# 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 $\angle{CAD}$?

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? $a=2^{48}, b=3^{28}, c=5^{24}$

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? $A=(2015)(2014)(2013)(2012)(2011) or B=2013^5$ ?

12. If $\displaystyle\frac{-12}{5}\leq x\leq\frac{-1}{2}$ and $3\leq y\le\displaystyle \frac{9}{2}$, what is the largest possible value of $\displaystyle\frac{x-y}{x+y}$

13. If $x^2-3x+1=0$, find the value of $x^2+\displaystyle\frac{1}{x^2}$

14. If $(x+3)(x-3)(x+1)=(x+2)Q(x)+(x+3)(x-2)$, what is $Q(x)$?

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 $x=-1$ find the value of $2013x^{2013}+2012x^{2012}+2011x^{2011}+\ldots+2x^2+x$?

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 $62(63^3+63^2+63+1)+1$ 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?