MATH 1 (A)

Easy

1.) What symbol should replace the blank so that the following statement would be correct? 20 _ 11 +
9

2.) What number is equal to 20 ones + 4 tens – 5 tens?

3.) I started counting from 11 to 33: 11, 12, 13, … ,32, 33. The first number I counted was 11, and the
last number I counted was 33. How many numbers did I count in all?

4.) 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 do the line cross the circle?

5.) There is a group of children standing in a circle. To the left of Alex, between Alex and Nick, there
are 4 children. To the right of Alex, between Alex and Nick there are 7 children. What is the total
number of children in the circle?

6.) A ship was attacked by pirates. One by one they climbed a long rope ladder to get to the ship. The
pirate captain was in the middle. If the captain was the sixth pirate to get on the ladder, how many
pirates were there on the ladder?

7.) It is 10:00 o’clock at the moment. What time is it going to e in 30 hours?

8.) Ben is five years old. His sister, Betty, is seven years older than him. What is the sum of their ages?

9.) A shirt costs three times a cap. The shirt cost Php 240. How much does the cap cost?

10.) Paula has 20 pencils and Micah has 6 pencils less than Paula. What is the total number of Paula
and Micah’s pencils?

11.) What is one-half of the sum of 4 and 14?

1.) Subtract the difference 70 and 40 from the sum of 20 and 80. What is the result?

2.) Gayle had 6 sandwiches for her and her 5 friends. She sliced each sandwich into halves. One friend
got 2 slices. The second one got 1 slice, the third and fourth got 2 slices each and the last one got 3.
How many hales of sandwiches were left for Gayle?

3.) A team of 3 pupils ran a 400-meter relay race. Jose ran 175 meters and Pedro ran 125 meters. How
many meters did the last pupil ran?

4.) The perimeter of a square garden is 60 m. What is the side length of the garden?

5.) The last Sunday of a month was on the 28th of the month. What day of the week was the firs day of
the month?

6.) Annie collected 28 empty bottles and Irish collected 23 empty bottles. They need to collect 90
empty bottles in all. How many more bottles do they need to collect?

Difficult

1.) My monkey eats only cabbage and bananas. Last week he ate either 10 bananas or 2 heads of
cabbage each day. If he ate a total of 6 heads of cabbage last week, how many bananas did he eat?

2.) Six boys are lining up to buy tickets. Let us call them A, B, C, D, E and F. Boy F is after boy A and
before boy D and he is also between boy B and boy C. Boy B is the first in the line and boy E is the last
in the line. In what position is boy F?

3.) How many numbers between 10 and 31 can be written using only the digits 1, 2, and 3, if the digits
may be repeated?

4.) There were 660 people who attended the school’s Family Day. One hundred twenty-five of them
were men, 330 of them were women and the rest were children. How many children were there?

5.) Write the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 on your scratch paper. Which two numbers should
you erase so that the remaining numbers will add up to 37?

6.) Annie is watching a movie. It is 2 hrs and 20 minutes long. There were 10-minute previews before
the movie. If the previews started at 2:30 PM, what time will the movie be finished?

Tiebreaker

1.) Lunch time begins at 11:45 AM. If lunch time is 45 minutes long, what time does it end?

2.) What is the sum of the smallest and largest two-digit numbers?

3.) Jane has two pieces of ribbon. One piece is 10 cm longer than the other. The total length of the two
pieces is 40 cm. How long is the longer piece?

Do-or-Die

1.) How many two-digit numbers are there which do not contain the digits 0 and 1?
Answer key (A)

1.) =
2.) 10
3.) 23
4.) 2
5.) 13
6.) 11
7.) 4 o’clock
8.) 17
9.) Php 80
10.) 34
11.) 9

Average

1.) 70
2.) 2
3.) 100 m
4.) 15 m
5.) Monday
6.) 39

Difficult

1.) 40
2.) 3rd
3.) 6
4.) 205
5.) 8 and 10
6.) 5 PM

Tiebreaker

1.) 12:30 PM
2.) 109
3.) 25 cm

Do-or-Die

1.) 64
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?

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: 4.) 5

Easy 5.) 50

1.) 750 6.) 30

2.) 262 Difficult

3.) 800 1.) 800

4.) 700 2.) Php 120

5.) 31 3.) 440 cm

6.) 1 1/5 4.) 95

7.) 8 5.) Php 50

8.) 18 6.) 40 cm

9.) 3 Tiebraker

10.) 17 1.)

11.) 24 liters 2.) 90

Average 3.) 47

1.) 40 Do-or-Die

2.) Php 1100 1.) 24 cm

3.) Php 170

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