Grade 6 mtap reviewer

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

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?
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(2000 – 2001) FIRST NATIONAL METROBANK-MTAP-DECS ELEMENTARY
MATH CHALLENGE Grade 6

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
did she buy in all?
_________ 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
who received most get?
_________ 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
Grade 6

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?

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_________ 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 ratio 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 scientific 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 questions in a Math test are on fractions, how many questions
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
__________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?
__________1. Five consecutive whole numbers have a sum of 225. What is the largest
number?
__________2. A piece of plastic 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 multiply 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 ratio 5:8. If 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 ratio 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 travel in 2 ½ hours?
__________4. Nine small squares are put together 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 ratio 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 multiples 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
Grade 6

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 multiplied by 100 and 80 divided by 5,
the product of the resulting numbers is the same as multiplying 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
condition 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 multiple 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 ratio 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 times 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 PartsII and III , solve each problem on scratch paper and write a neat
solution on the
space provided.Show detailsof 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. Solveeach 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 multiple of 13?
__________ 3. Express 13,860 as a product of prime factors using exponents.
__________ 4. What is the greatest common factor of 420 and 504?
__________ 5. What is the least common multiple of 420 and 504?
__________ 6.What is the reciprocal of the sum of 2
1
6
and 3
2
3
?
__________ 7. A jar filled with water weighs 10 kg. When half of the water is poured out,
the jar and its contents weigh 5
3
4
kg. What is the weight of the jar?
__________ 8.Of three numbers, two are ½ and 1/3. What must the third number be so
that the average of the three is 1?
__________ 9. One man can dig a hole 2 m x 2 m x 2 m in one day. At the same rate,
how long will it take 3 men to dig a hole 10 m x 6 m x 4 m?
__________ 10. The base of an isosceles triangle is 5 cm longer than a leg. If the perimeter
is 41 cm, find the base.
__________ 11.111 111 + 222 222 + 333 333 + 444 444 = 222 222 x N. Find N.
__________ 12. The cost of a watch including a tax of 25% is P937.50. Find the cost of
the watch without the tax.
__________ 13. The floor of a bathroom is 2.5 m by 1.8 m. How many tiles, 5 cm square, will
be needed to cover it?
__________ 14. A carpet, 12 m by 9 m is laid in a room, 17 m by 14 m. What percent of
the room is left uncovered?
__________ 15. Find the total surface area of a closed barrel with a diameter of 6 dm and
a height of 12 dm.
II. Solve each on scratch paper and write a neat and complete solution on the space
below. Label your solutions. [3 points each]
1. How many revolutions, to the nearest whole number, will a car wheel with a diameter
7 dm, make to cover a km?
2. 512,000 square tiles, each 5 cm on each side, are needed to pave a rectangular court
40 m long. What is the width of the court?
3. How many books, 24 cm long, 18 cm wide and 2.5 cm thick can be packed into a box
5 dm long, 3.7 dm wide and 2 dm high, internal dimensions?
4. There are 108 red, blue and green marbles in a box. Four more than one-third of
the marbles are red. There are 8 more green marbles than blue marbles. How
many marbles of each kind are there?
4. A square of 9 by 9 grid is colored alternately black and red. If the corners are black,
how many black and red squares are there?
III. Solve each problem on scratch paper and write a neat and complete solution
below. Label your solutions. [5 points each]
1.I went to a store and spent 1/3 of my money and P5.00 more. Then, I went to a second
store where I spent 3/5 of my remaining money plus P9.00 more. I had exactly P45.00 left.
How much money had I at first?
2. The digits 1, 2, 3, 4 can be arranged to form 24 different 4-digit numbers. If the 24 numbers
are listed from smallest to largest,
a. Give the smallest and largest numbers formed. [1 pt.]
b. What is the position of 3142? [2 pts.]
c. What is the sum of the 24 numbers? [2 pts.]
3. Tom ate 100 cookies in 5 days. Each day, he ate 6 more cookies than the day
before. How many cookies did he eat on each of the 5 days?
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 altitude 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 times 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 travels 140 km in 3.5 hours and a train travels 30 km in 50 min. Find the
ratio 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 ratio
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 multiple
of 3 stood UP. Then, the students who remained seated counted off again from 1 and
those who counted a multiple 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 bottles in one hour; another can cap 1,700 bottles an hour.
There are 20,000 bottles 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 aboveP50,000.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 abovethe 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 havealtogether?
