and subtracting the number that occurs once.

Use the set method to draw the plot, and solve x=5, which is not the same as above. If you think I'm right, ask me.

1. d 6 days.

Since the person who knows English, German, and French will appear in the person who knows both languages, it is enough to remove this person from each person who knows two languages.

ii. a 16 days.

Since the time he spent in the hotel all day during the rain was counted in the morning and afternoon at the same time, it was to be subtracted from the number of days he spent in the hotel in the morning and afternoon.

Then the number of rainy days is (8 + 12-12) 2 = 4 days, and the total number of days is 12 + 4 = 16 days.

The total number of bilingual speakers is 4+3+2 9 people.

Those who know three languages are counted once in each of the two languages, according to the topic, so subtract 3, 9-3 = 6 people.

Because the number of days without rain is 12 days, and the number of days he stays in the hotel in the afternoon is also 12 days, so he must have gone out to play in the morning of the 12 days, and because he stayed in the hotel in the morning for 8 days, he stayed in Beijing for a total of 12 + 8 = 20 days.

<> the circle on the left is the Olympic Games, and the right is the National Games, find the area of the shaded part (50 represents the area of the rectangle).

There were 50 people in total, and 30 of them didn't participate in anything, so there were 20 people who participated, and out of those 20 people, 10 people from the Olympics (including those who collected the National Games), then there must have been 10 people left who must have participated in the National Games, and there were 17 people in the National Games, so there were 7 people who also participated in the Olympics, so there should be 10 people who only participated in the National Games.

(30+10+17)-50=7 (people) - both kinds of volunteers.

17-7 = 10 (people) - just the National Games.

So choose C

You can't just count 50-17-10-30 to say it's 3, but you have to include the other volunteers, and I calculated it to be c

89 + 47 + 63 + 20-125 = 94 people··· The number of people who have only seen two of these films.

Suppose the number of people who have watched one is x, the number of people who have seen two is y, and the number of people who have seen all three is z.

w=x+y+z

a+b+c=1x+2y+3z

This gives 125-20=x+y+24

89+47+63=x+2y+72

The two formulas are cut together.

81=x+y

127=x+2y

y=46

To answer why I am wrong in this way and why the result is wrong in this way, you might as well start from the formula a b c=a+b+c-a b-c b-a c-a b c, so as to accurately grasp the meaning of each quantity in the formula, so as to find the problem.

1) Derivation of the formula a b c = a + b + c a b c b-c b-a c-a b c.

See the figure a+b+c=abc+blue set + 2x green set derivation steps:

The whole graph is a b c

This graph is equal to the sum and subtraction of the three sets of a, b, and c, and there are three coincident parts, namely: a b, b c, and a c

The green part is actually a b c, but in this way, the green part is subtracted.

So I have to add it back later.

Therefore, the whole graph = a figure + b figure + c figure - ab coincidence - bc coincidence -ac coincidence + more subtracted middle.

Translated into the language of mathematics is.

a∪b∪c=a+b+c-a∩b-b∩c-a∩c+a∩b∩c.

In connection with this question, the meanings of the corresponding quantities in the 1) formula are as follows:

A: 63 students participated in project A, 89 people participated in project B, and 47 people participated in project C.

Problem found:

The number of participants in the two projects shall be 46 and shall read: (a b) (b c) (a c);

Instead of: a b+c b+a c

Hello! You did the right thing, I didn't find anything wrong, and I verified it.

If it helps, please adopt! Thank you!

The answer is C! The explanation is as follows:

4 courses, 2 for each person, 6 options; At this time, according to the drawer principle, imagine that the 6 middle election method is 6 drawers, and if 4 party members are placed in each drawer, there will be 24 party members; At this time, if there is one more party member, no matter which drawer it is arranged in, one of the six drawers must contain five party members. Therefore, the organ has at least 24 + 1 = 25 party members.

This is a simple ternary repulsion problem, the formula a b c = a + b + c - a b - b c - c a + a b c

I like soccer A, I like basketball B, I like volleyball C, and the whole class A B C brings in the formula 20+10+12-5-4-3+1=42-12+1=31 If you don't understand clearly, just draw a picture and add up each individual part. See.

If it's not a big problem, the best way is to draw a Wayne diagram, if you want to use a big problem, you need to use a formula, for example, a crosses b=c, a and b should be a+b-c, and your above problem can be solved with this.