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. Samaira is 8th from the front in a queue. Jaden is 7th from the back in a queue.
If there are 3 people between them, then find the difference between least possible and maximum possible people standing in the queue.

2. There are 8 distinct (different) counting numbers. If you pick any 5 at random, their product is always even however the sum of all the 8 numbers is odd.
What could be the least sum of all these 8 numbers?

3. Shyam has twice as many apples as bananas. If he gives 3 bananas to each student in his class, 2 bananas are left. If he gives 8 apples to each student then he needs 12 more apples. How many total fruits (bananas + apples) are there?

4. A packet of sweets was distributed equally among 30 students. 8 students did not like sweets so they returned their sweets which was again distributed in the rest of the students equally who now got 4 more each than earlier. How many sweets were there in the packet?

5. 3 packs of French Fries , 2 cheese burgers and 1 soft drink costs 19 $and 1 pack of french fries, 2 cheese burgers and 3 soft drinks costs 21$. Find the price of 1 set (1 french fries + 1 cheese burger + 1 soft drink) in \$.

6. Jonathan multiplies the month of his birthday by 31. He then multiplies the date of his birthday by 12. The sum of the two products is 213. When is Jonathan’s Birthday ? Give your answer in the format of eg. 02 July

7. In how many ways 19 apples can be divided into 3 identical baskets so that at least one of the baskets has an odd number of apples? Every basket needs to have at least 1 apple and no two baskets should have the same no. of apples.

8. There are two 3-digit numbers. In each number, the digits face values are in the ratio of 1:2:3 but not necessarily in the same order. What would be the maximum difference of these two 3-digit numbers.

9. Form two of 2-digit numbers using 1,2,3,4 without repeating any digits and using all of them once. What will be the minimum product of these two numbers?

10. There are 28 natural 1-digit numbers, not necessarily all different, arranged in some order. If you pick any 4 consecutive numbers from this order, the sum is same. If the fifth number is 3, tenth number is 5, 15th number is half of the 20th number, then what is the maximum possible sum of all 28 numbers?

11. Pratik takes 2 minutes to cut a log into 9 smaller logs. How many more pieces he could have cut it into if he would have taken 5 more minutes?

12. Little Joy takes 1 minute and 40 seconds to complete a round of a circular park at a constant speed of 5 m/s. Trees are planted at the distance of 20 m around the park. How many trees are there around the park?

13. There are 20 rows of seats in a school auditorium.Each row has 4 seats more than the row in front of it. If the last row has 86 seats and the first 12 rows are full and rest all rows empty, then how many students are there in the auditorium?

14. Babita can order a french fries or a soft drink or both with her burger. There are 4 kinds of burgers, 2 varieties of french fries and 3 types of soft drinks to choose from. How many different combinations are there for Babita to choose from for her order of a burger meal (at least 2 items in the meal)?

15. 16 unit squares (1 x 1) are joined to make a rectangular figure. Then they are taken apart and again joined to make a square. Find the maximum possible difference of the perimeters of these two shapes.

16. There are 3 different points on each of two parallel lines. How many different triangles can be formed using the dots as the vertices of the triangles?

17. You gave 3 more than half of your toys to your sister and now the total toys both of you have is 25 and she has 9 more than you. How many more toys than her did you have in the beginning?

18. Little Zebra said to its mother, “Mum, by the time I get to be as old as you, you will be 23.” She replied, “You were only 2 years old when I was your age.” How old is the little zebra in years?

19. In how many ways you put 4 identical flowers in 2 different shaped vases if no vase is to be left empty and all flowers are to be put in the vases?

20. 20 students of a class appeared for Math Term 1 and Term 2 tests. In the 1st term, 16 students passed and in the 2nd term exam 3 students failed. If 15 students passed in both terms, then how many students failed in both terms?

21. How many different triangles with integer (counting number) length sides can be made whose perimeter is 20?

22. What is the perimeter of a rectangular floor in feet that is made from 91 one-foot square tiles if all the sides of the floor are longer than 1 foot?

23. Jaideep and Amandeep live 9 km from each other. Amandeep lives 7 km from the supermarket. What is the difference between maximum and minimum
possible distance in Kms between Jaideep’s house and supermarket?