# Grade 7 Metrobank – MTAP Math Challenge Sample Problems Part 4

1. In teacher Ella’s class, a student receives a final grade of A if the student garners an average of at least 92% in the five long tests. After four long tests, Jonathan got an average of 91%. At least how much should he get in the last long test to get a final grade of A?

2. A class of 47 students took examinations in algebra and in Geometry. If 20 passed Algebra, 26 passed Geometry and four failed in both subjects, how many passed both subjects?

3. A runner started a course at a steady rate of 8 kph. Five minutes later, a second runner started the same course at 10 kph. How long did it take for the second runner to overtake the first?

4. A rectangle has sides (2x+3) cm and (4x+5) cm. how many squares of side x cm can be cut from it?

5. Let ABCDE is a regular Pentagon. What is the measure of ?

6. The average of five numbers is 20. If the sum of two numbers is 23, what is the average of other 3 numbers?

7. A long steel bar is to be cut in the ratio of 2:3:5. If the middle piece is 7 , how long is the steel bar?

8. Marvin is 10% taller than Homer and homer is 10% taller than August. How much (in percent) is Marvin taller than August?

9. Which is the largest?

10. When 3n is divided by 7 the remainder is 4. What is the remainder when 2n is divided by 7?

11. Which is smaller? ?

12. If and , what is the largest possible value of

13. If , find the value of

14. If , what is ?

15. All faces of a 4-inch cube have been painted. If the cube is cut into 1-inch smaller cubes, how many of them have no paint on all their faces?

16. If find the value of ?

17. The sum of two numbers is 20 and their product is 15. Find the sum of their cubes?

18. How many positive factors does have?

19. If the sides of the cube are tripled, what percent of the original volume is the new volume?

20. If the number 100 is expressed as a sum of 100 consecutive positive odd integers, what is the largest among all numbers?