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1 Grade 6 Metrobank MTAP DepEd Math Challenge Courtesy by: Pids Nogales Files Prepared by: Dulce Buenaventura 2008 Elimination Metrobank-MTAP-DepEd Math Challenge Grade 6 Solve each item and write the answer on the blank before the number. Use π = 3.14

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1

Metrobank

MTAP

DepEd

Math Challenge Courtesy by: Pids Nogales Files

Prepared by:

Dulce Buenaventura

2008 Elimination Metrobank-MTAP-DepEd Math Challenge Grade 6

Solve each item and write the answer on the blank before the number. Use π = 3.14

2

_________ 1.Write “two billion, fifty-five million, eighty-six thousand, three hundred eighty”

in symbols.

_________ 2 How many times as great is the underlined 6 in 465 786 745 as the 6 that

is not underlined?

_________ 3.Evaluate: 24 x 12 – 9 ÷ 3.

_________ 4 Express 3960 as a product of its prime factors.

_________ 5.What digit(s) can be placed in the blank in 56 8__9 to make it divisible by 3?

_________ 6.How many numbers between 30 and 150 leave a remainder of 1 when divided by 5?

_________ 7.What number is 397 more than 3456?

_________ 8.What is the value of 6 in 864 357 475?

_________ 9.Write 8 x 106 + 4 x 104 + 5 x 103 + 7 x 102 + 8 x 10 + 9 as a single number.

_________ 10.What is the average of the numbers 54, 56, 58, 60 and 62?

_________ 11.A number is multiplied by 9. To the product, 145 is added. If the result is 721,

what is the original number?

_________12.Round 34 995 450 to the nearest ten thousand.

_________ 13.What is the smallest 5-digit number, with no zero in it, that rounds to 36 000

to the nearest thousand.

_________ 14. Write MCMLXXVII in Hindu-Arabic.

_________ 15. Find the GCF of 154 and 198.

_________ 16. Find the LCM of 154 and 198.

_________ 17.Change 6 7

12 to an improper fraction.

_________ 18.Reduce 96

108 to lowest terms.

_________ 19.Change 147

15 to a mixed number with the fraction part in lowest terms.

_________ 20.Nina bought 8 pieces of cartolina. She used 2 1

3 pieces for one project and 3

3

4 for

a second project. How many pieces of cartolina did Nina use?

_________ 21. How many pieces of cartolina remained with Nina?

_________ 22.Tom received some money for Christmas. He gave ½ of it to his mother and 1

5

of it to his sister. If he had exactly P150 left, how much did he receive?

_________ 23. An H. E. teacher bought 121 m of cloth for her pupils. If each pupil was given

2 3

4 m of cloth and the cloth was just enough for all of them, how many pupils are there?

_________ 24. If 34.5 x 623.8 = 345 x N, what is N?

_________ 25. Find the value of 15 – 6 + (-3) – (-5).

_________ 26. The sides of a triangle are 21.5 cm, 24.25 cm and 18.6 cm. Find its perimeter.

_________ 27. If n:50 = 18:30, find n.

_________ 28. A 240 cm3 solution of acid contains 12 cm3 of acid. How many cm3 of acid

would 1 liter of the solution contain?

-1-

_________ 29. 54 plywood boards, each with a thickness of 1.25 cm, are piled together one

on top the other. How high is the pile?

3

_________ 30. How many pieces of tape 3.4 cm each, can be cut from a roll of ribbon 25 m long?

_________ 31.Change 9

13 to a decimal correct to the nearest hundredth.

_________ 32. If 162 = n% of 450, what is n?

_________ 33. If 575 = 46% of N, what is N?

_________ 34. A vendor borrowed P7,500 from their cooperative at 8% a year. If he paid at the

end of 1 ½ years, how much in all did he pay?

_________ 35. The factory cost of a car is P650,000. If the dealer added 20% to the cost as

gain, how much did he sell the car?

_________ 36. An advertisement says: Regular price – P45; now only P31.50.What is the

percent discount?

_________ 37. A family spends 35% of their monthly salary on food. On a circle graph, how

many degrees will represent food?

_________ 38. ∠x and ∠y are supplementary. If ∠y is 32° more than ∠x, find ∠y.

_________ 39. A base angle of an isosceles triangle is 9° more than the vertex angle.

Find the vertex angle.

_________40.A man-made lagoon has a radius of 25 m. If you walk thrice around it, how

many meters will that be?

_________41.One milk can has a radius of 5 cm and a height of 16 cm. Another has a radius of

6 cm and a height of 14 cm. How much more milk does the second can hold than

the first can?

_________42.A ricefield is trapezoidal in shape. The parallel sides are 67 m and 85 m in length

and the distance between them is 82 m. What is its area?

_________43.A box for raffle stubs is to be completely wrapped with colored paper. If the box is

5 dm long, 3.4 dm wide and 6 cm high, what is the area to be covered?

_________44.A lounge is 4 m long and 3.2 m wide. It is to be tiled with square tiles of side 2 dm.

How many tiles are needed?

_________45.A triangle with a base of 9 dm and a height of 8 dm is to be cut from a thin cardboard

1 m long and 9 dm wide. How much of area of the cardboard will be left?

_________46.How many circles of radius 4 cm can be cut from a piece of cartolina 65 cm by 50 cm?

_________47.The shadow of a man 6 ft tall is 10 ft at the same time that the shadow of a

telegraph pole is 35 ft. Find the height of the pole?

_________48.By selling an article for P68, a man loses 15%. How much must he sell it to gain 20%?

_________49.A hollow metal pipe has an external radius of 5 cm and an internal radius of 4.5 cm.

If the pipe is 1 m long, find the volume of the metal used to make the pipe.

_________50.The scale of a house is 2 cm to 3 m. If a living room is 3 cm by 4 cm on the scale,

what is its actual area?

-2-

(2000 – 2001) FIRST NATIONAL METROBANK-MTAP-DECS ELEMENTARY

4

Solve each item and write the answer on the blank before the number.

_________ 1. What is the place value of 9 in 393,648,618?

_________ 2. What is the value of 7 in 457,809,050?

_________ 3. How many ten thousands are there in 6.5 billion?

_________ 4. Round off 456,670 to the nearest ten thousand.

_________ 5. What is the multiple of 100 closest to 776?

_________ 6. Round off to the nearest thousand and find the sum: 7 376 + 5 539 + 8 412

_________ 7. Write MCMLXXII in Hindu-Arabic.

_________ 8. Mang Tasyo picked 256 mangoes from one tree, 319 from a second and 278 from

a third. How many mangoes in all did he pick?

_________ 9. How many times as great is the underlined 7 in 4 756 272 than the 7 not underlined?

_________ 10.Which is larger, 13

15 or

16

19 ?

_________ 11. Write 3 x 105 + 5 x 104 + 7 x 102 + 8 x 10 + 5 in standard form.

_________ 12. Change 8 5

6 to an improper fraction.

_________ 13.Change 123

8 to a mixed number.

_________ 14. Luz bought 21 5

6 m of white cloth and 16

7

9 of blue cloth. How many meters of cloth

_________ 15.Liz has 6 7

8 m of lace. She needs 15

5

6 m. How much more lace does she need to buy?

_________ 16 Multiply: 5 3

5 x 3

4

7.

_________ 17.A scout master has 45 3

4 m of rope. How many 2 ½ pieces of rope can he cut from it?

_________ 18. How many twelfths are there in 2 3

4 ?

________ 19. Round off 34.56551 and 4.781675 to the nearest thousandth and find the sum.

_________ 20. If 23.56 x 878.6 = 0.2356 x N, what is N?

_________ 21. The three sides of a triangle have lengths of 3.52 cm, 4.8 cm and 5.7 cm.

Find its perimeter.

_________ 22. Roly bought 3 ballpens at P4.75 each and 3 notebooks at P8.50 each. How much

did he pay?

_________ 23. If Roly gave the salesgirl a P50-bill, how much change did he get?

_________ 24. If caimitos cost P5.50 each, how many can I buy with P100?

_________ 25. What is the ratio of 75 cm to 1.2 m?

_________ 26. If 9 : 13 = 108 : N, what is N?

_________ 27. If Rita can type 55 words a minute, about how many minutes, to the nearest

minute, will it take her to type a 1695-word article?

_________ 28. A piece of cartolina 35 cm long and 10 cm wide was cut into strips 2.5 cm long

and 2 cm wide. How many strips were cut?

page1

_________ 29.If 5

7 of a number is 35, what is the number?

_________ 30. Write 0.353535… as a ratio of two whole numbers.

5

_________ 31. P765 is divided among three children in the ratio 2:3:4. How much did the child

_________ 32. The ratio of the areas of 2 pieces of land is 3:4. If the smaller piece has an area

of 270 m2, what is the area of the larger piece?

_________ 33.Change 1 2

5 to percent.

_________ 34. Change 175% to a fraction in lowest terms.

_________ 35.Change 7

9 to percent. Give the answer to the nearest tenth of a percent.

_________ 36. During a sale, Nancy bought a dress marked P175 at a 15% discount. How

much did she pay for it?

_________ 37. Aling Nena borrowed P8,500 from their cooperative at 12% simple interest. If she paid

P5,000 after one year and paid what remained with its interest at the

end of the second year, how much in all did she pay?

_________ 38. One angle of ABC measures 105°. What is the triangle called?

_________ 39. An aquarium is 6 dm long, 4 dm wide and 5 dm high. What is its volume when

it is 4

5 full?

_________ 40. The length of a rectangular field is 123 m and the width is 86m. If a jogger goes

around it 5 times, how many meters will that be?

_________ 41. What is the area of the field in No. 40?

_________ 42. The figures are made up of equal squares. If Fig. A has a perimeter of 54 cm,

what is the perimeter of Fig. B?

Fig. A Fig. B

_________ 43. A circular garden has a radius of 5 m. What is its area? [Use π= 3.14]

_________ 44. Santan bushes are to be planted, around the circumference of the circular

garden in #43, at 3 dm apart. How many bushes will be planted?

_________ 45. A conical tent has a radius of 4 meters and a height of 6 meters. How much air does it

enclose?

_________ 46. A 10 cm by 7 cm picture is pasted on a cardboard 16 cm by 13 cm. What area

of the cardboard is seen?

