This is the 2011 Math Challenge for Grade 6 questions 26-50. Questions 1-25 can be found **here**.

26.) A pyramid-like circus tent has a 32 m by 28 m rectangular base. If it is 15 m high, what volume of air does it enclose?

Answer:

Solution: v = (lwh)/3

v = (32 × 28 × 15)/3

v = (13440)/3

v = 4480 cu m.

27.) The parallel sides of a trapezoidal farm are 210 m by 150 m. If they are 120 m apart, what is the area of the farm in hectares?

Answer: 2.16 hectares

Solution: A = ((a+b))/2 h

A = ((210+150))/2 120

A = 360/2 (120)

A = 21600 sq m

Convert meter to hectares = 2.16 hectares

28.) A beach ball has a radius of 5 dm. What is its volume?

Answer: 65.42 cu dm

Solution:

cu dm

29.) A room is 6 m long, 5 m wide and 3 m high. The 4 walls and ceiling are to be painted. If the windows and door have an area of 14 m2, what is the area to be painted?

Answer: 82 m2

Solution:

ceiling: 6m x 5m = 30 sq m

opposite walls 1: (6m × 3m) × 2 = 36 sq m

opposite walls 2: (5m × 3m) × 2 = 30 sq m

Total area painted is 96 sq m.

Subtracting the windows and walls we have 96 sq m – 14 sm = 82 sq m.

30.) How many square tiles of side 1 dm are needed to tile the floor of a bathroom 2.2 m long and 1.8 m wide?

Answer: 396 dm

Solution: A = lw

A = 22 cm x 18 dm = 396 dm.

31.) The length of a rectangle is 7 cm longer than the width. If the perimeter is 62 cm, find the length.

Answer: 19 cm

Solution: Let x – side

P = 2l + 2w

62 = 2(x + 7) + 2(x)

62 = 2x + 14 + 2x

62 = 4x + 14

62 – 14 = 4x

48 = 4x

12 = x

Length = x + 7 = 12 + 7 = 19 cm.

32.) I used 2/5 of my money in one store and 1/3 of what remained in a second store. If I had exactly P56 left, how money did I have at first?

Answer: P 140.00

Solution:

From the first store, 2/5 of the money was spent, so only 3/5 of it was left. In the second store, 1/3 of 3/5 = (1/3)(3/5) = 1/5 was spent which means that 2/5 of the entire money was left. Now, 2/5x = 56, x = 140.

33.) A car traveled at 50 km/h for 4 hours and at 60 km/h for 3 ½ hours. What was the average speed for the whole journey?

Answer: 54.67 km/hr

Average speed: total distance/ total time.

Total distance = (50 km/hr × 4 hrs) + (60 km/hr × 3 ½) = 200km + 210 km = 410 km

Total time – 4 + 3.5 = 7.5

Average speed: 410 km/7.5 hrs = 54.67 km/hr

34.) About how many times must a jogger go completely around a park 120 m by 140 m to make sure he has run at least 3 km?

Answer: 6 times

Solution:

Perimeter of the park = 520 meters

Jogger has to run at least 3km or 3000 meters

3000 m ÷ 520 = 5.769 or at least 6 times

35.) A salesman has a basic salary of P3,500. He gets a commission of 5% on all sales above P50,000. How much did he get in a month when his sales amounted to P264,600?

Answer: P 16, 730.00

Solution:

264,600 × 0.05 = 13, 230 (commission)

13, 230 + 3,500 = 16, 730

36.) How many circles of radius 5 cm can be cut from a piece of paper 50 cm by 60 cm?

Answer: 30

Solution:

The diameter of a circle is 10 cm which means that you can cut 5 along the width and 6 along the length. This means that you can cut 5 × 6 = 30 circles.

37.) A piece of cartolina is 60 cm by 48 cm. What is the least number of squares that can be cut from it with no material wasted?

Answer: 20 pcs

GCF of 48 and 60 is 12. This means that we can cut squares with side length 12 cm. We can cut 5 along the length and 4 along the width. So, we can cut 5 x 4 = 20 squares.

