Reason + percentages - practice problems
Number of problems found: 119
- Non equivalent ints
Two n-digit integers are said to be equivalent if one is a permutation of the other. Find the number of 5-digit integers such no two is equivalent. If the digit 5,7,9 can appear at most one, how many non-equivalent five-digit integers are there?
- Probability 72324
We used the digits 2, 3, 4, 5, and 7 when entering the PIN code, and we only used each digit once. What is the probability that someone will guess our PIN code on the first try?
- VAT example
The following data were provided by Halo Mango Delight, a VAT taxpayer, for October, November, and December 2021 (VAT excluded): Compute the Value added tax of the store for the 4th Quarter of 2021. (Show computation in solving the problem). VAT ratio = 1
- Three-digit 69114
How many three-digit numbers have a digit sum of 6? Write the ratio of the number of created even and odd numbers and adjust it to the basic form.
- Divisible 68644
List all divisible numbers by six and seven that are greater than 79 and less than 91.
- Find two digits
Find the possible values of A and B if the six-digit number 2A16B6 is divisible by 4 and 9. Please write the result as a composed number.
- Percentage 65844
Mr. Josef sold home-grown potatoes at 79 cents per kilogram. When he had the last 5 kg, he told the customer: collect them all for 3 euros! By what percentage did Mr. Josef reduce the potatoes?
- Numbers 65734
There are 100 tickets in a pocket with the numbers 1 to 100. What is the probability that we will randomly draw a ticket with a number starting with the number 5?
- Extinguishing 63834
40% of the foam was sprayed from the foam fire extinguisher during the fire extinguishing exercise. The weight of the entire device was 7 kg, and after training, it dropped to 4.6 kg. What was the weight of the empty device?
- Error rate
The exam has six questions. Students have an error rate of 20% and can have a maximum of 1 question wrong. What is the probability that they will succeed?
- The vaccination
The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated and more likely to be infected? Consider N = 10,000 inhabitants and K = 1,000 infected. b. How many times more likely are unvacci
- Cost structure
You are currently trying to decide between two cost structures for your business: one with a greater proportion of short-term fixed costs and another more heavily weighted to variable costs. Estimated revenue and cost data for each alternative are as foll
- Gym center
80% of all visitors to the gym center enjoy a discount. 3/4 of all visitors go to practice regularly. All visitors who go to the gym regularly benefit from a discount. What percentage of all visitors do not go to the gym regularly but still use the discou
- Evaluation 34581
There are a total of 26 students in the class. During the evaluation of the control work, the teacher said: "4 pupils got the number one, and that is 16%. "Did all the students write the control work?
- Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice
- Beer tapping
When checking compliance with the beer tapping, it was found that 60% of the offered beers were underfilled. The others were fine. Thus, instead of 0.5 l, the volume was 4.4 deciliters on average. What was the volume of one average underfilled beer?
- Manufacturer 24801
With a repeat check, five hundred of the series of products are to be inspected. The manufacturer guarantees 2% scrap for a given production. Determine the probability of scraps among the 500 products reviewed between 12 and 20.
- Birthday paradox
How large is the group of people so that the probability that two people have a birthday on the same day of the year is greater than 90%?
- Defective 23221
The factory sets a standard that 2% of products may be defective. Last week, out of 1,250 products, 32 were defective. How many defective products were the standard exceeded?
- The manufacturer
The manufacturer found that 3% of the plates produced had a malfunction. Of the complaint, 75% are first and 25% second. What is the probability of producing first and second-class plates?
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