_________ 47. A metal ball has a radius of 3 cm. What is its volume?

_________ 48. The vertex angle of an isosceles triangle is 72°. Find each base angle.

_________ 49. An angle is 16° more than its supplement. Find the angle.

_________ 50. The scale in the house of Mr. Cruz is 3 cm to 2 m. If the living room is 8 cm by 9 cm in

the plan, what is its actual area? page2

FIRST NATIONAL - Metrobank-MTAP-DepEd-NCR Math Challenge

6

Solve each item and write the answer on the blank before the number. [Use π = 3.14]

_________ 1. What is the place value of 6 in 762,435,029?

_________ 2. How many times greater is the underlined 8 in 586,738,060 than the 8 that is

not underlined?

_________ 3. Gemma can type 350 words in 5 minutes. How many words can she type in ¾

of an hour?

_________ 4. Luis and Carlo repaired a computer and were paid P1,165.50. If Carlo worked for

12 hours and Luis worked for 9 hours, how much was their pay per hour?

_________ 5. Chester worked for 8 hours each day for 5 days. He earned P2190.00. How much

did he earn per hour?

_________ 6. Write MDCXLVI in Hindu-Arabic.

_________ 7. If (8386 + 5236) – 6863 = N, find N.

_________ 8. Stephen earns P25.00 per hour at a fast food restaurant. He worked 37 hours last

week and 32 hours this week. How much did he earn?

_________ 9. Write six hundred eighty millionths in figures.

_________ 10. Write 22 x 52 x 17 in standard form.

_________ 11. Subtract 8189 from 9304.

_________ 12. What is the largest number that rounds to 150 to the nearest ten?

_________ 13. At the rate of 50 kph, how long will it take a train to cover 600 km?

_________ 14. If N : 12 = 60 : 84, find N.

_________ 15.If 5

6 :

3

4 = 10 : N, find N.

_________ 16 If 57 men can do a job in 10 days, how many men can do it in 19

_________ 17.The average of two fractions is 13

16 . One fraction is

3

2 . What is the other?

-1-

_________ 18.What number is midway between 3

8 and

3

4 on the number line?

_________ 19. What is the reciprocal of (1 ÷ 2/3) ÷ 2/3 ?

7

_________ 20.How many 2 1

3 m pieces of cloth can be cut from a roll 50 m long?

_________ 21. What decimal is two-thirds of the distance from 2.1 to 3.9 on the number line?

_________ 22. There are 60 students in a Grade 6 class. If 35 of them are boys,what is the ratio

of boys to girls?

_________ 23. What is the average of 1

2 ,

2

3 and

1

6 ?

_________ 24. Nine out of 12 pupils who study their lessons in Math get high grades. If 240 pupils

in a school study their lessons, how many will get low grades?

_________ 25. Mr. Carlos was born on December 16, 1897. He died on December 16, 1989.

How old was he when he died?

_________ 26. What is 12% of 540?

_________ 27. 56 is what percent of 224?

_________ 28. What is the value of (0.1)2 – (0.1)3 ?

_________ 29. A carpet originally priced at P2000.00 is on sale at 15%. What is the sale price?

_________ 30. What fraction of a kilogram, in lowest terms, is 650 grams.

_________ 31. A dining room is 5 m long, 4 m wide and 3.5 m high. How many square meters of

wall paper are needed to cover the 4 walls if the door and windows have an area of

5m2?

_________ 32. A grass lawn is 56 m long and 42 m wide. Near each corner there is a flower plot

6 m by 4 m. How many square meters of the lawn is covered with grass?

_________ 33. An angle is 24o more than its complement. Find the angle.

_________ 34. In FGH, ∠F = ∠G = 70° . Find∠ H .

_________ 35. In DEF, ∠D = 20° more than ∠E and ∠F = 90°. Find ∠D .

_________ 36. What is the volume of a rectangular box with a length of 7.6 dm, a width of

4.5 dm and a height of 6 dm.

_________ 37. The angles of a triangle are in the ratio 2 : 3 : 5. Find the largest angle.

-2-

_________ 38. A club starts with 6 members. Beginning with the next meeting, each member is

to bring 2 new members. If the procedure continues, how many will be present

in the fourth meeting?

8

_________ 39. A piece of work can be done in 40 days by 25 men. After 16 days, 13 men

are transferred. In how many days can the remaining men finish the work?

_________ 40. There are 12 people in a room; 6 people are wearing socks, 4 people are

wearing shoes and 3 people are wearing both. How many people are bare feet?

_________ 41. Three-fourths of the area of a square is 108 cm2. How long is one side of the square?

_________ 42. Aling Tina borrowed P 8,500 from their coop with a simple interest of 12% a year.

How much in all will she pay after 3 years?

_________ 43. A salesman has a basic salary of P2500 and a commission of 5% on all sales.

How much did he earn in a month when his sales amounted to P185,650?

_________ 44. The ratio of two numbers is 3 : 5. If the sum is 136, find the bigger number.

_________ 45. A courtyard is 24 m long and 20 m wide. In the middle, a circular area of radius

4 m is covered with colored tiles. What percent of the area of the courtyard, to the

nearest tenth of a percent, is the area covered with tiles?

_________ 46. The scale of the plan of a house is 2 cm to 3 m. If the room is 7 cm by 6 cm in the

plan, what is the actual area of the room?

_________ 47. If represents 20 families and 36 are drawn on a graph to represent

the families in a barrio, how many families are there in the barrio?

_________ 48. Using all the 4 digits 1, 2, 3, and 4 and no digits repeat, how many 4-digit

telephone extension numbers can be produced?

_________ 49. A frog tries to climb an 8 m deep well. Each day, it climbs 2 m but at night, it slips

down 1 m. How many days will it take the frog to climb out of the well?

_________ 50. Find the sum of 1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100.

-3-

2005 Regional Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

9

A. 15-second questions – 2 points each

__________1. Give the prime numbers between 30 and 40.

__________2. What is the biggest number N that will make N – 7 < 35 true?

__________3. Lino worked for 9 ½ hours on Monday and 7 ¾ hours on Wednesday. How much longer did he work on Monday than on Wednesday?

__________4. If 𝑛

24 =

52

96 , what is n?

__________5. The sum of two numbers is 135. The second number is twice the first . What is the

bigger number?

__________6. Express 270 as a product of its prime factors.

__________7. What is the value of (6 𝑥 16 + 8)

5?

__________8. What percent of 80 is 52?

__________9. If you buy a P350 shirt at 15% discount, how much will you save?

__________10. Ellen uses 3.5 liters of water on her houseplants each week. Find the average

number of milliliters of water she uses a day.

__________11. What is the rat io of 250 m to 0.25 km?

B. 30-second questions – 3 points each __________1. Lina pays P6 for a one-way fare to school. For how many twoway fares will P100

be enough?

__________2.What is the value of k in 𝐾

60 + 56 = 87?

__________3. Write the product of 30,000 x 5,000 in scient ific notation

__________4. What is the mean of 16, 14, 15, 16, 17, 16, 11?

__________5. If 54% of the 150 Grade 6 pupils in a school are boys, how many are girls?

__________6. If 25 x N – 56 = 19, what is N?

1 C. 1-minute questions – 5 points each Use π = 3.14

__________1. The distance from Manila to Baguio is 250 km. If we left Manila at 5:00 a.m. and reached Baguio at 1:20, what was our average speed for the journey?

10

__________2. A painter can paint a room in 12 hours. An apprentice can paint the same room

in 24 hours. How long will it take them to paint the room together?

__________3. Three-eights of the 480 students in a school are boys and 2/3 of them are in the primary. How many boys are in the intermediate?

__________4. The cost of a book increased from P95 to P110. By how many percent, to the

nearest whole percent, did the cost increase?

__________5. A child glues together 42 cubes with 1 cm edges to form a solid rectangular brick. If the perimeter of the base is 18 cm, find the height of the brick in centimeters.

__________6. Find the value of 2 x (33 + 103 – 23).

Clincher questions:

__________1. If 75% of the 48 quest ions in a Math test are on fractions, how many quest ions

are on fractions?

__________2. Dave had P500. He bought 3 pocket books and had P9.50 left. What was the average cost of the pocket books?

__________3. What whole numbers will make the sentence 10 – x ≥5?

Do-Or-Die questions: ___________1. There are 15 more ducks than pigs in a farm. If there are 102 legs, how many

ducks are there?

2

2006 Regional Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

11

A. 15-second questions – 2 points each

__________1. 17 more than the sum of 33 and 19 is equal to what number?

__________2. If 3.05 x 76.9 = 234.545, what is 30.5 x 0.769?

__________3. What digit(s) placed in the blank in 377__4 will make it divisible by 12?

__________4. What is the sum of the largest prime less than 100 and the smallest prime greater than 100?

__________5. If ¾ of the area of a rectangle is 84 cm2, what is the whole area?

__________6. If 6 men can finish a job in 8 days, how long will 4 men finish the same job if they

work at the same rate?

__________7. Rita can put her pictures 4, 5 or 6 to a page in her album, with 2 pictures left

over in each case. What is the smallest number of pictures for this to happen?

__________8. A 15 cm by 10 cm picture was enlarged so that its dimensions increased by 20%.

What is the area of the enlarged picture?

__________ 9. The vertex angle of an isosceles triangle is 9o more than a base angle. What is

the vertex angle?

__________10. What is the largest 5-digit number which rounds to 27,000 to the nearest thousand?

__________11. The perimeter of a square is 186 cm. How long is one side?

B. 30-second questions – 3 points each

__________1. Five consecutive whole numbers have a sum of 225. What is the largest

number?

__________2. A piece of plast ic sheet is 4 m by 3.2 m. What is the smallest number of equal

squares into which it can be cut?

__________3.How many ribbons, each 1 7

8 dm long can be cut from a roll 3 m long?

__________4. What is the smallest number by which you can mult iply 2520 to make it a perfect

square?

__________5. Find the product of the prime numbers immediately before and after 30.

__________6. Two numbers are in the rat io 5:8. I f the difference is 36, what is the larger of the

two numbers?

1

C. 1-minute questions – 5 points each

12

__________1.One cube has an edge of 9 cm. A second cube has an edge 2

3 that of the first

cube. What is the rat io of the volume of the first cube to that of the second cube?

__________2. A bunch of new 50-peso bills are consecutively numbered A23486 to A23500. What is the total peso value of the bills?

__________3. A train travels 60 km in ¾ hour. If it maintains the same average speed, how far will it t ravel in 2 ½ hours?

__________4. Nine small squares are put toget her to form a bigger square. If the perimeter of the big square is 192 cm, what is the area of each small square?

