2019 Grade 1 Math Challenge Division Finals Questions and Answers

Below are the 2019 MTAP Grade 1 Math Challenge questions and answers. Solutions will be posted later. More reviewers can
be found on the Past Tests and All Posts pages.
Part I: Questions
Easy
In a street with house numbers 1, 2, 3, until 100, Mark delivered flyers to all houses numbered from 25 to 57. How many
houses got the flyers?
Twelve friends came to Juan’s birthday party. Seven of them were girls. How many boys went to Juan’s birthday party?
In the number pattern 41, 37, 33, 29,___, what number should be on the blank?
Carlos has thirteen10-peso coins. How much money does Carlos have?
Dino bought packs of noodles worth Php54.How much change will he get from Php100?
A red ribbon is 35 centimeters long. A yellow ribbon is 15 centimeters long. What is the total length of the ribbons?
Nena cuts a pizza into 3 equal parts. Then she cut each part into halves. What part of the whole pizza is one piece?
It takes half an hour for Joan to walk half of the way from school to home. If Joan maintains the same speed, how long does it
take her to walk to school from home?
Some monkeys were climbing a rope one by one. The biggest monkey was in the middle and is the eighth from the last. How
many monkeys were on the rope?
Sonny needs 45 minutes to finish his project. If he starts at 4:30 pm what time will he end?
Janice puts only ₧10-coins in her piggy bank. When she opened her piggy bank, she counted 86 coins altogether. How much
money does she have?
Average
What is the sum of the largest two-digit number and the smallest three-digit number?
How much less is six pesos and fifty centavos than ten pesos?
Doggie is 1year and 3 months old now.In how many months will Doggie be 2years old?
In Shoeland, a centipede needs one shoe for each of its 100 feet. It has 25 pairs of shoes now. How many more shoes does the
centipede need?
There were 11 flags on a straight track of a race. The first one was at the starting point and the last one at the end of the track.
The distance between each flag was 8 m. How long was the track?
Mother ordered 2 pizzas and sliced each of them 8 pieces for Leny’s birthday. There were 14 children at the party including
Leny. How many slices are left over if Mother gives one slice to each child?
Difficult
The entrance fee to a park is Php50 for each adult. The entrance fee for each child is Php15 cheaper than the price for an adult.
How much will a family of 3 adults and 4 children have to pay for the entrance fee?
Nico had 304 baseballs cards. He then gave some of his cards to Alex. Now he has 276 cards left. How many cards did Alex
receive?
Using the digits 1, 5, and 0, Pat wrote down both the largest and the smallest three-digit numbers that can be formed. She
then solved for the difference between the two numbers. What answer did she get?
Auntie went out to the yard and called all her hens and her cat. All ran to her and there were 20 legs. How many hens does
Auntie have?
The book I am reading has 120 pages. I read 36 pages on Monday, 28 on Tuesday and 32 on Wednesday. How many more
pages do I need to read?
Mrs. Garcia has three 100-peso bills and two 20-peso bills. How much money does Mrs. Garcia have?
Tiebreaker
A group of girls stand in a circle. Vina is the fourth on the left from Remy. She is also the seventh on the right from Remy. How
many girls are in the group?
A rectangle is 25 cm long and 15 cm wide.What is the perimeter of the rectangle?
Jose saves Php20 on the first week, Php25 on the second week, ₧30 on the third week, and so on. If this pattern continues,
how much was his total savings on the tenth week?
Do-or-Die
In a mathematics test, the sum of Eva’s and Ivy’s scores is 172. Also, the sum of Eva’s and Maine’s scores is 175. If Ivy’s score
is 87, what is Maine’s score?
Answers
Easy
33
5
25
Php130
Php46
50cm
1/6
1 hour
15
5:15pm
Php860
Average
199
Php350
9
50
80m
2
Difficult
Php290
28
405
8
24
Php340
Tie Breaker
11
80 cm
Php425
Do or Die
90

