Hunan civil servants mathematical operation exercises;
1. Known13+23+33 …+n3 = * *1+2+3 …+n * * 2, Q:13+33+53 …+1.
A. 19500
19900
C.20300
D.22500
2.
A. 1
B.0.5
C.2
D. 1.5
3. The racecourse has four * * * channels, A, B, C and D, which can be provided for people to play. If A and B are opened now, all tourists can enter after 4.5 hours. If B and C are turned on, all tourists can enter within 3 hours. If C and D are turned on, all tourists will enter in 3.5 hours. If only A and D are open, how many hours will it take for tourists to enter? *** ***
A.63/ 1 1
B.63/32
C. 196/33
D. 172/33
4. In order to promote sales, a shopping mall sold a brand air conditioner at a 10% discount on the basis of the pricing in June 5438+February, which coincided with Christmas and New Year's Day. The mall decided to make a profit of 100 yuan on the basis of discount, and the mall can still make a profit of 7.5% by selling at this price. If the purchase price of air conditioner is 2000 yuan, what is the price of this air conditioner in this shopping mall?
A.2400
B.2500
C.2600
D.2700
Every day, Xiao Zhang's watch is 30 minutes fast and Xiao Li's watch is 20 minutes slow. One day at noon, 12, two people set their watches to the standard time at the same time, so the minimum number of days for their watches to display the standard time again is * * * * *.
A.24
b36
C.72
D. 144
：
Answer: b
Analysis:
Because 13+23+33+ ah ... +n3 = * * 1+2+3+...+n * * 2,
Then13+33+53+…+193 =13+33+…+193-* * * 23+43+…+183.
=*** 1+2+3+……+ 19***2-23×*** 13+23+33+……+93***
=
-23×*** 1+2+3+……+9***2 =-8×= 19900
Therefore, the answer to this question is option B.
2. Answer: B
Analysis:
3. Answer:
Analysis:
If the total number of people is 1, two ports A and B can enter 2/9 people within 1 hour; Open ports B and C, 1 hour can enter 1/3 people; Open ports C and D, and you can enter 2/7 people in one hour; When three conditions exist at the same time, the number of people who can enter in one hour is a+b+b+c+d = 2 * * b+c * *+a+d = 2/9+1/3+2/7 = 53/63 * *. Because B+C = 1/3*** people * *, A and D are open at the same time, the number of people entering 1 hour is1/63. Therefore, it takes 63/ 1 1 hour for ports A and D to open, and all tourists can enter.
4. answer: b
Analysis: According to the meaning of the question, if the price of this air conditioner in the shopping mall is X yuan, then it is 90%x- 100-2000=2000×7.5%, and x=2500.
5. Answer: C
Analysis: Xiao Zhang's watch: 30 minutes fast every day, then the realistic standard time needs to pass 12 hours ÷30 minutes/day =24 days; Xiao Li Watch: If it is 20 minutes slow every day, it will take 12 hours ÷20 minutes/day =36 days to realize the standard time again; The least common multiple of 36 and 24 is 72, so it takes 72 days for two watches to display the standard time at the same time. Therefore, the correct answer to this question is C.