__________5. Today, March 10, is Friday. What day is it 100 days from today?

__________6. A piece of rope 75 m long is cut into three pieces in the rat io 4:5:6. How long is the longest piece?

Clincher questions

__________1. What is the 20th odd counting number?

__________2. To what exponent should 2 be raised to give a value of 512?

__________3. How many mult iples of 12 are there between 200 and 290?

Do-Or-Die questions __________1. How many digits are printed by a printer that prints all the whole numbers from

1 to 728 inclusive?

2

2005 Regional Individual Finals Metrobank-MTAP-DepEd Math Challenge

13

Solve each problem on scratch and write the answer on the blank before the

number.[ 2 points each] Use π = 3.14

__________ 1. Write MCMLXXII in Hindu-Arabic numerals.

__________ 2. Write nine billion, sixty-five million, nine thousand, seven hundred

eighty-six in Hindu-Arabic. __________ 3. The product of 74 x 80 is 5,920. If 74 is mult iplied by 100 and 80 divided by 5,

the product of the result ing numbers is the same as mult iplying 5,920 by what number?

__________ 4. When water freezes, its volume increases by 0.9%. What volume of water, to

the nearest mL, must be frozen to get 1000mL of ice? __________ 5. A car went at 55 kph for 3 hours and at 65 kph for 2 hours. What was

the average speed for the whole journey? __________ 6. Lulu can put her pictures 4, 5, or 6 to a page, in her album, with 2 left over

in each case. What is the smallest number of pictures that Lulu has for the

condit ion to hold? __________ 7. A man left home by bus at 8:15 a.m. and reached a town 45 km away

at 9:45. What was his average speed per hour to the nearest kilometer?

__________ 8. What is the least common mult iple of 36, 60 and 54?

__________ 9.Which is greater,14

17 or

23

29 ?

__________ 10. On a boat, 16% travel first class, 56% travel third class. If 238 travel second class, how many passengers are on the boat?

__________ 11. One of the parallel sides of a trapezoidal field is 187 m and the other is

157 m. If those two sides are 125 m apart, find the area of the field in hectares, to the nearest hectare.

__________ 12.One cube has an edge of 15 cm. Another cube has an edge 2

3 that of the

first cube. What is the rat io of their volumes? __________ 13. What digit(s) can be placed in the blank in 377__4 so that it is divisible by 12?

__________ 14. A rectangular park is 115 m long and 95 m wide. How many t imes must a jogger go completely around it to make sure he has covered 5 kilometers?

__________ 15. What is the surface area of a beach ball of radius 4.5 dm?

In Parts II and III , solve each problem on scratch paper and write a neat

solution on the

space provided. Show details of the solution as partial credit will be given.

Part II. Solve each problem. [3 points each] 1. A boy sold two magazines for P60 each. One was sold at a loss of 20% and the

second at a gain of 20%. How many percent is the gain or loss on both

transactions?

2. 3.

4.

5.

Part III. Solve each problem. [5 points each] 1. 2.

3.

1

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]

14

__________ 1. 5 more than thrice the sum of 12 and 17 equals_____.

__________ 2. What is the largest 3-digit number that is a mult iple 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 mult iple 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 t iles, 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 revolut ions, to the nearest whole number, will a car wheel with a diameter

7 dm, make to cover a km?

2. 512,000 square t iles, 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 posit ion 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?

1

2007 Regional Individual Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

15

Solve each item and write the answer on the blank before the number. [ 2 points each]

Use π = 3.14

__________ 1. A typist can type an average of 85 words in 2 minutes. At this rate, how long would it take to type a term paper of about 1232 words if a 5-minute allowance is

given for change of paper? Give the answer to the nearest minute.

__________ 2. The base of isosceles ABC is 3 cm less than a leg. If the perimeter is

42 cm and the alt itude to the base is 12 1

5 cm, what is its area?

__________ 3. The outer dimensions of a picture frame are 36 cm by 24 cm. If the frame

is uniformly 3 cm around a picture, what is the area of the picture?

__________ 4. A park is 115 m long and 95 m wide. How many t imes must a jogger go

around the park completely to make sure he has run at least 5 kilometers?

__________ 5. A job can be done by 30 men in 35 days. After 10 days, 5 men left. How long

will the remaining men finish the job?

__________ 6. A car t ravels 140 km in 3.5 hours and a train travels 30 km in 50 min. Find the

rat io of the speed of the car to that of the train.

__________ 7. A hectare of riceland yields an average of 75 cavans per harvest. At that rate about how many cavans, to the nearest cavan, is the yield per harvest of a field 275 m by

250 m.

__________ 8. A piece of rope 165 m long is cut into 3 pieces in the rat io 1

2 :

1

3 :

5

12 . How long

is the longest piece?

__________ 9. Electric posts are 50 m apart. How many posts are needed from town A to town B which are 2.6 km apart if the first post is at A and the last post is at B?

__________ 10. A salesman has a basic salary of P4,500 and a commission of 5% on all sales above P50,000. What were his total sales in a month when he earned P13,177.50?

__________ 11. How many cubic meters of soil will be needed to raise a circular plot of radius

7 m by 1.2 dm?

__________ 12. What is the remainder when 330 is divided by 4?

__________ 13. If 6401 ÷ N gives a quotient of 74 and a remainder of 37, what is N?

__________ 14. PQ is a straight line. If ∠b = 3 ∠a – 15o, find ∠b.

C

P b a Q

__________ 15. A can 2 ½ dm long and 2 ½ dm wide and 4 dm high is full of oil. How many 250 ml of oil can be filled from it?

1

II. Solve on scratch paper. Then, write a neat and complete solution on the given

space. Label all parts of the answer. [3 points each]

16

1.A lounge needs 72 m of carpet 5

4 m wide to cover it . How many meters of carpet,

3

2 m wide will cover the same lounge?

2. A boy cycles a certain distance for 42 minutes at 10 km/hr. If he tries to cover the same distance in 35 minutes, what must be his speed?

3. A wooden cube is of side 12 cm. Find the volume of the largest sphere that can

be cut from it . [Use π = 3.14]

4. How many degrees is the smaller angle between the hands of a clock at 1:40?

5. A class of 33 students counted off from 1 to 33. Each student who counted a mult iple of 3 stood UP. Then, the students who remained seated counted off again from 1 and

those who counted a mult iple of 3 stood UP. The procedure was repeated. How many students remained seated after the 3rd standing UP?

III. Solve on scratch paper. Then, write a neat and complete solution on the given

space. Label all parts of the answer. [5 points each]

1. A machine can cap 1,800 bott les in one hour; another can cap 1,700 bott les an hour.

There are 20,000 bott les to be capped. How long will it take the 2 machines to do the

capping together?

2. City A is 625 km from City B. Greg left City A at 6:30 A.M. at 100 km/h for City B. Fifteen

minutes later, Rey left City B for City A at 80 km/h. At what time will Greg and Rey meet assuming they are using the same road?

3. In one year, the gross income of a company was P16,500,000, which after the payment of all working expenses including salaries, left a balance of P625,000. The next year, the gross

income increased by 10% and the working expenses

increased by 12%. What balance remained?

2

2008 Regional Individual Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

I.Write the answer on the blank before the number. [2 points each]

17

__________ 1. Express 13,860 as a product of prime factors using exponents.

__________ 2. What is the greatest common factor of 420 and 630?

__________ 3. What is the least common multiple of 420 and 630?

__________ 4.What is the reciprocal of the sum of 2 3

7 and 4

2

3 ?

__________ 5. A radio is marked at P740. If a discount of 20% is given, the

shopkeeper will lose P18. What is the cost price of the radio?

__________ 6. A jar filled with water weighs 13 kg. When half of the water is

poured out, the jar and its contents weigh 6 3

4 kg. What is the weight of the jar?

__________ 7. The total cost of 3 rulers at P9.50 each and a dozen similar

notebooks is P322.50. How much does 8 of the notebooks cost?

__________ 8. May guessed their classroom to be 9.5 m long. When measured, it

was 10.3 m. What was her error percent to the nearest tenth of a percent?

__________ 9. A salesman has a basic salary of P4,500 a month. He gets a

commission of 6% of all sales above P50,000. How much did he get in a month

when his sales amounted to P497,550?

__________ 10. The cost of a watch including a tax of 25% is P937. If the watch

was sold for P1087, how many percent is this above the cost price, to the nearest whole percent?

__________ 11. An 18 cm by 24 cm picture is framed on colored cardboard so

that there is a 5 cm margin at the bottom along the 24 cm width and 4 cm on

each of the other 3 sides. What area of the cardboard can be seen?

__________ 12. Lita has m pencils. Jim has 6n pencils, and Wendy has 3n more

pencils that Lita. How many pencils do they have altogether?

__________ 13. A piece of wire was 16 m long. Mr. Lin used 2 m 56 cm of it. What

percent of the piece of wire was left?

__________ 14. If n = 9, what is the value of {15 – n}3 – 5n?

__________ 15. On a map with a scale of 4 cm : 1 km, an estate has an area of

12 cm2 on the map. How many square meters is the area of the estate?

1

II.Solve each item on scratch paper; then write a neat and complete solution on the space after Part III and the paper provided. [3 points each]

18

__________ 1. How many books, 25 cm long, 12 cm wide and 2.4 cm thick can

be packed into a box 5 dm long, 3.7 dm wide and 2 dm high, internal

dimensions?

__________ 2. 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?

__________ 3. What is the ones digit of 7345?

__________ 4. A speculator lost 35% of his capital in one operation, and lost 40%

of the remainder in a second operation. If he then had P15,600, how much had

he at first?

__________ 5. The marked price of a pair of shoes is P680. If a discount of 30% is

given, the shopkeeper will lose P94. How much must he sell the shoes so that he

has a gain of 20% on the cost price?

III. Solve each on scratch paper; then write a neat and complete solution on

the space provided. [5 points each]

__________ 1. Lita and Rose start jogging on a 110 m circular track. They begin

at the same point, but jog in opposite directions. Lita at 8

3 meters per second

and Rose at 7

3 meters per second. Find the number of times that they will pass

each other during the first 15 minutes of jogging.

__________ 2. Each of the numbers 622 and 831 have digits whose product is 24,

i.e. 6 x 2 x 2 =24. How many 3-digit whole numbers have digits whose product is

24? Show all those you find.

__________ 3. What is the sum of all the 4-digit numbers that can be obtained by

using each of the digits 3, 5, 7 and 9 once?

2

2007 Regional Team Finals Metrobank-MTAP-DepEd Math Challenge

19

A. 15-second questions – 2 points each

__________1. What is the sum of the largest prime number less than 100 and the smallest prime

number greater than 100?