2019 Grade 2 Math Challenge Division Finals Questions and Answers

Posted on February 27, 2019 | Leave a comment
Below are the 2019 MTAP Grade 2 Math Challenge Division Finals questions and answers. Solutions will be posted later. More
reviewers can be found on the Past Tests and All Posts pages.
PART I: Answers
In a line to buy movie tickets, Greg is fourteenth from the front. In the same line, his friend Jose is twenty-third from the front.
How many people are between them?
In a barn, there are 2 horses, 1 cow, and 3 pigs. Later, 5 horses, 3 cows, and 4 pigs joined them. How many animals are in the
barn now?
The sum of Juan and Paulo’s ages is equal to 15. What will be the sum of their ages in 6 years?
Diana is 16 1/2 years old. Her cousin Samantha is seven years younger. How old is Samantha?
How many thirds are there in seven and two-thirds?
Rico has Php300 in bills. He requested to change one-half of his money into five-peso coins. How many five-peso coins should
he get?
A movie started at 4:30 pm and ended at 6:20 pm. How many minutes long was the movie?
If oranges are sold for Php13 each, how many can you buy if you have one hundred fifty pesos?
A school field is 58 m long and 42 m wide. If you walk around it once, how many meters would be?
A line and a circle are drawn on a piece of paper so that the line passes through the center of the circle. How many times does
the line cross the circle?
There were some children riding in the bus. At the next bus stop, 7 more children got in. Then, there were 25 children altogether
in the bus. How many children were there at first?
Average
There are 48 passengers in a bus. If 5/6 of the passengers are seated, how many are not seated?
Altogether, my dogs have 18 more legs than noses. How many dogs do I have?
Lambert has 4 pieces of wood with a total length of 35 decimeters. Three of the pieces are of the same length and one piece is 8
decimeters long. How long is each of the other pieces?
Patty has Php225. Each of her four sisters has Php100. How much does Patty have to give to each of the sisters, so that she and
her sisters will have the same amount of money?
The jogging lane of a park is a square with side length 25 meters. How many complete rounds must a jogger go around the
jogging lane to make sure that he has run 2 kilometers?
A basket contains 9 mangoes, 15 bananas and no other fruit. If 3 morebananas are added to the basket what fraction of the fruit
in the basket will be bananas?
Difficult
The sum of the digits of the year 2018 is equal to 2+0+1+8 = 11. What is the nearest year, after 2018, when the sum of the digits
of the year will be equal to 11 again?
Rona gave 3 mangoes to each of her friends. In all, she gave two dozen mangoes. How many friends received mangoes from
Rona?
There are 30 pieces of chips on the table. One-fifth of the chips are red. One-sixth of the chips are green and the rest are yellow.
How many chips are yellow?
After reaching home from school, Andres played for 10 minutes. Then, he watched television for 25 minutes before taking his
dinner. It took him 15 minutes to finish dinner. When he looked at the clock, it says 6:35 pm. At what time did Andres reach
home?
How much more is the sum of 46 and 24 more than their difference
The perimeter of a rectangular garden is 54 m. If the length is 3 m longer than the width, what is the width of the garden, in
meters?
Tiebreaker
Ben spent Php215 for his school supplies while his sister spent Php350. How much more did his sister spend than him?
Father has Php180 to be shared among his 4 children. How much will each kid get?
A large kettle can hold up to 6 liters of water. The water in the kettle can fill three jugs. Nine jugs of water can fill two pails of
water. How many liters of water can be placed in one pail?
Do or Die
Iris had a sum of money. She spent 1/5 of it in September, 1/4 of it in October and Php120 in November. After spending these
amounts of money, she still had Php540 left. How much money did she have at first?
Answers
Easy
8
18
27
9 1/2 years old
23
30
110
11
200
2
18
Average
8
6
9 dm
Php25
20
2/3
Difficult
2027
8
19
5:45pm
48
12
Tie Breaker
Php35
Php45
9
Do or Die
1200
2019 Grade 3 Math Challenge Division Finals Questions and Answers (with PDF)
Posted on March 24, 2019 | Leave a comment
Below are the 2019 MTAP Grade 3 Math Challenge Division Finals questions and answers. Solutions will be posted later. More
reviewers can be found on the Past Tests and All Posts pages.
Easy
1.) What is the smallest whole number that can be rounded to 800?
2.) Three hundred forty is 78 more than what number?
3.) What number gives 1780 when added to 980?
4.) What is the sum of 5 hundreds and 20 tens?
5.) What is the largest whole number n such that when 3 × n is rounded to the nearest tens, will equal to
90?
6.) What must be added to 4/5 to get a sum of 2?
7.) What is the largest number that can exactly divide 24 and 40?
8.) What is one-half of three-fifths of 60?
9.) Isabel has 1-peso coins and 5-peso coins in her bag and its total amount is ₧22. If there are 10 coins in all, how many Php 5
coins are there?
10.) Arlene has a basket of apples. Her mother gave her 4 apples more. Then she gave 5 apples to her sister. How many apples
did Arlene have if she had 18 apples in her basket at first?
11.) A container is three-fourths full of water. When 6 liters of water were taken from it, it became one-half full. What is the
total capacity of the container?
Average
1.) The ratio of two numbers is 3 ∶ 7. If the smaller number is 21, what is their sum?
2.) Liza earned Php 4400 in one week. She gives her mother two-thirds of this amount and spends one-fourth of the money to
clothes. How much money is left?
3.) The cost of 10 kg of rice is Php 475. How much is 3 1/2 kg of rice to the nearest tens?
4.) Mary has 60 bundles of flowers. She wants to place them in boxes. If each box contains a dozen bundles of flowers, how
many boxes are needed?
5.) One number is two-thirds of the other number. If the larger number is 30, what is their sum?
6.) Terrie listed all the numbers from1 to 30. She was told to erase every third number. Then after erasing every third number,
she was told to erase all remaining even numbers. What is the sum of the smallest and the largest number that were left?
Difficult
1.) The weight of a basket containing 8 pieces of pomelo is 7 kg. A basket without the pomelo weighs
600 grams. How many grams is each pomelo if they have the same weight?
2.) Maria bought a blouse that was originally sold for Php 420. It was sold at a price that was two-thirds of its original price. If
she gave two 200-peso bills to the cashier, how much change will she receive?
3.) Teresa cuts a string into 8 pieces of different lengths. The shortest piece is 20 cm and the longest piece is 90 cm. If the length
of the string differs by 20 cm in length, how long was the original string?
4.) What is the largest two-digit number that gives 7 as a remainder when divided by 8?
5.) Three boys and 3 girls went to watch a stage play. The total cost of the 6 tickets was Php600. After paying their tickets, each
of the boys pays half of the girls’ tickets. How much was paid by each girl?
6.) The area of a rectangle is 96 cm2. If the width is 12 cm, what is the perimeter of the rectangle?
Tiebreaker
1.) What is the sum of the digits of the product of 123 and 6?
2.) 15 is one-third of 50% of what number?
3.) Marie and Kristel had Php 478 together. They decided to save one-half of this amount. Then they went out for a lunch
together and spent Php145. If they decide to divide equally the remaining amount, how much will each of them get?
Do-or-Die
1.) The area of the rectangle is 32 cm2. If its width is twice its length, what is the perimeter of the rectan-gle?
Answer key:
Easy
1.) 750
2.) 262
3.) 800
4.) 700
5.) 31
6.) 1 1/5
7.) 8
8.) 18
9.) 3
10.) 17
11.) 24 liters
Average
1.) 40
2.) Php 1100
3.) Php 170
4.) 5
5.) 50
6.) 30
Difficult
1.) 800
2.) Php 120
3.) 440 cm
4.) 95
5.) Php 50
6.) 40 cm
Tiebraker
1.)
2.) 90
3.) 47
Do-or-Die
1.) 24 cm

