This ” Sample Questions ” test is not to check the rote learning of concepts and application of simple procedures. This test would require the student to first understand the question properly and then they need to think and try out different possibilities to solve the question. The method is not important but the mindset to take on the challenge is. This test might cover much more than what the school syllabus/curriculum gives an exposure to. Please note that some problems would require more than one topic/concept to be applied as Math is not about just calculations but it is about well reasoned application of concepts and operations in a systematic and logical way. The focus here is on understanding, applying and problem solving and relating Math with the world around us and how we use it daily for small decisions. (sc : Global Olympiads Academy)

1. Amrita has some flowers and vases. If she puts 4 flowers in each vase then one flower is left and if she instead arranges 5 flowers in each vase then one vase is left empty. Find the sum of number of flowers and number of vases she has.

2. Jay participates in a chess tournament. There are 14 players in the tournament. Each player played once with every other player. Each player gets 1 point for a win, $$\frac{1}{2}$$ point for a draw and 0 points for a loss. Every player except Jay scored 6 points. How many points did Jay score?

3. If $$\frac{3}{8}$$ of class are Boys and the girls are 6 more than the boys then how many students are there in the class?

4. Deven has 3 apples and 4 oranges. What is the least number of fruits that Deven has to buy so that $$\frac{2}{3}$$ of them are apples?

5. $$\frac{2}{5}$$ students of the class are boys. Exactly 75% students of the class like Math. If 21 girls like Math, find the difference between the possible maximum and minimum number of students in the class?

6. Ahana and Beena have some pocket money saved. Ahana has $10 more than half of the total pocket money between them. How much more money in$ should Beena get from her parents if she wants to have $5 more than half of total amount they will have altogether? Answer : 30 7. A square shape is divided into two non-overlapping rectangular shapes. Each of these two rectangular shapes is divided into three non-overlapping square shapes. Compute the sum of the perimeters of these six squares (in feet) if the perimeter of the original square is 60 feet. (The perimeter of a square is the sum of the lengths of all of its sides.) Answer : 140 8. In 2019, a long row of trees was planted in the empty GOA park. In 2020, a tree was planted between every two adjacent (next to each other) trees planted in the previous year. In 2021, a tree was planted between every two adjacent trees planted in the previous years, bringing the total number of trees in GOA Park to 877. How many trees were planted in GOA Park in 2020? Answer : 219 9. Niharika and Vandana each drew a rectangle (could be a square). Niharika’s rectangle has a perimeter of 88 cm. Vandana’s rectangle is 2 cm shorter and 8 cm wider than Niharika’s. If Vandana’s rectangle’s area is the maximum value it can have with for it’s own perimeter, find the area of Niharika’s rectangle in sq. cm. Answer : 459 10. There are 4 boys and 6 girls in a class. 3 students will be selected for representing the class in a debate competition and there should be at least 1 boy and 1 girl in the team. How many different teams can be formed? Answer : 96 11. If 3 flowers out of a choice of 5 flowers are to be put in 3 different vases with one flower in each of the 3 vases, then how many arrangements will be there? Answer : 60 12. How many 3-digit even numbers are there with all different digits and sum of digits 7? Answer : 13 13. Find the sum of perimeters of all rectangles whose sides are integer lengths and area is 24 square units. Answer : 120 14. A train runs at 150 m per second and another train runs at 120 m per second. They start at the same time from two different stations and travel towards each other. If they cross each other 30 kms away from the mid- point of the distance of the two stations, how far are the two stations in kms? Answer : 540 15. The difference of two numbers is 182, and their quotient is 3 (i.e. when one number is divided by the other, the answer is 3). Find the sum of the two numbers. Answer : 364 16. A rectangular floor of 1584 cm by 1134 cm is to be covered completely by identical square tiles. What is the greatest possible length of the tiles in cm? Answer : 18 17. If 91 or 107 or 131 are divided by a number N the remainder is same R. What is the maximum value of N? Answer : 8 18. Three consecutive even numbers are multiplied and the result is 13728. Find their sum. Answer : 72 19. Sum of 3 prime numbers is 44. What will be the difference between their maximum and minimum products? Answer : 504 20. Ajay, Bikas and Chandan each had some books. Ajay gave Bikas and Chandan some books that doubled the number of books they had at first. Bikas then gave some books to Ajay and Chandan that doubled the number of books they had. Lastly Chandan gave Ajay and Bikas some books that doubled the number of books they had. Each of them had 32 books at the end. How many more books did Ajay have than Bishal and Chandan put together at first? Answer : 8 21. Arjun ‘s father’s is five times as old as Arjun.If after 6 years, his Arjun will be one third of his father’s age. How old is Arjun’s father now? Answer : 30 22. Raghav has some 5$ coins, some 2$coins and some 1$ coins and altogether he has 20 coins. If he has at least 1 of each kind and the total value of the coins is $77, then at least at how many$5 coins he has?