__________2. If 3.05 x 76.9 = 234.545, what is 30.5 x 7.69?

__________3. What 2 digits may be placed in the blank in 73528__ to make it divisible by 6?

__________4.If 2

3 of the area of a rectangle is 84 cm2, what is one-half of the area?

__________5. In a Grade 6 class of 45 pupils, 80% got a grade of 80 and below. How many pupils got a grade of 80 and below?

__________6. For every 9 garlands that Jane can make, Ann can make 8. If Ann made 56 one

afternoon, how many garlands did the two make?

__________7. A 16 cm by 12 cm picture was enlarged so that its dimensions increased by 25%.

What are the dimensions of the enlarged picture?

__________8. Give the smallest and the largest numbers that round to 250 to the nearest ten.

__________9. Carla bought green mangoes at P20 a dozen and sold them at 3 for P8. If she

sold 20 dozens, how much did she gain?

__________10. What is the smallest mult iple of 7 that is divisible by 13?

____________11. What is MCMXCIV in Hindu-Arabic?

B. 30-second questions – 3 points each

_____________1. Five consecutive odd numbers have a sum of 215. What is the largest number?

_____________2. A piece of plast ic sheet is 3 m by 2 m. How many 6-dm by 5-dm pieces can be cut from it?

_____________3. What is the smallest number by which you can mult iply 2520 to make it a

perfect square?

_____________4. What digit can be placed in 52,14__ to make it divisible by 7?

_____________5. A stove marked P1750 was bought for P1505. What was the percent of discount?

_____________6. What is the sum of 137 and the quotient of 540 divided by 12?

1

C. 1-minute questions – 5 points each Use π = 3.14

20

_____________1. A distance of 65 km is represented on a map by 8 cm. To the nearest tenth of

a cm, how long is a line representing 95 km?

_____________2. A train travels 60 km in 3

4 hour. If it maintains the same average speed, how

far will it t ravel in 2 ½ hours?

_____________3. A cube of side 4 dm is made up of individual 1 dm cubes. How many of the 1 dm cubes are face to face with exactly 4 other cubes?

_____________4. A grass lawn is 85 m by 60 m. At each end of the length, there is a circular

flower plot of radius 9 m. What is the area covered by grass to the nearest square meter?

_____________5. What is the smallest number that leaves a remainder of 5 when divided by 12, 14, 18?

_____________6. What is the sum of the cubes of the first 3 odd prime numbers?

Clincher questions

_____________1. What is the largest 3-digit number divisible by both 2 and 3?

_____________2. Each base angle of an isosceles triangle is 9o more than the vertex angle.

Find each base angle.

_____________3. A piece of rope 75 m long is cut into three pieces in the rat io 4:5:6. How long

is the longest piece?

Do-Or-Die questions

_____________1. A class of 25 stood in a circle. They counted off 1,2,3,1,2,3, … Each student

that counted 3 sat down. After the third round of counting, how many students remained

standing?

2

2004 Sectoral Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

21

A. 15-second questions – 2 points each

__________1. What is the largest whole number less than 190 that is div isible

by 78?

__________2.I am thinking of a number. If 2

5 of the number is

4

9 , what is the

number?

__________3. Shoes that cost P600 are sold for P750. What is the gain percent?

__________4. Bus fare is P4.00 for the first 4 km and 50¢ for each additional km.

How much is the fare for 10 km?

__________5. One-fourth of Jose’s age plus ½ of his age equals 15 years. How old is Jose?

__________6. How many times as great is 140,000 than 104

__________7. A rectangle has an area of 108 cm2. If the length is 12 cm, what

is the width?

__________8. From Manila, it takes 3 ½ hours to reach Lucena. To reach Lucena

at 4:15 PM, what time should I leave Manila?

__________9. If the total surface area of a cube is 216 cm2, what is the length of

an edge?

__________10. What digit may be used to replace 4 in 849 to make it div isible

by 11?

__________11. 40% of 70 is what percent of 280?

B. 30-second questions – 3 points each

__________1. An equilateral triangle has a side of 30 cm. How many smaller

equilateral triangles of side 10 cm can be cut from it?

__________2. A plane travelling at 600 km/hr was 50 km from an airport at 5:30.

At what time will it be over the airport?

__________3. A rich man div ided P900,000 among his three sons in the ratio 3:4:5 according to age. How much did the eldest got?

__________4. The mean of three numbers is 37. If two of the numbers are 34 and

32, what is the third number?

1

__________5. If the side of a square is increased by 40% by how many percent

22

is the area increased?

__________6. A rectangular garden has an area of 368 m2. If the length is 23 m,

what is its perimeter?

C. 1-minute questions – 5 points each

__________1. A salesman has a basic salary of P4,500 and a commission of 5%

on all sales above P50,000. How much did he earn when his monthly sales

amounted to P285,000?

__________2. An isosceles triangle has a base of 20 cm and an altitude of 12 cm.

If each leg is 15 cm, find the length of the altitude to a leg.

__________3.John, Jun and Joey together have P240. P6 more than 1

3 of the

money belong to John. Of the remaining money, Jun has P20 more than Joey. How much of the money belong to Jun?

__________4. What is the reciprocal of 0.016?

__________5. In a 4-digit number, the thousands digit is thrice the units digit; the

hundreds digit is 3 more than the units digit and the tens digit is the difference

of the thousands and the units digit. Find at least 2 numbers that satisfy the

conditions.

__________6. If s:r = 3:5 and r:t = 4:7, what is s:t?

Clincher questions

__________1. If thrice a number decreased by 10 equals 53, find the number.

__________2.Mother has a P500-bill. At her bank, she asked that 2

5 be changed

into P20-bills, ½ into P50-bills and the rest into 5-peso coins. How many bills and

coins did she get?

__________3. The cost of a book increased from P95 to P110. By how many

percent, to the nearest whole number, did the cost increase?

Do-Or-Die questions

__________1. A beam 2 m long, 14 cm wide and 8 cm thick weighs 1.4 kg per

cubic decimeter. What is the weight of the whole beam? [

__________2. Four small squares are put together to form a bigger square. If

the perimeter of the big square is 72 cm, what is the area of each

small square?

2

2005 Sectoral Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

23

A. 15-second questions – 2 points each

__________1. What digits can be put in the blank in 785__ to make it div isible

by 3?

__________2. What is 160% of 250?

__________3. What is the sum of the squares of the first 4 odd numbers?

__________4. What is the least common multiple of 5, 8 and 9?

__________5. 60% of 40 is what percent of 240?

__________6. What is 4872 div ided by 24?

__________7. How many times as great is 325,000 than 103?

__________8. The area of a rectangle is 240 cm2 and its width is 15 cm. What is its length?

__________9.66 2

3 % of the 186 Gr. 6 students in a school are 13 years old or

younger. How many of the students are above 13 years old?

__________10. What digit can be used to replace 1 in 817 to make it div isible

by 11?

__________11. How long is ¾ of a string of length 216 m?

B. 30-second questions – 3 points each

__2__

__________1.What is the value of 4 + 1

5 ?

__________2. The perimeter of a rectangle is 64 cm. What is the length if the

width is 6 cm shorter than the length?

__________3. The ratio of the earnings of a man and his helper is 5 : 3. If the man

__________4. A radio was sold for P900 at a profit of 20%. How much was the

profit?

__________5. If the side of a square is increased by 50%, by how many percent

is the area increased?

1

__________6. When an 8-m post cast a shadow of 10 m, a flagpole cast a

24

shadow of 18 m. How tall is the flagpole?

C. 1-minute questions – 5 points each

__________1. If the sum of the edges of a cube is 72 cm, what is its total surface area?

__________2. A swimming pool can be filled in 12 hours by 6 equal pumps

working together. How many of the same pumps are needed to fill it in 9 hours?

__________3.Pete, Roy and Kim together have P240. P9 more than 1

3 of the

money is Pete’s. Of the remaining money, George has P8 more than Roy. How

much of the money belongs to Roy?

__________4. Four small squares are put together to form a bigger square. If the

perimeter of the big square is 104 cm, what is the area of each small square?

__________5. A car traveled for 4 hours at 58 km/h and for 3 hours at 51 km/h.

What is its average speed for the whole journey?

__________6.What is the reciprocal of 4 2

5 + 3

3

4 ?

Clincher questions

__________1. How many 2-digit numbers are div isible by 7?

__________2. The rooms in a hotel are numbered from 101 to 451. How many

odd numbered rooms are there?

__________3.Of three numbers, two are 1

2 and

1

3 . What must the third number be

so that the average of the three is 1?

Do-Or-Die questions

__________1. A beam 3 m long, 14 cm wide and 6 cm thick weighs 1.2 kg per

cubic decimeter. What is the weight of the beam?

2

2006 Sectoral Finals Metrobank-MTAP-DepEd Math Challenge Grade 6

25

A. 15-second questions – 2 points each

__________1. What is the largest whole number less than 200 that is div isible

by 79?

__________2.I am thinking of a number. If 2

7 of the number is

6

11 , what is the

number?

__________3. Shoes that cost P600 are sold for P720. What is the gain percent?

__________4. Bus fare is P7.50 for the first 4 km and 50¢ for each additional km.

How much is the fare for 20 km?

__________5.One-fifth of Jose’s age plus ½ of his age equals 14 years. How old is Jose?

__________6. An equilateral triangle has a perimeter of 36 cm. What is the area of a square with the same perimeter?

__________7. A rectangle has an area of 180 cm2. If the length is 15 cm, what is the width?

__________8.From Manila, it takes 5 ½ hours to reach Baguio. To reach Baguio at 1:30 p.m., what time should I leave Manila?

__________9. If the total surface area of a cube is 150 cm2, what is the length of an edge?

__________10. 754,000,000 is how many times as great as 7,540?

__________11. If a*b = ab – b2, what is 8*4?

B. 30-second questions – 3 points each

__________1. A plane traveling at 800 km/hr was 80 km from an airport at 5:30.

At what time will it be over the airport?

__________2. A rich man div ided P108,000 among his three sons in the ratio 3:4:5

according to age. How much did the middle son get?

__________3. 60% of a class consists of girls. If 24 boys are in the class, how many

students are in the class?

1

__________4. The mean of three numbers is 61. If two of the numbers are 43 and

57, what is the third number?

26

__________5. There are 65 electric posts with the first being in Town A and the

last in Town B. If the distance between posts is 50 m, how far is Town A from

Town B?

__________6. A rectangular garden has an area of 270 m2. If the length is 18 m,

what is its perimeter?