2019 Grade 4 Math Challenge Division Finals Questions and Answers (with PDF)
Posted on March 31, 2019 | Leave a comment
Below are the 2019 MTAP Grade 4 Math Challenge Division Finals questions and answers. Solutions will be posted later. More
reviewers can be found on the Past Tests and All Posts pages.
Easy
1.) Find the number of the digit 1 in the numbers 1, 2, 3, . . . , 100.
2.) Admission tickets to a variety show costs Php 80 for adults and Php 50 for kids. The ratio of kids to adults is 5:2. If they
paid Php 10,000, find the number of adults in the group.
3.) How large is a base angle of an isosceles triangle if its vertex angle is 52○?
4.) The volume of a cube is 216 cm3. What is the total area of the faces of the cube?
5.) What is the largest 4-digit number that is a common multiple of 3 and 4?
6.) A sack of rice weighs 50 kilograms. If the rice is to divided equally among 8 families, how many grams of rice would each
family receive?
7.) What is the remainder when 4823 is divided by 11?
8.) A four-digit number has three equal digits, and the sum of the digits is 35. Which one is the different digit?
9.) Armand sold 40 cupcakes and Liza sold 50 cupcakes. The cupcakes were sold at the same price. If the total amount received
was Php 6300, how much did Liza receive?
10.) T o go to school, it took Krystel 1hour and 40 minutes. She arrived at 7:25am. What time did she leave her house?
11.) The sum 9 + 99 + 999 is equal to 9 times what number?
Average
1.) At home, a jar contains a number of candies. Andrew ate 2/7 of the number of candies. The next day he ate 1/5 of the
remaining number of candies. On the third day, he ate 1/2of the remaining number of candies. If 8 candies remain, how many
candies were there initially?
2.) The sum of two numbers is 78 and their difference is 14. Find the two numbers.
3.) Three-fifths of the students in class like to play football while the rest like basketball. If there are 18 students who like
basketball, how many more students like football than basketball?
4.) Elsa is running at a rate of 360 meters/min. Find her rate in cm/sec.
5.) A basketball team scores an average of 53 points per game in its first 4 games and an average of 52 points per game in its
first 5 games. How many points did the team score in its 5th game?
6.) Yvonne needs 3 1/3 cups of raisins for baking fruitcake. A package contains 2/3 of a cup of raisins. How many packages
should Yvonne buy?
Difficult
1.) The area of the shaded region is 48 cm2. Find the area of the circular ring in terms of π.
2.) Find the sum of the numbers in the 20th triple: (1, 4, 7), (2, 6, 9), (3, 8, 11), (4, 10, 13) …
3.) Three guavas cost two apples cost Php 155, while five guavas and four apples cost Php 285. What is the cost of each guava?
4.) The figure shown is formed by 17 identical squares of side 3 cm. Find the perimeter of the figure.
5.) Three cans and three pails can hold 18 liters of water. A pail can hold 1.5 liters more than a can. What is the capacity of one
can?
6.) A square piece of paper is folded into two halves to form two rectangles. If each rectangle has a perimeter of 27 cm, find the
perimeter of the original square paper.
Tiebreaker
1.) The value of √2019 is between what two consecutive integers?
2.) Two pieces of circular tablecloths with areas 25π cm2 and 49π cm2 are overlapped as shown. There is
an overlap of 10π cm2. Find the total area of the two pieces of tablecloths in terms of π.
3.) Find the area of the shaded region.
Do-or-Die
1.) What is 0.177 ÷ 0.02?
Answer key
Easy
1.) 21
2.) 100
3.) 64○
4.) 216 cm2
5.) 9996
6.) 6250
7.) 5
8.) 8
9.) Php 3500
10.) 6:45 AM
11.) 123
Average
1.) 28
2.) 32, 46
3.) 9
4.) 600 cm/sec
5.) 48
6.) 5
Difficult
1.) 96π cm2
2.) 107
3.) Php 25
4.) 108 cm
5.) 2.25 liters
6.) 36 cm
Tiebreaker
1.) 44 and 45
2.) 64π cm2
3.) 72 cm2
Do-or-Die
1.) 8.85

2019 Grade 5 Math Challenge Divisionals Questions and Answers (with PDF)
Posted on May 5, 2019 | Leave a comment
Below are the 2019 MTAP Grade 5 Math Challenge Division Finals questions and answers. Solutions will be posted later. More
reviewers can be found on the Past Tests and All Posts pages.
Easy
1.) If x = 5 + 10 + 15 + 20 + 25 and y = 13 + 14 + 15 + 16 + 17, what is x – y?

2.) If , what is the value of ?

3.) Express as decimal the sum of .

4.) If x : 8 = y : 32 and x + y = 25, what is y – x?
5.) S = How many prime factors does S have?
6.) A bell sounds at the indicated number of times at regular intervals as follows: …, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 1, 1, ___,
___… What are the next two numbers?
7.) What is “one hundred thousand and one hundred-thousandths” when written as a decimal number?

