Grade 7-Sample Questions GJMOC

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. Mahesh had 740 stickers and he was able to give them away equally among his classmates. His class had between 30 to 40 pupils. How many more stickers would Mahesh need if he wanted to give each classmate 25 stickers instead?

Answer : 185

2. Mr Dasgupta had 144 kg of red and green beans. 25% of the beans were red. He bought some more red beans and the percentage of red beans increased to 40%. How many kilograms of red beans did he buy?

Answer : 36

3. There are two plants in Mrs. Saumya’s garden. One is 44 cm tall, and it grows 3 cm every 2 years. The other is 80 cm tall, and it grows 5 cm every 6 years.
In how many years will the two plants have the same height?

Answer : 54

4. A tournament had six players. Each player played every other player only once, with no ties. If Harshali won 4 games, Ishmeet won 3 games, Jahnvi won 2 games, Kimaya won 2 games and Laila won 2 games, how many games did Mysha win?

Answer : 2

5. A car moved 1 second at a constant rate of 2 m/sec, then 1 second at a constant rate of 4 m/sec, then 1 second at a constant rate of 6 m/sec, and so on. All movements were in the same direction. In how many seconds would the total distance covered by the car be 110 meters?

Answer : 10

6. Fatima drew a rectangle with side lengths that were whole numbers. The perimeter of the rectangle was a multiple of 7 and the area was a multiple of 9.
Compute the least possible perimeter of Fatima’s rectangle.

Answer : 28

7. How many different whole numbers are there containing only the digits 1 and/or 2 (each of these digits can be used one or more times or not at all) such that for each of these numbers, the sum of all of its digits equals seven?

Answer : 21

8. Lokesh and Triloki each had several $20 and $50 bills. Lokesh gave Triloki several of his $20 bills and got from him the same number of $50 bills, and as a result of this exchange, the money was divided equally between the boys. If after that Triloki gives Lokesh all six remaining $50 bills, each of the boys would have as much money as other one had originally. How many $20 bills did Lokesh give to Triloki?

Answer : 10

9. Sumit bought several pizza pies. He cut the first pie into 2 slices, the second pie into 3 slices, the third pie into 4 slices, and so forth. Then he ate one slice from each pie and counted that only 21 slices were left. How many slices did Sumit eat?

Answer : 6

10. The Circumference of a circle is 44 cm. An inscribed square has its four vertices on the circumference. Find the area of the square in square cm (Just write the number without units).

Answer : 98

11.If you increase the length of a rectangle by 3 cm, then the area increases by 24 sq cm however the area can increase by 24 cm also by increasing the width by 2 cm only. If a square has the same perimeter as the original rectangle then what will be the area of the square in sq. cm. (write the numerical value only without units)?

Answer : 100

12. Consider two squares. The side length of the larger square is 4 meters longer than the side length of the smaller square. If the area of the larger square is 80 \(m^2\) larger than the area of the smaller square, what is the sum of their areas in \(m^2\) (Answer with the number only without units)?

Answer : 208

13. 5 identical flowers are to be put into 3 different Vases. Each Vase should get at least 1 flower and all 5 flowers are to be put in the vases. How many ways can the flowers be arranged in the different vases?

Answer : 6

14. The least common multiple of 12, 15, 20, and k is 420. What is the least possible value of the positive integer k?

Answer : 7

15. I climb half the steps in a staircase. Next I climb one-third of the remaining steps. Then I climb one-eighth of the rest and stop to catch my breath. What is the least possible number of steps in the staircase?

Answer : 24

16. What is the 100th digit to the right of the decimal point in the decimal form of \(\frac{4}{37}\)?

Answer : 1

17. Grapes are 80% water (by weight), and raisins are 20% water (by weight).
If we start with 500 grams of grapes and remove enough water to turn them into raisins, then what is the weight of the raisins that result?

Answer : 125

18. There are 120 seats in a row. What is the fewest number of seats that must be occupied so that the next person to be seated must sit next to someone?

Answer : 40

19.There is a series of more than 10 natural numbers. If a natural number N is added to each of the term then the sum of all the numbers increases by 105. Find the sum of all possible values of N.

Answer : 16

20. A large sheet of paper is cut into 2 pieces on 1st day. Then each resulting piece is cut into further 2 pieces on 2nd day and then again each resulting piece is cut into 2 pieces on the 3rd day and so on. How many pieces will be there at the end of 10 days?

Answer : 1024

21. 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 their sum and difference?

Answer : 333

22. The remainders when a number A is divided by 4, 10 and 18 are 1, 5 and 9 respectively. Find the sum of all possible value(s) of the remainder when A is divided by 72.

Answer : 54

23. A teacher wants to distribute all 48 candies he has to the students of his class. At, most how many students are required in the class to ensure that at least one student will end up getting 4 or more candies.

Answer : 15

24. Joshua and Mike went to buy a video Game console which costs $91. If Joshua pays for it then the ratio of money left with him and Mike will be 3:7 but if Mike pays for it then the ratio of money left with him and Joshua will be 4:11. How much money in $ did they have altogether in the beginning?

Answer : 301

25. A train running at a speed of 3 m/s takes 25 minutes to completely cross a bridge from the moment it gets on the bridge. If the same train is completely (entire train on the bridge) on a bridge of double size of the previous bridge for 35 minutes, find the length of the train in metres?

Answer : 900