C. 1-minute questions – 5 points each

__________1. A salesman has a basic salary of P3,000 and a commission of 6%

on all sales above P50,000. How much did he earn when his monthly sales

amounted to P240,500?

__________2. A swimming pool is 50 m long and 35 m wide. It is 2.8 m deep at

one end and 1.4 m deep at the other. If the water surface is 1dm from the rim of the pool, what volume of water is in it?

__________3. If r:s = 3:5 and s:t = 4:7, what is r:t?

__________4. What is the reciprocal of 0.012?

__________5. On a boat, 16% travel first class; 56% travel third class and 252

travel second class. How many people are on the boat?

__________6. What digit(s) can you put in the blank in 377__4 to make it div isible

by 12?

Clincher questions

__________1. If thrice a number decreased by 10 equals 53, find the number.

__________2.Mother has a P1000-bill. At her bank, she asked that 1

5 be changed

into P20-bills, 1

4 into P50-bills and the rest into P5-coins. How many of P5-coins did

she get?

__________3. The cost of a book increased from P95 to P110. By how many

percent, to the nearest whole number, did the cost increase?

Do-Or-Die questions

__________1. ABFG is a rectangle, AB = 10 cm, EF = 3cm, Area (ABFG) = 20

cm2 and Area (BCDE) = 5 cm2. Find ED. A B C

G F

2 E D

27

2004 Division Orals Metrobank-MTAP-NCR Math Challenge Grade 6

A. 15-second questions – 2 points each

__________1. Arrange the digits in 4716 to make the biggest and the smallest numbers.

__________2. Write 82 million, 45 thousand, 3 in symbols.

__________3. Find the value of (12 x 18) – (12 x 8) by using the distributive law in

reverse.

__________4. Write 103 + 105 as one number.

__________5. Water makes up 70% by weight of the human body. Nick has a

weight of 45 kg. How many kg of water make up Nick’s weight?

__________6.The product of two numbers is one. If one number is 2 2

3, what is the

other?

__________7. What digit must replace 3 in 837 to make it div isible by 11?

__________8. The base of an isosceles triangle is 4 cm more than a leg. If the

perimeter is 43 cm, find the base.

__________9. The sum of two numbers is 42.9. If one number is twice the other,

what is the smaller number?

__________10. What is the regular price of a dress that is sold for P320 at 20%

discount?

__________11. What is the ratio of 25 cm to 2.5 m?

B. 30-second questions – 3 points each

__________1. If a school has 6000 pupils and 240 teachers, what is the teacher to pupil ratio?

__________2. Three times a number plus 17 equals 62. What is the number?

__________3. For working for 1 ½ hours, a man was paid P60. At the same rate

how much will he be paid for a day of 8 hours?

__________4. A room is 11 m by 9 m. There is a 5 m by 4 m carpet in the middle.

What area of the room is not covered by the carpet?

1

28

__________5. One morning an electrician spent 1 ½ hours on his first job. 2 ¼ hours on his second job and ¾ hour on his third job. How many hours did he

work that morning?

__________6. Of 120 students, 55% are girls. How many are boys?

C. 1-minute questions – 5 points each

__________1. Water flows out of a pipe at the rate of 10 liters per minute. At that

rate, how long will it take to fill a tank 12 dm by 9 dm by 8 dm?

__________2. Sixteen squares are put together to form a bigger square. If the

perimeter of each small square is 24 cm, what is the area of the big square?

__________3. One number is 4 more than twice another number. If the sum of the two numbers is 97, find the smaller number.

__________4. Frank received a bonus of P5,000. He gave ¼ of it to his mother. His

mother gave 1

5 of her money to her sister Marta. How much did Marta receive?

__________5. In a closing out sale, a sala set costing P15,000 was sold for

P12,300. What was the percent discount?

__________6. What is the least number of students needed for different dances if the teacher wants to be able to put them in groups of 6, 8 or 10?

Clincher questions

__________1. How many hundreds are there in a million?

__________2. In a bus, the ratio of the number of people standing to the number

of people sitting is 5:16. If 48 people are sitting, how many are standing?

__________3. On a trip, Mr. Cruz drove for 2 ½ hours, stopped for lunch and then

drove again for 1 ¾ hours. If the whole trip took 5 hours, how long did he stop

for lunch?

Do-Or-Die questions

__________1. A pipe has a diameter of 2.0 cm. If 1 cm is added to its

circumference to make it larger, what is the new diameter to the nearest tenth of a cm? [Use π = 3.14]

__________2.A number is div ided by 2 and the result is multiplied by 1

3. The

second result is squared and 1 is added. If the result of the 4 operations is 50,

what is the original number?

2

29

2005 Division Orals Metrobank-MTAP-DepEd Math Challenge Grade 6

A. 15-second questions – 2 points each

__________1. What is the greatest common factor of 72 and 90?

__________2. 15 is what percent of 20?

__________3.If 3

4 of a number is 450, what is

3

5 of the number?

__________4. One edge of a cube is 10 cm. What is the sum of all the edges of the cube?

__________5. An angle is 95o, what is its supplement?

__________6. The length of a rectangle is 24 cm and the width is 15 cm. What

is its perimeter?

__________7. If 125% of a number is 150, what is the number?

__________8. In a class, there are 8 girls for every 11 boys. If there are 24 girls,

how many boys are there?

__________9. What is the value of 4(15 - 3) + 18 ÷ 3 ?

__________10. Write 7,800,000,000 in scientific notation.

__________11. The number pairs 11 & 13, 17 & 19 are called twin primes. Give

any other twin primes less than 50.

B. 30-second questions – 3 points each

__________1. In a test, Connie missed 6 items and got 80%. How many items

were in the test?

__________2. What is 16% of 450?

__________3. What is the area of a 24.5 cm by 9.3 cm rectangle?

__________4. Norma practices her piano lessons for 35 minutes a day. How many hours does she practice in 7 days?

__________5. I have enough money to spend P180 a day for 40 days. If I

reduce my expenses to P150 a day, how long will my money last?

1

30

__________6. What is the regular price of a school bag bought for P315 at a

30% discount?

C. 1-minute questions – 5 points each

__________1. A laborer can finish a job in 5 hours. What part of it can he finish

from 8:30 AM to 9:45 AM

__________2. If a car covers 85 km on 10 liters of gasoline, how many liters, to

the nearest liter, will it use to cover 300 km?

__________3. A vendor buys tilapia at P59.50 a kg and sells them at P70 a kg.

How much will he gain if he sells 150 kg?

__________4. A square measures 8 ¾ cm on one side. What is the perimeter of

a rectangle formed by 3 squares placed side by side?

__________5. A circle has a radius of 7 cm. How much bigger is the area of a

circle whose radius is 3 times as long as that of the smaller circle? [Use π = 22/7]

__________6. Liza has 12 five-peso and 12 ten-peso coins. She gave her

brother P85. How much money had she left?

Clincher questions

__________1.Which is bigger,9

5 or

11

6?

__________2. At 12% discount, how much will a toaster marked P1200 cost?

__________3. A bag and a blouse cost P240. If the blouse costs P15 less than

twice as much as the bag, how much does the blouse cost?

Do-Or-Die question

__________1. Lucy has P550 but she owes someone P1000. She received a

certain amount as gift. After paying her debt, she had P1120 left.

2

31

2008 Division Orals Metrobank-MTAP-NCR Math Challenge Grade 6

A. 15-second questions – 2 points each

__________1. Give two consecutive even numbers whose sum is 54.

__________2.If 3

5 of a number is 24, what is ½ of the number?

__________3. A bee flies 0.4 km in 1 minute. About how many kilometers does it fly in 1 hour?

__________4. How many perfect squares, like 4, are there from 1 to 110 inclusive?

__________5. The sum of the squares of two consecutive integers is 85. What is the sum of the

integers?

__________6.The sum of two numbers is 5

6. I f one is ½ , what is the other?

__________7. Write 68% as a fraction in lowest terms.

__________8.The product of two numbers is 1. If one number is 1 5

8 , what is the other?

__________9.Give the number midway between ¼ and 1/3.

__________10. How many t imes as great is 1 billion than a thousand?

__________11. The sum of two numbers is 33. If one is twice the other, what are the two

numbers?

B. 30-second questions – 3 points each Use π = 3.14

__________1. If four t imes a number plus 7 is 55, what is 7 t imes the number?

__________2. The area of a parallelogram is 100 cm2. I f the base is 8 cm, what

is the height?

__________3. Find the area of a circle with a diameter of 16 cm.

__________4. If a*b = a + b + ab and x*1 = 5, what is x?

__________5. How many 3-cm cubes can be cut from a block of wood 9 cm by 12 cm

by 15 cm?

1

32

__________6.If the product of two numbers is 15 5

6 and one number is 3

1

3 ,

what is the other?

C. 1-minute questions – 5 points each

__________1.Three squares of side 8 3

4 cm are placed side by side to form a rectangle. Find

the perimeter of the rectangle formed.

__________2. Mr. Santos had P4,000 in his current account. After deposit ing some amount and making a check for P7,500 to pay a debt, he had P900 left in the account. How much did he

deposit?

__________3. The sum of the squares of two consecutive posit ive integers is 145. What is the

sum of the two integers?

__________4. A 25 cm by 15 cm by 10 cm rectangular tank contains 3 metal cubes of edge 5

cm and is filled with water to the brim. Find the volume of the water.

__________5. A 12 cm by 5 cm rectangle is cut along one diagonal. What is the sum of the

perimeters of the two triangles formed?

__________ 6.If 11

15 of a pole is above the ground and 8 dm of it is in the ground, how many

meters long is the pole?

Clincher questions

__________1. The rat io of 2 numbers is 5:6. If the sum is 275, find the bigger number.

__________2. Two numbers have a product of 56 and a sum of 18. Find the numbers.

(2+ 3

4 )

__________3.Find the value of ?

(2 - 3

4 )

Do-Or-Die questions __________1. What is the sum of all the posit ive factors of posit ive 225?

2

33

2007 Division Team Competition Metrobank-MTAP-DepEd Math Challenge

A. 15-second questions – 2 points each

__________1. The diameter of a circular lot is 15 m. What is its radius in

centimeter?

__________2.Reduce the fraction 108

132 to simplest form.

__________3. A regular pentagon has a perimeter of 140 cm. How long is one

side?

__________4. Express 32 as a sum of 2 prime numbers.

__________5. The sum of two numbers is 150.6. One number is twice the other.

What is the bigger number?