8.) If I add a number to 4 and subtract the same number from 5, the result differ by What is the number?
9.) What is the greatest four-digit number that is divisible by 6?
10.) What is the least 5-digit number with no zero digit that rounds of to 45000?
11.) What is the greatest one-digit divisor of ?
Average
1.) What is the least common multiple of 2, 3, 4, 6, 8, 21, and 60?

2.) The proper fractions , and have the same numerator greater that 1 and are in simplest form. What is the least
value of n?
3.) The GCF and LCM of two numbers are 6 and 216, respectively. If one number is 24, what is the other number?

4.) What is expressed in percent without decimal.

5.) What is the value of n in the sequence 1, 3, 6, 10, 15, n?
6.) What is the difference in the value of 8 and 6 in 456 789 123?
Difficult

1.) What is exactly halfway between and

2.) What is the last digit of the number when written in standard form?
3.) The average of 12 numbers is 80. If two numbers are discarded, namely 53 and 47, what is the average of the remaining
numbers?
4.) The numbers 5 and 29 are the first and fifth terms of an equally spaced sequence of five prime numbers. What are the other
three numbers?
5.) What is n in n = 100 – 99 + 98 – 97 + 96 – 95 + 94 – 93 + 92 – 91 + … and so on up to + 10 – 9 + 8 – 7 + 6 – 5 + 4 – 3 + 2 –
1?
6.) The sum of the digits of the greatest possible three-digit even number is 26. If the number is multiplied by 1001, what is the
product?
Tie-breaker
1.) A coin bank is filled with 25-cent coins amounting to Php 504.75. How many coins are there in all?
2.) What is the value of ?
3.) The LCM of the number pair m and n is 12. Give a complete list of all possible pairs m and n.
Do-or-die
What is the product of

Answers:
Easy
1.) 0

2.)
3.) 2.45
4.) 15
5.) 2
6.) 2,1
7.) 100 000.000 01

8.)
9.) 9996
10.) 44511
11.) 9
Average
1.) 120
2.) 7
3.) 54

4.)
5.) 21
6.) 5 920 000
Difficult

1.)
2.) 6
3.) 86
4.) 11, 17, 23
5.) 50
6.) 998 999
Tie-breaker
1.) 2019
2.) 999 999
3.) 3 and 4; 4 and 6; 1 and 12; 2 and 12; 3 and 12; 4 and 12; 6 and 12; 12 and 12
Do-or-die
Grade 7 MTAP 2015 Questions with Solutions Part 1
Posted on December 17, 2015 | 5 Comments

Below are actual MTAP Questions that has been released. I have created a detailed solution for each question. In this post, we
answer 1-10. You can also read the solutions of problems 2-20. The file can be downloaded here.
1.) Simplify:
Solution

Answer:
2.) By how much is 3 – 1/3 greater than 2 and 1/2?
Solution

Subtracting the two results, we have

.
Answer:

3.) Write 9/20000 in scientific notation.

Solution

can be written as .

Since and ,

Answer:
4.) What is the product of three consecutive multiples of 5 if the middle number is n?
Solution
If is a multiple of 5 and the middle number of the three numbers, then the other numbers are and .

So, the product is .

Answer: .
5.) If water pours into a tank at a rate of 100 liters per minute, at what rate is the tank being filled in kiloliters per hour?
Solution
100 liters/minute 60 minutes per hour = 6000 liters per hour
6000 liters per hour = 6 kiloliters per hour.

Answer: 6 kiloliters per hour

6.) Subtract the sum of and from .
Solution
.

Answer:

7.) Simplify .
Solution
Simplifying we have,

The expression further simplifies to

 .

Answer: 22.5
8.) The sum of the interior angles of a polygon is 1620 degrees. How many sides has the polygon?
Solution

The sum of the interior angles of a polygon with angles is .

Answer: 11

9.) Simplify: .
Solution

10.) The sum of the two angles of a triangle is three times the third angle. What is the sum of the first two angles?

Therefore,
.

Answer: 135

Grade 7 MTAP 2015 Questions with Solutions Part 2

Posted on December 22, 2015 | 12 Comments

This is the second part of the full solution series for the MTAP 2015 Questions with solutions. You may also want to read the
solutions for problems 1 – 10 and download the questions.
11.) Danny had some stickers. He gave 1/3 of the stickers plus 1 sticker to his brother. Then, he gave 1/3 of the remaining
stickers plus 4 stickers to his sister. Finally, he gave ½ of what remained plus 3 stickers to best friend. He found that he had 4
stickers left. How many stickers did Danny have at first?
Solution
If we let = number of stickers
= number of stickers given to his brothers. If we subtract the stickers given to his brother, we have
(*)

which is the number of remaining stickers.

Now, Danny gave 1/3 of this remaining stickers plus 4 stickers to his sister. That is, he gave

(#) stickers.

Now, subtracting the stickers given to her sister (#) from the remaining stickers (*), we have

(**).

Next, he gave 1/2 of the remaining stickers (**) and an additional 3. That is, he gave
 (##).

Now, subtracting ## from **, we have

..

After this, only 4 stickers are left.

So, giving us .

Answer: 42
12.) What number is 2/5 of the way from – 3 to 5?
Solution
The distance between -3 and 5 is 8. So, (2/5)(8) = 16/5.
Now,

Answer: 1/5
13.) The number is divisible by 3. The number is . What digit does represent?
Solution
Since the number is divisible by 3, the number is divisible by 9. By the divisibility rules, a number is divisible by 9 if the
sum of its digits is divisible by 9. Therefore, must be divisible by . Now, since is a
1-digit number, the only possible value for since and 27 is divisible by 9. Therefore, .
Answer: 8
14.) What is the smallest positive integer that must be multiplied to 60 to get a perfect cube?
Solution
The prime factorization of 60 is . The smallest possible number that we are looking for is .

