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. am thinking of a fraction $$\frac{A}{B}$$. The sum of its numerator and denominator is 41. When I add 39 to its denominator, the fraction becomes $$\frac{1}{4}$$. Find the minimum product of A and B

2. A total of 170 students are in a hall. $$\frac{3}{5}$$ of the boys and $$\frac{3}{7}$$ of the girls wore spectacles. The number of boys who do not wear spectacles is equal to the number of girls who do not wear spectacles.
How many girls are there in the hall?

3. A group of boys were picking apples. They each picked 3 apples. Then three other boys joined them. They wanted to share the picked apples equally among all the boys present, but found out that this was not possible. However, one of the boys picked one more apple. Now everyone could have exactly two apples.
How many boys were there in the original group?

4. Maya cut off $$\frac{2}{5}$$ of a piece of string. Later, she cut off another 14 m. The ratio of the length of string remaining to the total length cut off is 1 : 3. What is the length of the remaining string?

5. Govind and Meena have the same number of candies. If Govind gives Meena half of all his candies, and then Meena gives Govind half of all the candies she has at the moment, Govind would have 12 more candies than Meena. How many candies do Govind and Meena have altogether?

6. Lambu and Chotu are friends. Every January 1st they get measured and they write down the date, Lambu‘s height, Chotu’s height, their total height, and their height difference (the amount by which Lambu is taller than Chotu). From January 1st, 2020, to January 1st, 2021, Lambu grew 5%, Chotu grew 2%, their total height increased by 4%, and their height difference increased by X%. Compute the value of X.

7. A Fruit drink is made from 25% pure fruit juice and the rest is water. A barrel contained some amount of this fruit drink, but then by mistake, 60 litres of water was added to the barrel. How many litres of pure fruit juice must be added to the barrel to correct the mistake, so the barrel would again contain fruit drink with 25% pure fruit juice?

8. A factorial number is the product of all whole numbers from one through some whole number. For example, 720 is a factorial number because 720 = 1x2x3x4x5x6. Now let’s say that a positive whole integer K is “interesting” if some factorial number ends in exactly K zeroes, and “boring” if no such factorial number exists. So the number 1 is interesting since the factorial number 720 ends in exactly one zero. Find the sum of the six smallest boring numbers.

9. A teacher asked her students to find a 2-digit whole number which has as many as possible different positive factors. Jack realized that there was more than one such number, and listed each of them once. Find the sum of all of Jack’s numbers.

10. All possible diagonals drawn from the two adjacent vertices A and B of a regular hectogon divide the hectogon’s interior into a number of non-overlapping shapes – triangles and quadrilaterals (without any part of a line inside them).
How many of these shapes are triangles? (A hectogon is a polygon with 100 sides.)

11. A regular polygon has 54 possible diagonals. The ratio of each external angle to each internal angle is A:B . Find the least possible value of A + B

12. If you roll three regular (Normal) six faced dice, then the probability of getting a sum of 10 is $$\frac{A}{B}$$? Find the least value of $$A+B$$.

13. There are 4 different fiction novels and 5 different encyclopaedias kept on a book shelf. In how many ways you can arrange them if all of the same kinds need to be together?

14. How many 4 digit numbers are there whose sum of digits is 7?

15. The squares of two consecutive positive integers differ by 67. What is the smaller of the two integers?

16. Pihu can’t quite read the board in her math class. She writes down the equation she reads on the board as 2x – 7 = 23. She correctly solves the equation she wrote down, but is surprised to hear the teacher say the answer is 5 less than the answer Pihu found. When Pihu asks the teacher to check her work, the teacher says that Pihu copied the coefficient of x incorrectly (but copied everything else correctly). What should the coefficient of x have been?

17. For a set of ten numbers, removing the largest number decreases the average by 1. Removing the smallest number increases the average by 2. What is the positive difference between the largest and the smallest of these ten numbers?

18. A 1000-digit number N has 6 in its unit (ones) place. If you pick any two consecutive digits from N, the 2-digit no. picked up is either divisible by 17 or 23.
What is the first (extreme left one with highest place value) digit of N?

19. 63 of 1×1 squares are combined to form a big rectangle with smallest possible perimeter. In this resulting rectangle, how many more rectangles are there than squares in this large rectangular figure?

20. A pathway of $$10\times 3$$ dimension has to be filled with 1*3 tiles. In how many ways can you fill it?

21. A $$7\times 7[/latex[ square is made of 49 [latex]1\times 1$$ squares.The large square has one * in each of all the four corner small squares. How many rectangles in the large square do not include even a single * in them?

22. A tourist starts from Town A on Monday morning and he can go to one of the nearby towns B, C, D, E. Subsequently, every day in the morning he goes from one town to another town out of these 5 towns. He reaches the next town on the same day by afternoon. It’s not necessary to go to each town and he can also revisit the same town on an another day. If he lands up in Town C on Thursday afternoon and comes back to Town A on Sunday afternoon, how many different possible routes (assume one route from one particular town to any other particular town) are there for the 7 days?(Assume that he reaches from one town to another on the same day in a few hours).

23. Determine the number of ordered pairs $$(a, b)$$ if the 5-digit number $$2a3b4$$ is divisible by 12.