38.) A sewing box is 24 cm by 18 cm by 6 cm. What is its total surface area?

Answer: 1368 cm2

Solution:

A=2(wl+hl+hw)

A = 2[(18 × 24)+(6 × 24)+(6 × 18)]

A = 2((432) + (144) + (108))

A = 2(684)

A = 1368 sq cm.

39.) A 450-m long nylon string is to be cut into 35 pieces for kites. How many kites will have string?

Answer: 12 kites

40.) There are 5 red balls, 6 white balls and 7 green balls in a box. If one ball is taken without looking, what is the probability that it is white?

Answer: 1/3

41.) Mona Luise has 78 foreign stamps; she has 16 less than twice as many Philippine stamps. How many stamps has she?

Answer: 125

Solution: Let x – Philippine’s stamps

2x-16 = 78

2x = 78 + 16

2x = 94

2x/x = 4/2

x = 47

Number of stamps = 47 + 78 = 125

42.) Karyl’s garden is 24 m long and 18 m wide. If her fence needs posts that are 2 m apart, how many posts does she need?

Answer: 40 posts

Solution: For the length, he will need (12 + 1) × 2 = 26 posts (why?) and for the width, he will need (9 – 2) × 2 = 14 posts.

43.) What is the smallest number that can be divided by all the numbers 1 to 10?

Answer: 2520

Solution: Get the LCM of all numbers form 1 to 10.

44.) A book is 24 cm by 17 cm by 2.5 cm. How many books can be packed into a box 5 dm by 3.5 dm by 2.5 dm, internal dimensions?

Answer: 40

Solution: Three things can only be arranged in 6 ways. So, pair the length, width, and height of the box with length, width, and height of the books, and then divide. The pairs whose integer quotients have the highest result when multiplied are (50, 2.5) × (35, 17) × (25, 24) = 20 × 2 × 1 = 40.

45.) A rectangular block of wood 56 cm by 16 cm by 12 cm is to be cut into cubes of side 4 cm. How many can be cut from it?

Answer: 168 pcs

Solution: (Volume of block of wood)/(volume of cubes)

=(56 × 16 × 12)/(4 × 4 × 4)

=(10752)/(64)

=168 pcs

46.) One cube has an edge twice the edge of another cube. What is the ratio of the volume of the bigger cube to the smaller cube?

Answer: 8 : 1

47.) A crew of 8 people can build a concrete wall in 6 days. How long would it take a crew of 3 people working at the same rate, build the same wall?

Answer: 16 days

Solution: 8 people building for 6 days is equivalent to 1 person building it for 48 days. If there are 3 people, then they can do the work in 48/3 = 16 days.

48.) The cost of mailing a letter first class is P29 for the first ounce and P23 for each additional ounce. A letter weighs exactly N ounces, where N is a counting number, and the total cost of mailing is P190. What is the value of N?

Answer: 8

Solution: N = [(190 – 29)/23] + 1

N = [171/23] + 1

N = 7 + 1

N = 8

49.) A farmer sold some melons at P40 each and twice as many mangoes at P10 each. He received a total of P720. How many melons did he sell?

Answer: 12

Solution: Let x – number of melon

2x – mango

40(x) + 10(2x) = 720

40x + 20x = 720

60x = 720

60x/60 = 720/60

x = 12

50.) Jomariz, Janus and Jolas have P268 together. Janus has P15 more than Jomariz and Jolas has twice as much money as Janus. How much money do Jomariz and Janus have together?

Answer: P126.50

Solution:

Let x – Jomariz’s money

x + 15 – Janus’ money

2(x + 15) – Jolas’ money

x + (x + 15) + 2(x + 15) = 268

x + (x + 15) + 2x + 30 = 268

4x + 45 = 268

4x = 223

4x/4 = 223/4

x = 55.75 (Jomariz’ money)

x = 55.75 + 15 = 70.75 (Janus’ money)

Jomariz’ and Janus’ money together = 55.75 + 70.75 = 126.50

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