Therefore,

Answer: 450
15.) Compute

Solution
Simplifying, we have

Now,

or .

Answer:
16.) What three-digit number is both a square of an integer and a cube of an integer?
Solution
The only numbers that will produce a 3-digit number when cubed are the numbers from 5 to 9. The only perfect square among
this numbers is 9. Therefore, the answer is . Note that its square root is 27.
Answer: 729
17.) Simplify

Solution

Answer: where (from the restriction in the original expression)

18.) If x is twice as far as -9 as it is from 3, what are the possible values of x?
Solution
The distance between -9 and 3 is 12. Now 2/3 (12) = 8 and -9 + 8 = -1. Therefore, the distance from -9 to 1 is twice that distance
from -1 to 3.

Also, if we let 3 be the center of the circle, we can draw a diameter from -9 to 15. Therefore, x = 15 is twice the length from -9
than from 3.

Answer: x = 1, x = 15

19.) Sandra is 18 years older than Paulo. In 13 years, Sandra will be as twice as old as Paulo will be then. How old is Sandra
now?
Solution
Let x = age of Paulo
x + 18 = age of Sandra

In 13 years, Sandra will be twice as old as Paulo. That is,

2(x + 13) = x + 13 + 18

Simplifying, we have

2x + 26 = x + 31
x=5

So, Sandra is 5 + 18 = 23 years old now.

Answer: 23
20.) Which is bigger or ?
Solution
and .

Converting the exponents to similar fractions, we have

and .

Converting them back to radicals, we have

Since , .

Answer:
This entry was posted in Grade 7-8, Problems with Solutions and tagged grade 7 mtap questions with answers, grade 7 mtap questions
with solutions, grade 7 mtap reviewer with answers, grade 7 mtap reviewer with solutions. Bookmark the permalink.
 12 RESPONSES TO “GRADE 7 MTAP 2015 QUESTIONS WITH SOLUTIONS PART 2”
1. Pingback: Grade 7 MTAP 2015 Questions with Solutions Part 1
2. Pingback: Grade 7 MTAP 2015 Questions with Solutions Part 3

3. Unknown | January 5, 2016 at 7:44 pm | Reply

Number 19,

On the equation, “2x+26 = x+33” the 33 there should be 31. Because on “2(x+13) = x+13+18”, 13+18= 31. Thnkx

o Sarah | January 5, 2016 at 7:45 pm | Reply

Yep! I think sO

o admin | January 6, 2016 at 5:15 am | Reply

Fixed. Thank you.

4. Pingback: Grade 7 MTAP 2015 Questions with Solutions Part 5

5. Pingback: Grade 7 MTAP 2015 Questions with Solutions Part 4

6. paul | December 22, 2016 at 2:52 pm | Reply

nice, so interesting and helpful for me. coz im the one of contestantsin mtap

7. sirymun | January 31, 2017 at 10:33 pm | Reply

At #13, is there a square number ending with digits 85?

8. sirymun | January 31, 2017 at 10:40 pm | Reply

At #18,
Using |x+9|=2|x-3| I think is a better way to solve the problem.

9. unknown | January 16, 2018 at 9:01 pm | Reply

the other number is to hard to understand “for me”

10. Fritz | December 31, 2018 at 3:24 pm | Reply

Number 18,

please recheck, the answer should be x= -1, 15 not x= 1, 15. Tnxx

Grade 7 MTAP 2015 Questions with Solutions Part 3

Posted on December 26, 2015 | 5 Comments

This is the third part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to
number 21-30. You can also read the solutions to 1-10 and 11-20.
21.) The average of five numbers is 14. The average of the three of the numbers is 12. What is the average of the other two
numbers?
Solution
The average of five numbers is 14 means that their sum is 70. The average of the three of those numbers is 12 means that their
sum is 36. Now, 70 – 36 = 34 is the sum of the remaining two numbers. Their average is 34/2 = 17.

Answer: 17
22.) A sandwich costs p pesos. A cookie costs Php9 pesos less than a sandwich. How much more expensive are 8 cookies than 5
sandwiches?
Solution
8 cookies – 5 sandwiches = 8(p – 9) – 5p = 8p – 72 – 5p = 3p – 72.

Answer: 3p – 72
23.) Which values of x satisfy |2x + 1| = |2x – 9|?
Solution
2x + 1 = -(2x – 9)
2x + 1 = -2x + 9
4x = 8
x=2
Answer: 2
24.) A car leaves P at 8 AM and travels to Q at a constant speed. A bus leaves Q at 8:45 AM and travels to P at a speed three
times that of the car. If they meet at 10 AM, find the ratio of the distance traveled by the bus to the distance traveled by the car
when they meet?
Solution
Let x = speed traveled by the car
3x = speed traveled by the bus
The time traveled by the car from 8:00 AM to 10:00 AM is 2 hours.
The time traveled by the bus from 8:45 to 10:00 AM is 1 hour and 14 minutes or 5/4 hours. Since distance is the product of the
rate and the time, the ratio of the distance traveled by the car to the bus is

So, the ratio of the distance traveled by the car to the distance traveled by the bus is 8:15.

Answer: 8:15
25.) How many 3-digit numbers are multiple of 18?
Solution
The smallest 3-digit number that is a multiple of 18 is (18)(6) = 108.
The largest 3-digit number that is a multiple of 18 is (18)(55) = 990.
So, there are 55 – 6 + 1 = 50 numbers.

