Grade 7 Metrobank – MTAP Math Challenge Sample Problems Part 4

by Dan · Published April 11, 2014 · Updated June 4, 2014

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 $\displaystyle\frac{x-y}{x+y}$