2. There is a six-digit abcdef. If you multiply it by 3, you will get a new six-bit bcdefa. What is this six-digit number?
3. When 10 people take the test, each person must answer 24 questions. 5 points for correct answer 1 and 3 points for wrong answer 1. As a result, the person with the lowest score will get 8 points, and everyone's score is different. How many points will the first place get at least?
The shepherd drives a flock of sheep to eat grass. After escaping from a ram, he found that the ratio of ram to ewe was 9: 7 among the remaining sheep. After a while, the escaped ram returned to the flock, but ran away from another ewe. At this time, the ratio of ram to ewe is 7: 5. There are many sheep in this group?
5. It is known that the railway bridge is 1 0,890 meters long, and a train passes through the bridge. According to the measurement, it takes 1.20 seconds for the train to get on the bridge, and 90 seconds for the whole train to stop completely on the bridge. What is the speed and length of the train?
1. Because 385=5×7× 1 1, among the 385 natural numbers of 1~385, the multiple of 5 is 385/5 = 76 (pieces), and the multiple of 7 is 385/7 = 55 (pieces). 5×7=35 = 1 1 (pieces), the multiple of 5× 1 1=55 is 385/55 = 7 (pieces), 7× 1 1 =.
According to the principle of exclusion, the divisible number in 1~385 is 77+55+35-(11+7+5)+1=1438.
2. Because it has no carry after multiplying by 3, it is less than 333333.
Let bcdef=x, then this six-digit number is100000a+x.
Multiply by 3 to get a new six-digit bcdefa =10x+a00x+a.
3 *( 100000 a+x)= 10x+a
300000a+3x= 10x+a
299999a=7x
a= 1，x=42857
a=2，x=857 14
A=3, x= 12857 1 (more than 5 digits, inconsistent)
These six digits are: 142857 or 2857 14.
Let the person with the lowest score answer the X question correctly.
Then the person with the lowest score answered question 24-X incorrectly.
Judging from the meaning of the question.
8 = 5X-3 *(24 X)
The solution is X= 10.
And because there are 10 people.
Then the number of questions answered correctly in the first place is10+10-1=19.
In this way, the number of wrong answers in the first place is 24- 19=5.
In this way, the score of the first place is
19*5-5*3=80
4. Set X rams and Y ewes.
According to the meaning of the question, the equation (x-1) can be listed: y = 9: 7.
x:(y- 1)=7:5
You can get X=28 y=2 1.
So there are 49 sheep in this group.
5. Let the length of the train be x meters, and the equation can be obtained:
( 1890+x)/ 120 =( 1890-x)/90
Solution:
x=270
The speed is (1890-x)/90= 18.
So the length of the train is 270 meters and the speed is 18 meters per second.
The school will hold a sports meeting. On the edge of the 400-meter circular runway, a colorful flag will be inserted every 16 meters. Later, some colorful flags were added to shorten the distance between every two colorful flags and keep the starting point unchanged. After plugging it back in, I found that five colorful flags had not moved. Q: What is the interval between colorful flags now?
7. Mark a piece of wood three times with a red pen: the first time divide the wood into 12 equal parts, the second time divide the wood into 15 equal parts and the third time divide the wood into 20 equal parts. Saw the wood along these red marks. How many small pieces will it be cut into?
8. A stationery store sells pencils for 50 cents, and few people buy them. So, the stationery store sold the pencil at a reduced price. As a result, all the pencils in stock were sold out, and * * * sold for 3 1.93 yuan. How many pencils does this stationery store have in stock? How much is each branch?
9.A and B are running at the speed of 10 meter per second on the road parallel to the railway. A train came to A at a constant speed, and it took 9 seconds to drive to A car, and then it took 39 seconds to drive to B car. Find out the speed of this train.
10. A goes from A to B, and B goes from B to A at the same time. 14 minutes later, the distance between them is 90 meters. It is known that A travels 24 minutes per minute and B travels 60 meters per minute. How many kilometers is it between A and B?
1 1. Party A and Party B walk in both directions at the same time, and they can meet in 30 minutes. If Party A walks 12 meters more than before, and Party B walks 8 meters less than before, they will meet in 29 minutes to find the distance between the two places.
6. There used to be 400/ 16=25 faces.
The five flags have not moved, so the interval between the five flags is 400/5=80. Because of the increase, the interval will not be very different, so only five flags have not moved, so the interval can only be 10 meter, otherwise there will be no situation where only five flags have not moved. Simply put, finding the constraints of 80 and 16 can form a number with the least common multiple of 80. . So the final answer is 5 and 10 meters.
7. This question depends on how many red lines are repeated. According to this idea, based on the first red line, the second line is 5/1510/5. At this time, there is 1 1 on the wooden stick for the first time and 14 for the second time. Draw N red lines and cut N segments) There are 7 red lines for the third time: 4/205/208/2010/2012/2015/2016/20, so the final number of red lines is/kloc-.
8. This problem is actually to find the constraint of 3 1.93. It is easy to see that 31.93 = 31*1.03, namely 103*0.3 1 (because it is less than 0.5), so a * * has 65438.
9.A is short, which means it is opposite to A and the same as B. A walked 90 meters in 9 seconds and B walked 390 meters in 39 seconds.
Set the train to x meters long.
Through simple drawing, we can know that it took 9 seconds for the train to run x-90 and 39 seconds for x+390 meters.
Subtracting the two, the train traveled 480 meters in 30 seconds, so the train speed was16 m/s.
10. By drawing, we can know that A left in 14 minutes 14/24 = 7/ 12, and B left 14*60=640 meters, and the sum of them is exactly the length of the whole journey.
Let the whole length be x meters.
7/ 12x+840=x+90
750=5/ 12x
X =1800m
1 1. Let a speed x m/s and b speed y m/s..
Get 30*(x+y)=29(x+ 12+y-8).
x+y= 1 16
So the total distance =30* 1 16=3480 meters.