__________6. The sum of 44 and 25 is equal to 84 minus a certain number.

What is that number?

__________7. A rectangle has an area of 300 cm2. If its length is 20 cm, what is its perimeter?

__________8. An angle is 42o. What is its complement?

__________9. What is n if 5n is equal to 252?

__________10. How many multiples of 5 are there between 1 and 1,000?

__________11. How many sq. centimeters are equal to one sq. meter?

B. 30-second questions – 3 points each [Use π = 3.14]

__________1. What is the product of 4,000 x 45,000 in scientific notation?

__________2.If ¼ of a number is 144, what is 1

3 of the number?

__________3.Three-eighths of 40 roses are red, 2

5 of the remaining roses are

white and the rest are pink. How many are pink?

__________4. A lady deposited P50-bills amounting to P30,000. How many

paper bills did she give the teller?

1

34

__________5. The radius of a circle is 2 dm. What is the area of a bigger circle

whose radius is 3 times the first circle?

__________6. Find 3 consecutive whole numbers whose sum is 138.

C. 1-minute questions – 5 points each

__________1. A ring with a diameter of 2 dm has 3.5 cm added to its

circumference to make it larger. What is its new diameter?

__________2. The dimensions of a 16 cm by 24 cm picture are enlarged by

20%. What is the area of the enlarged picture?

__________3. Mr. Santos had P4,000 in his bank but owed somebody P7,500.

After making a deposit and writing a check to pay his debt, his bank account

amounted to only P900. How much money did he deposit?

__________4. A child glued together 42 cubes with 1 inch edges to make a

solid rectangular brick. If the perimeter of the base is 18 inches, find the height

of the brick in inches.

__________5. Find two numbers whose sum is 53 and whose difference is 15.

__________6. The cost of a book increased from P180 to P200. By how many

percent to the nearest whole percent did the price increase?

Clincher questions

__________1.By how much does 2

3 of 48 exceed

2

5 of 25?

__________2. If apples cost 4 for P35 and oranges cost 4 for P42, how much

will a dozen apples and a dozen oranges cost?

__________3. A whole number div isible by 6 is greater than 170 but less than

210. what is the largest number that satisfies both conditions?

Do-Or-Die questions

__________1. The average grade of Lilia and Rose is 88, the average grade of

Lilia and Kate is 87 and the average grade of Rose and Kate is86.Find the

2

35

Solve each item and write the answer in the blank before the number.

__________________ 1. What number is 17 more than the difference of 95 and 37?

__________________ 2. Use exponents to express 5040 as a product of its prime factors.

__________________ 3. If 3,108 x 235 = 730,380, what is 31.08 x 2.35?

__________________ 4. What is the value of 43 – 6 x 3 + 52?

__________________ 5. What is the value of 5 in 358 348 129?

__________________ 6. The product of 55 x 75 is closest to which mult iple of 100?

__________________ 7. Change 2 ¾ to percent.

__________________ 8. Change 4.75 to a mixed number with the fraction in lowest terms.

__________________ 9. What is x in 4 : x = 36 : 63?

__________________ 10. What percent of 1,250 is 450?

__________________ 11. How many millions are there in 5 billion?

__________________ 12. A man travels 56 km in one hour. How far can he go in 2 5/7 hours?

__________________ 13. What is the GCF of 420 and 504?

__________________ 14. What is the LCM of 420 and 504?

__________________ 15. The car of Mr. Burayag consumes 9 liters of gasoline to cover

84 km. How far can it go on 12 liters of gasoline?

__________________ 16. How many segments can be named from the figure below?

A B C D E F G H

__________________ 17. The scale of a map is map is 1 cm to 30 km. Two cit ies are 7.5 cm on

the map. How far apart are they?

__________________ 18. An angle is 10˚ more than its supplement. Find the angle.

__________________ 19. 196 is what percent of 560?

__________________ 20. Three numbers are in the rat io 3 : 4 : 5. If their sum is 168 find the

biggest of the three.

__________________ 21. A family has a monthly income of P18,750. If they spend 35% of it on

food, how much do they spend on food?

__________________ 22. A radio was bought for P510 at 15% discount. What was the marked

price?

__________________ 23. If 2/3 of the area of a square is 54 cm2, what is its perimeter?

1

36

__________________ 24. A picture 12 by 7 cm is framed on a piece of colored board 18 cm by

11 cm. What area of the board can be seen?

__________________ 25. A rectangular tank is 1.2 m long, 0.8 m wide and 0.5 m high. How

many liters of water can it hold?

__________________ 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?

__________________ 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?

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

__________________ 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?

__________________ 30. How many square t iles of side 1 dm are needed to t ile the floor of a

bathroom 2.2 m long and 1.8 m wide?

__________________ 31. The length of a rectangle is 7 cm longer than the width. If the

perimeter is 62 cm, find the length.

__________________ 32. I used 2/5 of my money in one store and 1/3 of what remained in a

second store. If I had exact ly P56 left, how money did I have at first?

__________________ 33. A car t raveled 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?

__________________ 34. About how many t imes must a jogger go completely around a park

120 m by 140 m to make sure he has run at least 3 km?

__________________ 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?

__________________ 36. How many circles of radius 5 cm can be cut from a piece of paper 50

cm by 60 cm?

__________________ 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?

__________________ 38. A sewing box is 24 cm by 18 cm by 6 cm. What is its total surface

area?

__________________ 39. A 450-m long nylon string is to be cut into 35 pieces for kites. How

many kites will have string?

__________________ 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?

2

37

__________________ 41. Mona Luise has 78 foreign stamps; she has 15 less than twice as many

Philippine stamps. How many stamps has she?

__________________ 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?

__________________ 43. What is the smallest number that can be divided by all the numbers 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?

__________________ 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?

__________________ 46. One cube has an edge twice the edge of another cube. What is the

rat io of the volume of the bigger cube to the smaller cube?

__________________ 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?

__________________ 48. The cost of mailing a letter first class is P29 for the first ounce and P23

for each addit ional 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?

__________________ 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?

__________________ 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?

3

38

2009 NATIONAL FINALS TEAM ORAL

METROBANK-MTAP-DEPED MATH CHALLENGE

Part 1: 15 seconds (11 items)

1. Manila t ime is 4 hours ahead of Dubai t ime. A trip from Manila to Dubai, takes nine

hours. What t ime will you arrive in Dubai if you leave Manila at 8:00 P.M.?

2. How many digits are there in the number N = 210 x 58?

3. The faces of a big cube are painted. Then the cube is cut into 125 unit cubes. How

many of the unit cubes have exactly two painted faces each?

4. What is the smallest number which when mult iplied by 20 will give a perfect cube?

5. On a quiz show, each quest ion is worth four t imes as much as the previous quest ion.

The fourth quest ion is worth P1,600. How much was the first quest ion worth?

6. In 3 ___ 6 ___ (-9), what two different basic operations can you place in the ___ that will

7. What number will you add to the numerator and denominator of 7

1 so that the result

becomes 4 t imes?

8. In an election, one of the two candidates got 45% of the votes and this was 20 votes

less than that of the other candidate. How many votes did the winner get?

9. What is the sum of the even numbers from 1 to 100?

10. Use all the 4 one-digit prime numbers to form two fractions with the smallest possible sum. What are the fractions?

11. By how many percent is the volume of a rectangular prism increased when the length

and the height are each doubled?

-1-

39

Part 2: 30 seconds (5 items)

1. There are many numbers which divide 109 with a remainder of 4. List ALL two-digit numbers that have this property.

2. Nic puts together 42 one-cm cubes to form a rectangular prism. If the perimeter of the

base is 18 cm, what is the height of the prism?

3. Colored pens are sold in packs of 3 pens or packs of 5 pens. What is the least number of packs one needs to buy to have exactly 42 colored pens?

4. On four long quizzes where the scores could be from 0 to 50, Lina had an average

score of 45. What was the lowest score that she could have obtained on one test?

5. During typhoons, the weather is reported every 18 minutes on Channel 3 and every 12

minutes on Channel 6. Both stat ions broadcast the weather at 1:30 P.M. When is the

next t ime that the stations will broadcast again the weather at the same t ime?

Part 3: 60 seconds (5 items)

1. Using the digits 2, 3, 5, 6, and 7 what two-digit number and three-digit number can be

formed whose product is the smallest?

2. Two joggers run around an oval t rack in opposite directions. One jogger runs around the track in 56 seconds. The joggers meet every 24 seconds. How many seconds does

it take for the second jogger to run around the track?

3. Mang Jose makes wooden legs for stools and tables. Each stool uses 3 legs while each table uses 4 legs. Mang Jose has made 68 legs. How many stools and tables can he

make if he makes at least 1 of each kind? Give two possible combinations.

4. Ms. Cruz computed the average score of his mathematics class with 50 pupils as 83.

But she discovered that Lea’s score of 81 was misrecorded as 31 and Ben’s score of 65

was misrecorded as 85. What is the correct average of the class?

5. In the pattern below, what is the difference between the last number and the first

number in row 25?

1 3 5

7 9 11 13 15 17 19

21 23 25 27 29

-2

40

2009 METROBANK-MTAP-DEPED

MATH CHALLENGE NATIONAL FINALS GRADE 6 TEAM ORAL

Part 1: 15 seconds (11 items)

1.Solution 8:00 P.M. + 9 hours is 5:00 A.M.

5:00 A.M. – 4 hours is 1:00 A.M.

2.Solution 210 x 58 = (2 x 5)8 x 22 = 108 x 4 = 100 000

000 x 4 = 4 000 000 000

3.Solution bottom layer: 4 x 3 unit cubes upper layer: 4 x 3 unit cubes

middle layers: 4 x 3 unit cubes

total number of unit cubes with exactly two painted faces each

4.Solution 20 = 22 x 5

So the smallest number that should be mult iplied by 20 so that the product is a

perfect cube is 2 x 52 which is equal to 50.

5.Solution 1600 4 4 4 = 25

6.Solution The bigger the absolute value of a

negative number, the smaller is the

negative number. So x (for mult iplication) should be placed before -9.

÷ (for division) cannot be placed after 3

because it will be performed first and performing division then mult iplication will

not result to the least answer. - (for subtraction) cannot be placed

after 3 also because 3 – 6 is -3 which

when mult iplied by -9 gives a posit ive answer,

Therefore, + (for addit ion) should be placed after 3. So, 3 + 6 x (-9) = -51

Answers: +, x (order must be correct)

7.Solution

4 t imes 7

1 is

7

4.

