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Центр подготовки к международным экзаменам по английскому языку Математика online test

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1. Marge has n candies, where n is an integer such that 20 < n < 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
2. If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?
3. The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).
4. A soccer coach riding his bike at 24 km/h reaches his office 5 minutes late. Had he traveled 25% faster, he would have reached the office 4 minutes earlier than the scheduled time. How far is his office from his house?
5. Mary bought some kiwis, bananas, and lemons at the grocery store in proportion of 1:4:7 accordingly. How many lemons did Mary buy?

(1) The total number of fruits Mary bought is 24.

(2) Mary bought 8 bananas.

6. If 6x=6, then √x6=
7. Is x > y ?

(1) x + y > 0

(2) x2-y2 > 0

8. Which of the following could be the sum of three consecutive integers?
9. In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE? 10. If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ?
11. If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees?
12. If p and q are prime numbers, how many divisors does the product p3∙q6 have?
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