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2006 Regional Individual Finals Metrobank-MTAP-DepEd Math Challenge
Grade 6 I. Write the answer on the blank before the number. Use π = 3.14 [ 2 points each] __________ 1. 5 more than thrice the sum of 12 and 17 equals_____. __________ 2. What is the largest 3-digit number that is a multiple of 13? __________ 3. Express 13,860 as a product of prime factors using exponents. __________ 4. What is the greatest common factor of 420 and 504? __________ 5. What is the least common multiple of 420 and 504? __________ 6.What is the reciprocal of the sum of 2
1 6
and 3
2 3
?
__________ 7. A jar filled with water weighs 10 kg. When half of the water is poured out, the jar and its contents weigh 5
3 4
kg. What is the weight of the jar?
__________ 8.Of three numbers, two are ½ and 1/3. What must the third number be so that the average of the three is 1? __________ 9. One man can dig a hole 2 m x 2 m x 2 m in one day. At the same rate, how long will it take 3 men to dig a hole 10 m x 6 m x 4 m? __________ 10. The base of an isosceles triangle is 5 cm longer than a leg. If the perimeter is 41 cm, find the base. __________ 11.111 111 + 222 222 + 333 333 + 444 444 = 222 222 x N. Find N. __________ 12. The cost of a watch including a tax of 25% is P937.50. Find the cost of the watch without the tax. __________ 13. The floor of a bathroom is 2.5 m by 1.8 m. How many tiles, 5 cm square, will be needed to cover it? __________ 14. A carpet, 12 m by 9 m is laid in a room, 17 m by 14 m. What percent of the room is left uncovered? __________ 15. Find the total surface area of a closed barrel with a diameter of 6 dm and a height of 12 dm. II. Solve each on scratch paper and write a neat and complete solution on the space below. Label your solutions. [3 points each] 1. How many revolutions, to the nearest whole number, will a car wheel with a diameter
7 dm, make to cover a km? 2. 512,000 square tiles, each 5 cm on each side, are needed to pave a rectangular court 40 m long. What is the width of the court? 3. How many books, 24 cm long, 18 cm wide and 2.5 cm thick can be packed into a box 5 dm long, 3.7 dm wide and 2 dm high, internal dimensions? 4. There are 108 red, blue and green marbles in a box. Four more than one-third of the marbles are red. There are 8 more green marbles than blue marbles. How many marbles of each kind are there? 4. A square of 9 by 9 grid is colored alternately black and red. If the corners are black, how many black and red squares are there? III. Solve each problem on scratch paper and write a neat and complete solution below. Label your solutions. [5 points each] 1.I went to a store and spent 1/3 of my money and P5.00 more. Then, I went to a second store where I spent 3/5 of my remaining money plus P9.00 more. I had exactly P45.00 left. How much money had I at first? 2. The digits 1, 2, 3, 4 can be arranged to form 24 different 4-digit numbers. If the 24 numbers are listed from smallest to largest, a. Give the smallest and largest numbers formed. [1 pt.] b. What is the position of 3142? [2 pts.] c. What is the sum of the 24 numbers? [2 pts.] 3. Tom ate 100 cookies in 5 days. Each day, he ate 6 more cookies than the day before. How many cookies did he eat on each of the 5 days?