__________ 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 valueof {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 havedigits whose product is 24,
i.e. 6 x 2 x 2 =24. How many 3-digit whole numbers havedigits 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
Grade 6
__________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 multiple of 7 that is divisible by 13?
____________11. What is MCMXCIV in Hindu-Arabic?
_____________1. Five consecutive odd numbers have a sum of 215. What is the largest
number?
_____________2. A piece of plastic 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 multiply 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 travel 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 ratio 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
__________1.What is the largest whole number less than 190 that is divisible
by 78?
__________2.Iam 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 140,000than 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 leaveManila?
__________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 divisible
by 11?
__________11.40% of 70 is what percent of 280?
__________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 theairport?
__________3.A rich man divided 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?
__________1.A salesman has a basic salary of P4,500 and a commission of 5%
on all sales aboveP50,000.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 haveP240.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 thousandsdigit is thrice the units digit; the
hundredsdigit is 3 more than the units digit and the tens digit is the difference
of the thousandsand 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
__________1.What digits can be put in the blank in 785__ to make it divisible
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 divided by 24?
__________7.How many times as great is 325,000than 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 studentsin a school are 13 years old or
younger.How many of the studentsare above13 years old?
__________10.What digit can be used to replace 1 in 817 to make it divisible
by 11?
__________11.How long is ¾ of a string of length 216 m?
B. 30-second questions – 3 pointseach
__2__
__________1.Whatis the valueof 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
received P1,260,how much did the helper receive?
__________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?
__________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 haveP240.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 averagespeed for the whole journey?
__________6.Whatis the reciprocal of 4
2
5
+ 3
3
4
?
Clincher questions
__________1.How many 2-digit numbers are divisible by 7?
__________2.The rooms in a hotel are numbered from 101 to 451.How many
odd numbered rooms are there?
__________3.Of threenumbers, two are
1
2
and
1
3
. What must the third number be
so that the averageof 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
__________1.What is the largest whole number less than 200 that is divisible
by 79?
__________2.Iam 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-fifthof 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.FromManila, it takes 5 ½ hours to reach Baguio. To reach Baguio
at 1:30 p.m., what time should I leaveManila?
__________9.If the total surface area of a cube is 150 cm2, what is the length
of an edge?
__________10.754,000,000is how many times as great as 7,540?
__________11.If a*b = ab – b2, what is 8*4?
__________1.A plane traveling at 800 km/hr was 80 km from an airport at 5:30.
At what time will it be over theairport?
__________2.A rich man divided 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
studentsare 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.Thereare 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?
__________1.A salesman has a basic salary of P3,000 and a commission of 6%
on all sales aboveP50,000.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 volumeof 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% travelfirst class; 56% travelthird class and 252
travelsecond class. How many people are on the boat?
__________6.What digit(s) can you put in the blank in 377__4 to make it divisible
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
__________1.Arrangethedigits in 4716 to make the biggest and the smallest
numbers.
__________2.Write 82 million, 45 thousand,3 in symbols.
__________3.Find the valueof (12 x 18) – (12 x 8) by using the distributivelaw 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.Theproduct 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 divisible 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?
__________1.If a school has 6000 pupils and 240 teachers, what is the teacher to
pupil ratio?
__________2.Threetimes 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.Onemorning 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?
__________1. Water flows out of a pipe at the rate of 10 liters per minute. At that
rate, how long will it taketo 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.Onenumber 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 studentsneeded for different dances if
the teacher wantsto be able to put them in groupsof 6, 8 or 10?
Clincher questions
__________1.How many hundredsare 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 drovefor 2 ½ hours, stopped for lunch and then
droveagain 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 divided 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
__________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.Oneedge 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 11boys. If there are 24 girls,
how many boys are there?
__________9.What is the valueof 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.
__________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 haveenough 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?
__________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 covers85 km on 10 liters of gasoline, how many liters, to
the nearest liter, will it use to cover 300 km?
__________3.A vendor buystilapia 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 gaveher
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.
How much did she receive?
2