Answer: 50
26.) If the perimeter of the square is a 8x + 6, what is its area?
Solution
The side of a square with perimeter . The area of the square is .

Answer:

27.) Two vertical poles are 3 meters apart. Jack’s climbing one pole well Jill climbs the other. If the distance between Jack and
Jill is 5 m, how much higher is Jill than Jack?
Solution
By the Pythagorean Theorem, , , .
Answer: 4
28.) If the circumference of a circle increased by 20% how much is its area increased?
Solution
If we let C be the circumference of the circle and r be its D, then

If we increase the circumference by 20%, we have to multiply C by 1.2. That is,

Since 2 and pi are constant, we can only change r. That is, we multiply r by 1.2. Now, if we let the area of a circle be A,

So, the area increased by 0.44 or 44%.

Answer: 44%
 29.) A camp director prepared enough food for 100 students for six days. If only 75 students came, how long when the food
supply last?
Solution
100/75 = x/6
74x = 600
x=8

Answer: 8 days
30.) How many two digit numbers are not divisible by four nor by five?
Solution
There are 90 two-digit numbers. There are 22 numbers that are divisible by 4 (divide 90 by 4 and get the integer quotient).
There are 18 numbers that are divisible by 5 (divide 90 by 5 and get the integer quotient).
However, numbers which divisible by 20 were counted twice since they are both divisible by 4 and by 5. There are 4 of them
(divide 90 by 20 and get the integer quotient). In effect, there are 22 + 18 – 4 = 36 numbers that are either divisible by 4 or 5

Therefore, there are 90 – 36 = 54 numbers that are not divisible by 4 nor by 5.

Answer: 54
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questions, grade 7 mtap questions with answers, grade 7 mtap questions with solutions. Bookmark the permalink.

5 RESPONSES TO “GRADE 7 MTAP 2015 QUESTIONS WITH SOLUTIONS PART 3”

1. Pingback: Grade 7 MTAP 2015 Questions with Solutions Part 4

2. James Sierra | February 15, 2017 at 3:24 pm | Reply

So Difficult(LEVEL 9999999). Extermely difficult

3. James Sierra | February 15, 2017 at 3:25 pm | Reply

So difficult i cant answer it

4. paul | February 15, 2017 at 6:25 pm | Reply

can i ask some question?

5. freda | February 16, 2017 at 9:51 am | Reply

<3

Grade 7 MTAP 2015 Questions with Solutions Part 4

Posted on December 31, 2015 | 17 Comments

This is the fourth part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to
number 21-30. You can also read the solutions to 1-10, 11-20, and 21 – 30.
31.) If is a prime number not equal to 2, which of the following can be a prime:
, , .

Solution
All prime numbers not equal to 2 are odd. If is odd, then and are both even, while is odd. Therefore,
only can be a prime.

Answer:
32.) What must be added to the product of and to obtain ?
Solution
The product of and is .
Now, we subtract the result from .
Answer:
33.) If the greatest common divisor of two numbers is 12 and their least common multiple is 180, what are the possible pairs of
numbers?
Solution:
The product of the gcd and lcm of two numbers is equal to the product of the numbers. So, we need to examine the factors of
12(180) = 2160 where the gcd is 12 and lcm is 180. We only have two pairs of such numbers, 12 and 180 and 36 and 60.

Answer: {12, 180} and {36, 60}

34.) Given a positive integer n, arrange the following from least to greatest:
,

Solution
Squaring all the expressions, it is easy to see that

The details are left as an exercise.

Answer: .
35.) What is the largest integer which is always a factor on the sum of three consecutive even integers?
Solution
Let , , and be three consecutive even integers. Their sum is . Therefore, 6 is always
a factor of their sum.

Answer: 6
36.) If the sum of the first positive 100 integers is 5050, what is the sum of the next 100 integers?
Solution: The next 100 integers are 101, 102, 103, …, 200. That is, we add 100 to each one of the first 100 integers. In effect,
we added (100) (100) + 5050 = 15050.
Answer: 15050
37.) With what polynomial must be divided to get a quotient and a remainder of ?
Solution
Consider dividing 12 by 7. We get a quotient of 1 and a remainder of 5. From this, we can form the equation, 12/7 = 1 + 5/7. In
general, if we divide and get a quotient and a remainder of , we can have the equation

(1).

In the equation above, we are looking for the value for b, the divisor. Therefore, multiplying the equation in (1) by , we
get , giving us . If we let , , and ,
substituting the values in (*), we get .

Answer:

38.) If leaves a remainder of when divided by , what is the remainder when is divided by ?
Solution

The modular inverse of is equal to since . This means that . Multiplying

by 8, we have . Therefore, .

Answer: 7

39.) Find the solution set: .

Solution
, ,
, , .

Answer: -8 or 14
40.) Compute:
Solution
 Answer:

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2015 reviewer with solutions. Bookmark the permalink.

17 RESPONSES TO “GRADE 7 MTAP 2015 QUESTIONS WITH SOLUTIONS PART 4”

1. Harrold Glenn Perido Caidoy | January 9, 2016 at 8:29 pm |Reply

#38 is hard to explain although I found the answer. If (7n – 8)|9 , then (5n – ?)|9—-
Sol. if n = 5, the hypothesis is correct giving the remainder(?) be 7

o admin | January 10, 2016 at 3:25 am | Reply

Actually, this can be done easily using modulo division. I just want to have a solution accessible to high school students. As of
now, I have no time to go back to it yet. Still typing questions from 2015. I will complete the solutions once I have uploaded
everything. I’ll try to look at your solution later. Thank you.