But 7

4 is equivalent to

14

8, so 7 should be

added to both the numerator and

denominator of 7

1.

That is, 7

4

14

8

77

71

.

8.Solution Total number of votes = 20 (55% - 45%) = 20 .10 = 200

Number of votes of the winner = 200 x .55 =

9.Solution

2 + 4 + 6 + … 96 + 98 + 100

Pair the numbers so that each pair will total

102 as shown above. Then mult iply 102 by the number of pairs which is 25.

So 25 x 102 = 2550

10.Solution These prime numbers are 2, 3, 5, and 7.

For the sum of the two fractions to be the smallest, their denominators must be 5 and

7. Now,

35

29

7

3

5

2 while

35

31

7

2

5

3 .

3

5

2,

11.Solution Original volume = l x w x h

New volume = 2 x l x w x 2 x h = 4 x l x w x h Increase = 400% - 100% = 300%

Page1

102

102

41

Part 2: 30 seconds (5 items)

1.Solution 109 – 4 = 105 105 = 3 x 5 x 7

Mult iply two factors of 105 at a t ime, i.e. 3 x

5, 3 x 7, and 5 x 7. Answers: 15, 21, 35

2.Solution The area of the base must be a divisor of 42.

But 42 = 3 x 7 x 2. For the perimeter to be 18

cm, the base must be 7 cm x 2 cm. Therefore the height of the prism is 3 cm.

3.Solution To obtain the least number of packs,

maximize the packs of 5.

42 5 = 8 remainder 2 The sum of the smallest mult iple of 5 and

the remainder 2 that is divisible by 3 is 12. So, 4 packs of 3 pens and 6 packs of 5

pens. And 4 + 6 = 10.

4.Solution To get the lowest possible score on one

test, Lina’s score in each of the 3 other quizzes should be perfect. This gives 3 x 50

= 150 as her total score in 3 quizzes. Her

total score in 4 quizzes is 4 x 45 = 180. So, her score in 1 quiz must be 180 – 150 = 30.

5.Solution The least common mult iple of 18 and 12 is

36.

So 1:30 P.M. + 36 minutes is 2:06 P.M. Answer: 2:06 P.M. or 14:06

Part 3: 60 seconds (5 items)

1.Solution For the product to be smallest, the digit 2

must be the tens digit of the two-digit number and the digit 3 must be the

hundreds digit of the three-digit number.

Then 5 must be the ones digit of the two-

digit number and 6 must be the tens digit

of the three-digit number. This is so because the mult iplier 25 is the smallest

2.Solution

7

4

56

241

7

4

n

24 , n = 42

3.Solution 68 4 = 17 tables Therefore one possible combination is 4

stools and 14 tables.

For the other combinations on the number of stools (s) and the number of tables (t),

the number of stools should be mult iples of 4 in order to use all the legs.

Answer: (s, t) = (4, 14), (8, 11), (12, 8), (16,

5), (20, 2)

4.Solution 81-31 = 50 so Lea’s recorded score is 50 less

than her actual score. 85-65 = 20 so Ben’s recorded score is 20

more than his actual score.

50 – 20 = 30 should be added to the total of the scores of the class

30 50 = .6 So 83 + .6 = 83.6

5.Solution The differences between the last number

and first number in rows 1, 2, 3, 4, and 5,

respectively are 0, 2, 4, 6, and 8. The 25th number in this pattern is 48.

Page2

42

2009 NATIONAL FINALS INDIVIDUAL ORAL

METROBANK-MTAP-DEPED MATH CHALLENGE

GRADE 6 Part 1: 15 seconds (10 items)

1. If 45 x n = 805, what is the value of 45 x n + 7?

2. Gold purity ratings are proportional. If a 24-carat gold is 100% pure, what is the purity of

an 18-carat gold?

3. What number should be added to the numerator and denominator of 3

1 to get a fraction

that is equivalent to 4

3?

4. All 7 sticks of equal lengths will be used to form a triangle. How many such triangles can be formed?

5. You are asked to cut a 20-cm long stick into 10 equal lengths. How long will it take you

if each cut takes 3 seconds?

6. It takes one man one day to dig a 2m x 2m x 2m hole. How many days does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?

7. If x + y = 12, y + z = 20, and x = 5, what is z?

8. If 50% of a number is 20, what is 80% of the number?

9. If the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are all multiplied together, how many zeros are

at the end of their product?

10. What is 1010 divided by 1 billion?

Part 2: 30 seconds (5 items)

1. Aling Edna sells mangoes in bags of 5 kg and 10 kg. She has a total of 250 kg to sell in all. If she sells twice as many bags of one than the other and all the mangoes are sold,

how many bags of 10 kg mangoes each are sold?

2. There are as many boys as there are girls. When 16 boys left, the number of remaining boys became half the number of girls. How many pupils were there at the start?

1

43

3. What is the sum of 40% of 4

1 and 50% of

5

1?

4. A 7 unit x 7 unit x 7 unit big cube is painted on all faces and then cut into unit cubes.

How many of the unit cubes have no paint

5. What is the area of the trapezoid below? (Note: A printed strip will be given to each contestant.)

Part 3: 60 seconds (5 items)

1. A pail that contains 40 nails of the same weight, weighs a total of 175g. When it contains

20 such nails, it weighs a total of 95g. What is the weight of each nail?

2. In a 40-item multiple choice type of test, scoring is done as:

4

Lina had items with correct, incorrect and no answers. She got a score of 32. How could she have gotten it?

3. Observe the following pattern:

1 3 5 7 9 11

13 15 17 19

In which row is the sum of the numbers equal to 343?

4. Two opposite sides of a square were increased by 6 cm. The other two opposite sides were decreased by 6 cm. By how much was the area changed?

5. Different rectangular prisms will be formed out of 16 unit cubes. What are the dimensions of the prism with the least surface area?

2

44

2009 NATIONAL FINALS INDIVIDUAL ORAL GRADE 6

Part 1: 15 seconds (10 items)

1. Solution

45 x n + 7 = 805 + 7 = 812

2. Solution

%754

3

24

18

3. Solution

4

3

8

6

53

51

4. Solution

A triangle with sides 2 sticks, 2 sticks, and 3 sticks can be formed. Another triangle with sides 1

stick, 3sticks, and 3 sticks can also be formed. So there are 2 different triangles. Answer: 2

5. Solution

9 cuts x 3 seconds = 27

6. Solution

2m x 2m x 2m = day

m8 3

per person

day

m8 3

per person x 3 persons = 24 m3 in one day for 3 persons

4m x 4m x 4m 24 m3 per day = 3

8

24

64 days

22or

3

8

7. Solution

In x + y = 12, y = 7 since x = 5. In y + z = 20, z = 13 since y = 7.

8. Solution

50% of a number is 20, so the number is 40. 40 x 0.8 = 32

9. Solution

When 2 is multiplied by 5, there will be a zero at the end of their product. Also, when 10 is multiplied by any number there will be a zero at the end of their product. So there are 2 zeros at the end of the product of 1, 2, 3, 4, 5, 6, 7, 8, 9, and10.

1

45

10. Solution

1010 has 10 zeros while 1 billion has 9 zeros, so1010 1 billion = 10 Answer: 10

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part 2: 30 seconds (5 items)

1.Solution

10 x 5 kg + 20 x 10 kg = 50 + 200 = 250 kg Answer: 20

2.Solution

At the start, the number of boys equals the number of girls. When 16 boys left, the number of remaining

boys became one half the number of boys at the start. So there were 32 boys at the start. And there were 64 pupils in all at the start. Answer: 64

3.Solution

5

1

10

2

10

1

10

1

50

5

40

4

1

4.Solution

Removing all the unit cubes on the surface of the big cube will give a 5 unit x 5 unit x 5 unit cube. So there are

125 unit cubes that have no paint. Answer: 125

5.One possible solution:

Figure 1 Figure 2 Figure3

In Figure 1, the total area of the 2 triangles is 2 square units.

In Figure 2, the total area of the 3 squares is 3 square units.

In Figure 3, the total area of the 5 triangles is 2.5 square units.

Area of the trapezoid = 7.5 square units.

2

1

3

2

46

Part 3: 60 seconds (5 items)

1.Solution

175 - 95 = 80g

40 - 20 = 20 So, 20 nails weigh 80g. 80 20 = 4g

2.Solution

Having 29 correct answers is not possible because this means that there will be 12 incorrect answers and the total number of items will be 41 which is already over 40 without accounting for the items with no answer.

Having 32 correct answers is not possible because there will be no items with incorrect and no answer but it is

Answer: 30 correct, 8 incorrect, and 2 no answer; or 31 correct, 4 incorrect, and 5 no answer

3.Solution

The sums of the numbers in the rows are 1, 8, 27, and 64 which are all perfect cubes, i. e. 13, 23, 33, and 43, respectively. Continuing the pattern, the sums are 125, 216, and 343, i.e. 53, 63, and 73. So it is the 7th row.

4.Solution

Take any square with area greater than 6 cm say a 10 cm x 10 cm square. Its area is 100 square cm.

Considering the conditions given in the problem, the resulting figure becomes 16 cm x 4 cm. So the area is 64 square cm.

Therefore the area decreased by 36 square cm. Answer: [It decreased by 36 square cm.]

5.Solution

The possible rectangular prisms would have dimensions: 1unit, 1unit, and 16 units; 1unit, 2 units, and 8 units; 1unit, 4 units, and 4 units; and 2 units, 2 units, and 4 units. The rectangular prism with the least surface area has dimensions 2 units, 2 units, and 4 units.

