# Grade 5 MTAP Regional Finals Round (Individual Written Competition)

These are the Math Challenge Questions for Grade 5 Regional Finals.
More past tests can be found here and more Grade 5 reviewers can be found here. If you have old tests, kindly send it to mtapreviewers@gmail.com, so we can share it here with answers/solutions.

Part I

1.) What is the least common multiple of 90 and 126?

2.) A worker can assemble a toy boat in 6 hours. A machine can reduce the time in the ratio 3:10. How long will the machine take to assemble the toy boat?

3.) A square has a side of 8cm. A second square has a side of 12cm. What is the ratio of their areas?

4.) On a boat, 16% of the passengers travel first class and 56% travel third class. If 238 travel second class, how many passengers are in the boat?

5.) How many bags of cement will you buy to pave a path 28m long and 2.5m wide if a bag of cement can cover 12m^2?

6.) A store employs 2 men and 5 women. Each man is paid 1 ½ times that of a woman. If each day the store owner pays P2 400.00, how much does each man receive?

7.) A weighs 60kg. B weighs 25% less than C. If C weighs 20% less than A, what is the weight of B?

8.) How many pieces of string 3.6dm long can be cut from a roll 66m long?

9.) A room is 6m long, 4.5m wide and 3m high. The ceiling and 4 walls are to be painted. If the door and windows have a combined area of 14m^2, what area is to be painted?

10.) Lyn can paste in her album 4, 5 or 6 pictures, with 2 pictures left-over in each case. What is the smallest number of pictures that Lyn has?

11.) A pair of shoes was sold for P747.50 with a gain of 15%. What was the cost price of the shoes?

12.) A vendor bought 80 pineapples at P28.50 each. Three pineapples went bad but the vendor was able to sell the rest at P25.00 each. Find his percent loss to the nearest whole number.

13.) Nine small squares are put together to form a bigger square. If the perimeter of the big square is 72cm, what is the area of each small square?

14.) A piece of metal 84.7cm^3 is put into a cylindrical container of radius 3cm containing water to a depth of 30cm. What is the resulting depth of the water to the nearest whole number?

15.) Ninety litres of gasoline can be used by a machine to work at 8 hours a day for 3 days. With 270 litres of gasoline, how many hours a day can the same machine be made work for 6 days?

Part II

1.) Counting numbers like 1, 2, 3, 4 and so on are called consecutive numbers. The average of 11 consecutive numbers is 15. What is the sum of the last three numbers?

2.) One hundred fifty soldiers on a camp had enough food for 40 days. After 6 days, 20 more soldiers joined them. For how long will remaining food last?

3.) OABC is quarter of circle with a radius of 9cm. What is the area of the shaded region? (Use π ≈ 3.14) 4.) If the edge of a cube is increased from 6cm to 9cm, what is the ratio of the new volume of the cube to its original volume?

5.) A pipe has a diameter of 2.0cm. It is replaced by a new pipe whose circumference is 1cm longer than the circumference of the first pipe. What is the diameter of the new pipe to the nearest tenth of a centimetre?

Part III

1.) There were apples in a box intended for 6 persons. One-third, one-fourth, one-fifth and one-eighth of the apples were given to the four of the persons in the group. If 10 apples were given to the fifth and 1 apple to the sixth, how many apples were originally in the box?

2.) John agreed to work after school for 8 weeks for a fixed weekly rate. For this work, John agreed to receive P850.00 and a bag. After 5 weeks, John got sick. He was given P250.00 and a bag. How much the bag worth?

3.) In an ancient village, 10 rabbits can be exchanged for 2 turkeys, 6 turkeys can be exchanged for 2 goats, 10 goats can be exchanged for 2 cows. How many rabbits can be exchanged for 5 cows?

Part I
1.) 630
2.) 1.8 hours
3.) 4:9
4.) 850
5.) 6 bags
6.) P450.00
7.) 36kg
8.) 183
9.) C = 27; w1 = 27; w2 = 36
90 – 14 = 76m^2
10.) 62 pictures
11.) P650.00
12.) 15.6% loss or 16% loss
13.) 36cm^2
14.) 33cm
15.) 12 hours

Part II
1.) Average = 15
Sum = 165
Middle = 15
18 + 19 + 20 = 57

2.) 30 days

3.) $latex 81 \dfrac {\pi}{4} – \dfrac {81}{2}$ cm^2 = 23.085cm^2

4.) 27:8

5.) 2.3cm

Part III
1.)  120.
2.)  P750.00
3.) 375 rabbits