2. AnonymousPerson | January 14, 2016 at 9:24 am | Reply

This has a lot of grammatical mistakes (or maybe the test paper has. I don’t know, it’s not the same) so I was confused. All in

all, this was very very helpful and thank you for providing this info.

3. WTF??!! | January 15, 2016 at 6:12 am | Reply

I don’ understnad number 40 why is the answer 73/75…

o admin | January 16, 2016 at 1:20 pm | Reply

This is just a simple typo error, it’s 73/675. I fixed it already.

4. randy | January 31, 2016 at 11:46 am | Reply

try to fix no.35

o Tyeng | January 31, 2016 at 8:39 pm | Reply

no. 35 is asking for 3 consecutive even integers…

 admin | March 11, 2016 at 5:47 am | Reply

 Oh, thank you. I missed that. Changed it already.

 paul | December 25, 2016 at 1:20 pm | Reply

i think the solution in no. 35 is correct

 paul | December 25, 2016 at 1:22 pm | Reply

no, no.35 is asking for the largest integer in the factor

 paul | December 25, 2016 at 1:24 pm | Reply

it is not asking for 3 consecutive even integers

o admin | March 11, 2016 at 5:47 am | Reply

Fixed. Thank you.

5. shirley | February 16, 2016 at 9:14 pm | Reply

waiting for the solution of 38

o admin | February 17, 2016 at 8:45 pm | Reply

Done it already using modulo division. Sorry, I was looking for an easier solution, but I can’t find one.

6. Jasper | March 8, 2016 at 3:38 pm | Reply

Hello. I’m a student from A science school. I’m sorry to say but the answer in no.35 is 6 coz it says that “three consecutive even
integers”, not just integers. Try to solve it again.

o admin | March 11, 2016 at 5:43 am | Reply

Thank you very much for pointing that out. I missed the word“even.” I already changed the solution.

7. hazel | February 16, 2017 at 5:42 am | Reply

how can I download a copy of the solutions?
Grade 7 MTAP 2015 Questions with Solutions Part 5
Posted on January 2, 2016 | 11 Comments

This is the fifth part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to
number 41-50. You can also read the solutions to 1-10, 11-20, 21 – 30, and 31-40.
41.) Each square in the figure has side length 1. The curve each square is a circular arc with center at a corner of the square.
What is the area of the shaded region?
Solution: will be discussed in a separate post.

Answer: 8 square units

42.) What is the least common multiple of 168 and 420?
Solution
Left as an exercise.

Answer: 840
43.) A salesman receives a basic salary of Php10, 000 and a commission of 5% on all sales. Find his total sales in a month when
he earned Php25, 000?
Solution
10, 000 + .05x= 25, 000
0.05x = 15, 000
x = 300 000
Answer: Php 300, 000.00
44.) What is the absolute value of at ?
Solution

Answer:
45.) Find all real numbers for which (7 – x)/2 > (4x + 3)/4
Solution
Multiplying both sides by 4, we have

2(7 – x) > 4x + 3
14 – 2x > 4x + 3
11 > 6x
11/6 > x
x < 11/6
46.) For what values of x is (3x – 1)/4 < (2x + 5)/3?
Solution
Multiplying both sides by 12, we obtain

3(3x – 1) < 4(2x + 5)

9x – 3 < 8x + 20
x < 23
47.) Write an equation of the line through (-2, 3) and (1,4).
Solution

The slope of the line is m = (4 – 3)/(1-(-2)) = 1/3.

We use the point slope form. That is,

y – 4 = (1/3)(x – 1)

y – 4 = 1/3x – 1/3

3y = x + 11

y = (x + 11)/3
Answer: y = (x + 11)/3

48.) Solve for x and y: 7x – 3y = 23 and x + 2y = 13.

Solution
Multiplying x + 2y = 13 by -7, we have
-7x – 14y = -91 (*)
7x – 3y = 23 (**)
Adding (*) and (**), we obtain

-17y = -68
y = 4.
Substituting y to x + 2y = 13,
x + 2(4) = 13
x=5
49.) Pete is 12 years old and His grandfather 63 years old. And how many years we’ll be age be one fourth of his grandfather?
Solution
Let x be the number of years to be added to both ages.
(1/4)(63 + x) = 12 + x
Multiplying both sides by 4,

63 + x = 48 + 4x
3x = 15
x=5
Answer: 5 years

50.) ABC has its coordinates at A(a, -1), B(8, -1), and C(5,4). If the base is twice the height, find a.
Solution
If we let AB be the base, then the height is the difference between y-coordinate of C and -1. That is, |4 -(-1)| = 5.

Now, |a – 8| = 2(5) = 10
a – 8 = 10
a = 18
-(a – 8) = 10
8 – a = 10
–a = 2
a = -2
Answers: a = -2 or a = 18
Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 1
Posted on January 16, 2016 | 13 Comments

Below is the first part of the Grade 8 MTAP 2015 Elimination Questions with Solutions and answers. If you find any errors,
please comment on the box below.
1.) Find the average of the numbers -1, 3/2, and 1/2.

Solution
(- 1 + 3/2 + 1/2)/3 = 1/3
Answer: 1/3
2.) How much larger is 2/3 than 1/6?

Solution
2/3 – 1/6 = 4/6 – 1/6 = 3/6 = 1/2
Answer: 1/2
3.) If one ream contains 500 sheets of paper and a sheet of paper is 0.3 mm thick, how thick is one ream in meters?
Solution
500 × 0.3mm = 150 mm = 0.15m
Answer: 0.15m
4.) What is the second largest number among numbers , 3/2 , 1.4, and 1.6?