Answer: 2 units, 2 units, 4 units

3

47

KEYS

48

1. ten million 2. 10,000 3. 3,150 4. P 55.50 5. P 54.75 6. 1,646 7. 6,759 8. P 1,725 9. .000680 10. 1,700 11. 1,115 12. 154 13. 12 hrs. 14. 8 4/7 15. 9 16. 30 men 17. 1/8 18. 9/16 19. 4/9 20. 21 21. 3.3 22. 7:5 23. 4/9 24. 60 25. 92 years old 26. 64.8 27. 25% 28. 0.009 29. P 1,700 30. 13/20 31. 58 sq. m. 32. 2,256 m2 33. 57o 34. 40o 35. 55o 36. 205.2 dm3

37. 90o 38. 162 39. 50 days 40. 5 41. 12 cm. 42. P 11,560 43. P 11,782.5

44. 85 45. 10.5% 46. 94.5 m2 47. 720 families

48. 24

49. 7 days 50. 5,050

~~~~~~~~~~~~~~~~

2000-2001 FIRST NATIONAL 1. ten millions

2. 7,000,000 3. 650,000

4. 460,000

5. 800 6. 21,000

7. 1972 8. 853 9. 10,000 10. 13/15 11. 350,785 12. 53/6 13. 15 3/8 14. 38 11/18 m 15. 8 23/24 16. 20 17. 18 18. 33 19. 39.348

20. 87,860 21. 14.02 cm 22. P 39.75 23. P 10.25 24. 18 25. 5 : 8 26. 156 27. 31 mins 28. 70 29. 49 30. 35/99 31. P 340 32. 360 m2 33. 140% 34. 1 ¾ 35. 77.8% 36. P 148.75 37. P 5,540 but in the answer key is P10,062.40 38. Obtuse triangle but in the answer key is isosceles 39. 96 dm3 40. 2090 m 41. 10,578 m2 42. 42 cm 43. 78.5 m2 44. 104 but in the answer key is 105 45. 100.48 m3 46. 138 cm2 47. 113.04 cm3 48. 54° 49. 98° 50. 32 m2

49

~~~~~~~~~~~~~~~~~~~~~~

2005 Regional Finals

A. 15-second questions

1. 31, 37

2. 41

3. 1 ¾ h

4. 13

5. 90

6. 2 x 33 x 5

7. 20.8 or 20 4

5

8. 65

9. P52.50

10. 500

11. 1:1

B. 30-second questions

1. 8

2. 1860

3. 1.5 x 108

4. 15

5. 69

6. 3

C. 1-minute questions

1. 30 km/h

2. 8 h

3. 60

4. 16

5. 3; solid is 7 cm x 2 cm x

3 cm

6. 2038

Clincher questions 1. 36

2. P163.50

3. 0, 1, 2, 3, 4, 5

Do-Or-Die questions 1. 27

~~~~~~~~~~~~~~~

2006 Regional Finals

A. 15-second questions

1. 69

2. 23.4545

3. 0, 6

4. 198

5. 112 cm2

6. 12 days

7. 62

8. 216 cm2

9. 66o

10. 27,499

11. 46.5 cm

B. 30-second questions

1. 47

2. 20 Note:

(This quest ion has a problem because it did

not specify t he unit of

t he small square.)

3. 16

4. 70

5. 899

6. 96

C. 1-minute questions

1. 27:8

2. P750

3. 200 km

4. 256 cm2

5. Sunday

6. 30 m

Clincher questions 1. 39

2. 9

3. 8

Do-Or-Die questions

1. 2076

~~~~~~~~~~~~~~~~

2004 Sectoral Finals

A. 15-second questions

1. 156

2. 10

9

3. 25%

4. P7.00

5. 20 yrs. old

6. 14

7. 9 cm

8. 12:45 PM

9. 6 cm

10. 6

11. 10

B. 30-second questions

1. 9 1

2. 5:35

3. P375,000

4. 45

5. 96

6. 78 m

C. 1-minute questions

1. P16,250

2. 16 cm

3. P87.00

4. 125

2

5. 3421,

6542,

9663

6. 12:35

Clincher questions 1. 21

2. 25

3. 16%

Do-Or-Die questions 1. 31.36 kg.

[The answer in the paper is

22.4 kg but Dad said should be 31.36 kg

(V = lwh = 20dm x 1.4dm x 0.8dm = 22.4dm3 x 1.4 =

31.36kg)]

2. 81

50

2005 Sectoral Finals

A. 15-second questions

1. 1, 4, 7

2. 400

3. 84

4. 360

5. 10%

6. 203

7. 325

8. 16 cm

9. 62

10. 4

11. 162 m

B. 30-second questions

1. 10

20

2. 19 cm

3. P756

4. P150.00

5. 125%

6. 16 2

5 m

C. 1-minute questions

1. 216 cm2

2. 8

3. P71.50

4. 169 cm2

5. 55 km/h

6. 20

163

Clincher questions 1. 13

2. 176

3. 2 1

6

Do-Or-Die questions 1. 30.24 kg

~~~~~~~~~~~~~~~~~~

2006 Sectoral Finals

A. 15-second questions

1. 158

2. 21

11

3. 20%

4. P15.50

5. 20 yrs

6. 81 cm2

7. 12 cm

8. 8:00 a.m.

9. 5 cm

10. 100,000

11. 16

B. 30-second questions

1. 5:36

2. P36,000

3. 60

4. 83

5. 3,200 m or 3.2 km

6. 66 m

C. 1-minute questions

1. P14,430

2. 3,500 m3

3. 12:35

4. 250

3

5. 900

6. 0, 6

Clincher questions 1. 21

2. 110

3. 16%

Do-Or-Die questions 1. 1 cm

~~~~~~~~~~~~~~~~

2004 Division Orals

A. 15-second questions

1. 7641, 1467

2. 82,045,003

3. 120

4. 101,000

5. 31.5

6. 3

8

7. 4

8. 17 cm

9. 14.3

10. P400

11. 1:10

B. 30-second questions

1. 1:25

2. 15

3. P320

4. 79 m2

5. 4½ h

6. 54

C. 1-minute questions

1. 86.4 minutes

2. 576 cm2

3. 31

4. P250

5. 18%

6. 120

Clincher questions 1. 10,000

2. 15

3. 45 min or ¾ h

Do-Or-Die questions 1. 2.3 cm

2. 42

~~~~~~~~~~~~~~~~~~~~~

51

2005 Division Orals

A. 15-second questions

1. 18

2. 75

3. 360

4. 120 cm

5. 85o

6. 78 cm

7. 120

8. 33

9. 54

10. 7.8 x 109

11. Either 29 & 31 Or 41 &43

B. 30-second questions

1. 30

2. 72

3. 227.85 cm2

4. 4 1

12h or 4

5

60h

5. 48 days

6. P450

C. 1-minute questions

1. ¼

2. 35

3. P1575

4. 70 cm

5. 1232 cm2

6. P95

Clincher questions

1. 11

6

2. P1056

3. P155

Do-Or-Die question 1. P1570

~~~~~~~~~~~~~~~~~

2006 Division Team

Finals

A. 15-second questions

1. 21

250

2. 20.8 or 20 4

5

3. 1 ¾ h

4. 15

5. 104.8

6. 2 x 33 x 5

7. 5:05 a.m.

8. 65

9. P52.50

10. 500

11. 1:1

B. 30-second questions

1. 251.2 cm3

2. 1860

3. 1.5 x 108

4. 15

5. 69

6. 3

C. 1-minute questions

1. [ 7+17,11+13, 5+19] 2. 30 km/h

3. 523.33 dm3

4. 8 h

5. 3

6. 2038

Clincher questions 1. 36

2. P163.50

3. 0,1,2,3,4,5

Do-Or-Die questions 1. 3:8

~~~~~~~~~~~~~~~~~~~

2007 Division Team

Competition

A. 15-second questions

1. 750

2. 9/11

3. 28 cm

4. 13 + 19, 3 + 29

5. 100.4

6. 15

7. 70 cm

8. 48o

9. 125

10. 199

11. 10,000

B. 30-second questions

1. 1.8 x 108

2. 192

3. 15

4. 600

5. 113.04 dm2

6. 45, 46, 47

C. 1-minute questions

1. 21.1 cm

2. 552.96 cm2

3. P4,400

4. 3

5. 19, 34

6. 11

Clincher questions 1. 22

2. P231

3. 204

Do-Or-Die questions 1. Lilia – 89,

Rose – 87,

Kate – 85

~~~~~~~~~~~~~~~~~~~~

52

2008 Division Orals

A. 15-second questions

1. 26, 28

2. 20

3. 24

4. 10

5. 13 = The numbers

are 6 and 7

6. 2

6 or

1

3

7. 17

25

8. 8

13

9. 7

24

10. 1 million or1,000,000

11. 11, 22

B. 30-second questions

1. 84

2. 12.5 cm

3. 200.96 cm2

4. 2

5. 60

6. 4 3

4 or

19

4

C. 1-minute questions

1. 70 cm

2. P4,400

3. 17 [145 =64 + 81]

4. 3375 cm3

5. 60 cm

6. 3

Clincher questions 1. 150

2. 4, 14

3. 11

5 or 2

1

5

Do-Or-Die questions 1. 403

53

2007 Regional Team

A. 15-second questions

1. 198 [ 97 + 101 = 198 ]

2. 234.545

[ same because first factor is multiplied by 10

and the second is divided by 10 ]

3. 2 or 8

4. 63 cm2

[ 84 x 3/2 = 126;126/2 = 63 ]

5. 36 [ 45 x 4/5 ]

6. 119

[ Jane made 56/8 x 9 = 63 ]

7. 20 cm by 15 cm

[16 x 5

4 = 20 cm,12 x

5

4 =15 cm]

8. 245,254

9. P240

[12

3 x 8 = 32; 20 x P12 = P240 ]

10. 91 [ 91 = 7 x 13 ]

11. 1994

30-second questions

1. 47

[ Average = 215

5 = 43; 43 + 2, 43 + 4 = 47 ]

2. 20

[ No. of pieces = 30

6 x

20

5 = 5 x 4 = 20 ]

3. 70

[ 2520 = 22 x 32 x (2 x 5 x 7);

(2 x 5 x 7 = 70) needed ]

4. 3

5. 14

[ P1750 – 1505 = P245; P245/1750 = 0.14 or

14% ]

6. 182

[ 137 + 540

12 = 137 + 45 = 182 ]

C. 1-minute questions

1. 11.7

[ 65:8 = 95:n; n = 8(95)

65 = 11.69 ]

2. 200 km

[ 60 x 4

3 = 80 km/h; 2.5 x 80 = 200 km ]

3. 24

4. 4591 m2

5. 257

[ LCM (12, 14, 18) = 252, add 5

to have a remainder of 5 ]

6.495

[ 27 + 125 + 343 = 33 + 53 + 73 = 495 ]

Clincher questions

1. 996

[ Divide 1000

6 = 166

4

6 . Subtract 4

from 1000 = 996 ]

2. 63o

[ Let xo be each base angle.

2x + x – 9 = 180, x = 63 ]

3. 30 m [ largest piece = 6

15 (75) = 30 ]

Do-Or-Die questions

1. 8

[ 1st round – 8 will say 3 leaving 17 standing.

Among the 17, 5will say 3 leaving 12 standing.

Among the 12, 4 will say 3. In all,8 + 5 + 4 = 17

will sit, so 25 – 17 = 8 will remain standing. ]

54

55