# Quantitative relationship – 1

##### Quantitative relationship

1. It takes 12 days for factories A and B to complete a production order. After the two factories produce together for 8 days, factory B produces alone for 7 days, and a total of 90% of the total order is completed. If the entire order is produced by factory B alone, how many days will it take to complete?

A. 30
B. 26
C. 23
D. 20

Notes:

12*(A+B)*0.9=8A+15B, we get 2.8A=4.2B. Assuming the efficiency of A and B is 3 and 2 respectively, the total project volume = 12×(3+2)=60. B alone needs 60÷2=30 days. Choose Method A: 7/x=90%-8/12, x=30

2.The company allocates 12 technical training places to three R&D teams A, B, and C. Team B is required to be allocated fewer training places than Team A, but more than Team C, and each team is allocated at least 1 place. How many different allocation methods are there?

A. 36
B. 42
C. 7
D. 8

3. A right triangle green space has water pipes with an integer length of meters on all three sides. One of the water pipes outside the right angle side is 7 meters long. If a point is randomly selected on the water pipe to be marked, the probability that the marked point is on the hypotenuse is within the following range? (Ignore the diameter of the water pipe)

A. Less than 0.35
B. Between 0.35 and 0.42
C. Between 0.42 and 0.50
D. Greater than 0.50

Notes:

Pythagorean theorem, Gray Rabbit summarizes common Pythagorean numbers and directly locks in 7, 24, and 25. Probability = length of hypotenuse / (sum of lengths of two right-angled sides + length of hypotenuse) = 25 / (7 + 24 + 25) 25/56 = 44.6%. Choose C.

4. One day, the company wants to arrange 20 people to travel from place A to place B on business, and the total one-way budget does not exceed 20,000 yuan. It is known that the full-price air ticket from place A to place B is 2,000 yuan. If you buy a full-price or discounted ticket, you have to pay 120 yuan in taxes for each ticket. The high-speed rail ticket from place A to place B is 680 yuan. There are enough high-speed rail tickets now, and there are 2, 3 and 5 tickets left at 20%, 30% and 50% off, respectively, and the rest are full-price tickets. So how many people can be arranged to fly to place B within the budget?

A. 11
B. 12
C. 13
D. 14

Notes:

All options are more than 10, so all discounted tickets are bought, spending 2000*0.2*2+2000*0.3*3+2000*0.5*5+120*10=7600+1200=8800 yuan, with 11200 yuan left, and 10 people left, chickens and rabbits in the same cage. Assuming all buy high-speed rail, (11200-680*10)/(1880-680)=3.7, so at most buy 3 more tickets, a total of up to 13 tickets.

5. Five soldiers participated in a shooting competition and hit the target 88 times in total. It is known that the number of targets hit by any two people is different from each other, so how many times did the top two soldiers hit the target at least?

A. 39
B. 41
C. 58
D. 82