Solution
is around 1.41 and is around 1.7.
Answer: 1.6

5.) If an inch is about 2.54 cm, what is 1 cm to the nearest hundredth of an inch?
Solution
Answer: 0.39
6.) If U = {1, a, 2, b, 3, c, 4, d} and A = {1, 2, c, d}, what is Ac ?
Solution
Ac is the complement of A, or the elements of the set that is not in A but in U. So,
Ac = {a, b, 3, 4 }
Answer: Ac = {a, b, 3, 4 }
7.) Using the same sets in Item 6 and B = {1, 2, 3, 4}, how many subsets does A ∩ Bc have?
Solution
A = {1, 2, c, d} and B = {1, 2, 3, 4}. The complement of B denoted by Bc are the elements of U not in B. So, Bc = {a, b, c, d}.
Now, A ∩ Bc are the elements that are common to A and Bc. Therefore, A ∩ Bc = {c, d}. Now, the number of subsets of a set
with n elements is 2n (this includes the empty set), so there are 22 = 4 subsets.
Answer: 4
8.) If |P| = 10, |Q| = 12, and |P Q| = 15, what is |P ∩ Q |?

Solution 1
We know that the cardinality of the union of two sets is equal to the sum of the cardinality of these sets less the cardinality of
their intersection. That is, if we have sets P and Q, |P ∪ Q| = |P| + |Q| – |P ∩ Q|.

Substituting, we have
15 = 10 + 22 – |P ∩ Q|
|P ∩ Q| = 7

Answer: 7
Solution 2
x + y + z = 15 ()
x + y = 12 ()
y + z = 10 ()
Adding the (**) and (***), we have x + 2y + z = 22 (#)
Subtracting (*) from (#),
x + 2y + z – (x + y + z) = 22 – 15
y=7

Answer: 7
9.) If |M ∩ N| = 24 and |M ∪ N| = 26, what is |M| + |N|?

Solution
From number 8, we know that |M ∪ N| = |M| + |N| – |M ∩ N|. Substituting, we have,
26 = |M| + |N| – 24
|M| + |N| = 50.
Answer: 50
10.) There were 59 participants during the recent math camp. Among them, 37 liked doing projects, 30 liked solving problems,
and 13 liked both. How many of the participants did not like at least one of these two activities?

Solution
Solution will be discussed in a separate post.

Answer: 5

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questions with solutions, grade 8 mtap reviewer with answers, grade 8 mtap reviewer with solutions. Bookmark the permalink.

13 RESPONSES TO “GRADE 8 MTAP 2015 ELIMINATION QUESTIONS WITH SOLUTIONS – PART 1”

Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 2

Posted on January 22, 2016 | 10 Comments

This is the second part (questions 11-20) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the
solutions for questions 1-10 here. If you found any errors in the solution, please comment in the box below.
11.) If and , what is ?

Solution
Answer: -12
12.) Simplify .
Solution

Answer:

13.) If and are positive constants, simplify .

Solution
Note that , and

Now

This is already correct, but if you want your answer in radical form, the previous expression can be converted to

Answer: or
14.) What is the quotient when is divided by ?

Solution

Answer: remainder .
15.) In Item 14, what is the remainder?

Answer:
16.) If , what is ?

Solution
Answer:
17.) If and , what is ?

Solution
and

Substituting the given values above,

Answer: 238
18.) If the length, width, and height of an open-top rectangular box are cm, cm, and cm, what is its surface
area?

Solution
The formula for finding the surface area of a rectangular prism with length , width and
height is . Since the box is open, we subtract lw, which is the top face. So, the surface area of the
open box is .

Substituting, we have

Answer:
19.) A man walked km for 2.5 hrs, then jogged km for 3.5 hrs, and finally walked again km for 4 hrs. If
his average speed for the entire exercise was 4 kph, what is x?
Solution

Answer: 3/5 or 0.6

20.) Simplify .

Solution
We can group the expressions as sum and difference of two cubes.

Now, this is in the form of the difference of two squares .

So,
 Answer:
This entry was posted in Grade 7-8 and tagged 2015 grade 8 mtap questions with solutions, grade 8 mtap questions with
solutions, mtap reviewer for grade 8. Bookmark the permalink.

10 RESPONSES TO “GRADE 8 MTAP 2015 ELIMINATION QUESTIONS WITH SOLUTIONS – PART 2”

1. Jeaven Lozano | February 16, 2016 at 2:53 pm | Reply

YOUR BERY HELP! EAT realy helps me to revyu my nowtes! Bery usepull

2. nogie | July 17, 2016 at 11:45 am | Reply

nice

3. Phoebe | October 18, 2016 at 11:03 pm | Reply

18.5x^2-3x-18 dapat po

4. Phoebe | October 18, 2016 at 11:03 pm | Reply

18.5x^2-3x-18 dapat po

5. ronnie aljibe | December 29, 2016 at 7:40 am | Reply

this will be of great help

6. bret romeo | January 24, 2017 at 11:21 am | Reply

Question about number 19, please help, i dont get it, the question is the value of x, since the only constant is the
average speed for all the exercises, which is 4kph, can we just simply find the sum of all the distance traveled, divided by 10
and then equate it to 4?

7. desiree alyanna | February 16, 2017 at 9:47 pm | Reply

question number 19 is quite complicated.please help.

o Aeron | February 1, 2018 at 5:20 pm | Reply

(29.5x-1.5)/8x=4
29.5x-1.5=32x
2.5x=1.5

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