31
2008 Division Orals Metrobank-MTAP-NCR Math Challenge
Grade 6
__________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
. If 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 times 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 times a number plus 7 is 55, what is 7 times the number?
__________2. The area of a parallelogram is 100 cm2. If 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?
__________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 depositing 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 positive 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 ratio 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 positive factors of positive 225?
2

33
2007 Division Team Competition Metrobank-MTAP-DepEd Math Challenge
Grade 6
__________1.The diameter of a circular lot is 15 m. What is its radius in
centimeter?
__________2.Reducethefraction
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-eighthsof 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 givethe 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 consecutivewhole numbers whose sum is 138.
__________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.Byhow 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 divisible 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 averagegradeof Lilia and Rose is 88, the averagegradeof
Lilia and Kate is 87 and the averagegradeof Rose and Kate is86.Find the
grade of each girl.
2

35
2011 Math Challenge Grade 6
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 multiple 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 cities 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 ratio 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 tiles of side 1 dm are needed to tile 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 exactly P56 left, how money did I have at first?
__________________ 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?
__________________ 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?
__________________ 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
ratio 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 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?
__________________ 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
GRADE 6
Part 1: 15 seconds (11 items)
1. Manila time is 4 hours ahead of Dubai time. A trip from Manila to Dubai, takes nine
hours. What time 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 multiplied by 20 will give a perfect cube?
5. On a quiz show, each question is worth four times as much as the previous question.
The fourth question is worth P1,600. How much was the first question worth?
6. In 3 ___ 6 ___ (-9), what two different basic operations can you place in the ___ that will
result to the least answer?
7. What number will you add to the numerator and denominator of
7
1
so that the result
becomes 4 times?
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
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 stations broadcast the weather at 1:30 P.M. When is the
next time that the stations will broadcast again the weather at the same time?
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 track 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
SOLUTIONS & ANSWERS
1.Solution
8:00 P.M. + 9 hours is 5:00 A.M.
5:00 A.M. – 4 hours is 1:00 A.M.
Answer: 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
Answer: 9
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
=(4x3)+(4x3)+(4X3)
Answer: 36
4.Solution
20 = 22 x 5
So the smallest number that should be
multiplied by 20 so that the product is a
perfect cube is 2 x 52 which is equal to 50.
Answer: 50
5.Solution
1600  4  4  4 = 25
Answer: P25
6.Solution
The bigger the absolute value of a
negative number, the smaller is the
negative number. So x (for multiplication)
should be placed before -9.
÷ (for division) cannot be placed after 3
because it will be performed first and
performing division then multiplication will
not result to the least answer.
- (for subtraction) cannot be placed
after 3 also because 3 – 6 is -3 which
when multiplied by -9 gives a positive
answer,
Therefore, + (for addition) should be
placed after 3. So, 3 + 6 x (-9) = -51
Answers: +, x (order must be correct)
7.Solution
4 times
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



.
Answer: 7
8.Solution
Total number of votes = 20  (55% - 45%) =
20  .10 = 200
Number of votes of the winner = 200 x .55 =
110
Answer: 110
9.Solution
2 + 4 + 6 + … 96 + 98 + 100
Pair the numbers so that each pair will total
102 as shown above. Then multiply 102 by
the number of pairs which is 25.
So 25 x 102 = 2550
Answer: 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
 .
Answers:
7
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%
Answer: 300%
Page1
102
102

41
1.Solution
109 – 4 = 105
105 = 3 x 5 x 7
Multiply two factors of 105 at a time, 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.
Answer: 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 multiple 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.
Answer: 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.
Answer: 30
5.Solution
The least common multiple 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
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 multiplier 25 is the smallest
possible.
Answer: 25 and 367
2.Solution
7
4
56
24
1 
7
4
n
24
 , n = 42
Answer: 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 multiples 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
Answer: 83.6 or 83.60
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.
Answer: 48
Page2

42
2009 NATIONAL FINALS INDIVIDUAL ORAL
METROBANK-MTAP-DEPED MATH CHALLENGE
GRADE 6
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?
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.)
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:
1 point for correct answer
4
1
point for incorrect answer
0 for no answer
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
SOLUTIONS and ANSWERS:
1. Solution
45 x n + 7 = 805 + 7 = 812
Answer: 812
2. Solution
%75
4
3
24
18

Answer: 75%
3. Solution
4
3
8
6
53
51



Answer: 5
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
Answer: 27 seconds
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
Answer:
3
2
2or
3
8
7. Solution
In x + y = 12, y = 7 since x = 5.
In y + z = 20, z = 13 since y = 7.
Answer: 13
8. Solution
50% of a number is 20, so the number is 40.
40 x 0.8 = 32
Answer: 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.
Answer: 2
1

45
10. Solution
1010 has 10 zeros while 1 billion has 9 zeros, so1010
 1 billion = 10
Answer: 10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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

Answer: 2.0or
5
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.
Answer: 7.5 square units
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2
1
3
2

46
1.Solution
175 - 95 = 80g
40 - 20 = 20
So, 20 nails weigh 80g.
80  20 = 4g
Answer: 4 g
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
given that Lina had incorrect answers, and no answers.
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.
Answer: 7th or 7
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

48
Grade 6
FIRST NATIONAL
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
ANSWER KEY
GRADE 6 MTAP
~~~~~~~~~~~~~~~~~~~~~~
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
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
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
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
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
1. 9 1
2. 5:35
3. P375,000
4. 45
5. 96
6. 78 m
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
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
1.
10
20
2. 19 cm
3. P756
4. P150.00
5. 125%
6. 16
2
5
m
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
~~~~~~~~~~~~~~~~~~
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
1. 5:36
2. P36,000
3. 60
4. 83
5. 3,200 m or 3.2 km
6. 66 m
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
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
1. 1:25
2. 15
3. P320
4. 79 m2
5. 4½ h
6. 54
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
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
1. 30
2. 72
3. 227.85 cm2
4. 4
1
12
h or 4
5
60
h
5. 48 days
6. P450
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
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
1. 251.2 cm3
2. 1860
3. 1.5 x 108
4. 15
5. 69
6. 3
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
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
1. 1.8 x 108
2. 192
3. 15
4. 600
5. 113.04 dm2
6. 45, 46, 47
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
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
1. 84
2. 12.5 cm
3. 200.96 cm2
4. 2
5. 60
6. 4
3
4
or
19
4
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
ANSWER:
2007 Regional Team
A. 15-secondquestions
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 ]
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. ]

Grade 6 mtap reviewer

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