With Checking
With Checking
With Checking
COLLEGE OF EDUCATION
Questions in the Quantitative Reasoning measure ask you to model and solve problems using
quantitative, or mathematical, methods. Generally, there are three basic steps in solving a mathematics
problem:
Here is a description of the three steps, followed by a list of useful strategies for solving mathematics
problems.
The first step is to read the statement of the problem carefully to make sure you understand the
information given and the problem you are being asked to solve.
Some information may describe certain quantities. Quantitative information may be given in words or
mathematical expressions, or a combination of both. Also, in some problems you may need to read and
understand quantitative information in data presentations, geometric figures, or coordinate systems. Other
information may take the form of formulas, definitions, or conditions that must be satisfied by the quantities.
For example, the conditions may be equations or inequalities, or may be words that can be translated into
equations or inequalities.
In addition to understanding the information you are given, it is important to understand what you need to
accomplish in order to solve the problem. For example, what unknown quantities must be found? In what
form must they be expressed?
1
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Solving a mathematics problem requires more than understanding a description of the problem, that
is, more than understanding the quantities, the data, the conditions, the unknowns, and all other mathematical
facts related to the problem. It requires determining what mathematical facts to use and when and how to use
those facts to develop a solution to the problem. It requires a strategy.
Mathematics problems are solved by using a wide variety of strategies. Also, there may be different ways to
solve a given problem. Therefore, you should develop a repertoire of problem-solving strategies, as well as a
sense of which strategies are likely to work best in solving particular problems. Attempting to solve a problem
without a strategy may lead to a lot of work without producing a correct solution.
After you determine a strategy, you must carry it out. If you get stuck, check your work to see if you made an
error in your solution. It is important to have a flexible, open mind-set. If you check your solution and cannot
find an error or if your solution strategy is simply not working, look for a different strategy.
When you arrive at an answer, you should check that it is reasonable and computationally correct.
2
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Looking for a pattern is strategy that you can use to solve problems. The goal is to look for items or
numbers that are repeated or a series of events that repeat. The following problem can be solved by
finding a pattern.
Problem No. 1
b. Do: Solution
Number of jumps
Day 1 5-2 =3
Day 2 3+5-2 =6
Day 3 6+5-2 =9
Day 4 9+5-2 = 12
Day 5 12+5-2 =15
Day 6 15+5-2 =18
Day 7 18+5- =21
3
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 2
Number of triangles 4 6 8 10 12 14 16 18
4
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 3
b. Solution:
a) 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 120 exchanges
120 2 = 240 business cards
If there were 16 businessmen, 240 business cards were exchanged.
b) 380 2 = 190
190 = (19 20) 2 = 19 + 18 + 17 + + 3 + 2 + 1
If there was a total of 380 business cards exchanged, there were 20 businessmen at the
meeting.
5
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 4
A to B 2 2
B to C 2x3 6
A to C 2x6 12
C to D 70 70
A to D 70 x 12 840
D to E 2 2
A to E 2 x 840 1680
6
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
b. Solution:
Therefore, Gab has a P500 peso bill, 3 pieces of P100 peso bill and 4 pieces of P50 peso bill that makes it
1000 pesos
Checking:
7
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
b. Solution:
st
1 pattern Total dots
column
1 12 12
2 12+16 28
3 12+16 + 21 49
4 12+16 + 21 + 26 75
5 12+16 + 21 + 26 + 31 106
6 12+16 + 21 + 26 + 31 + 36 142
7 12+16 + 21 + 26 + 31 + 36 + 41 183
8 12+16 + 21 + 26 + 31 + 36 + 41 + 46 229
a) The number of dots for a pattern with 6 hexagons in the first column is 142
b) If there are 229 dots then the pattern has 8 hexagons in the first column.
Cheking:
8
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
When we do that, we find that lockers 1, 4, and 9 are open and the
others are closed. Now, that isn't much to go on, so maybe you could
let the next 10 students go do their thing. Then the first 20 lockers
are through being touched, and we find that lockers 1, 4, 9, and 16
are the only ones in the first 20 that are still open.
9
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Let's take any old locker, like 48 for example. It gets its state
altered once for every student whose number in line is an exact
divisor of 48. Here is a table of what I mean:
This Leaves
students locker
48
1 Open
2 Shut
3 Open
4 Shut
6 Open
8 Shut
12 Open
16 Shut
24 Open
48 Shut
Checking:
1,4,9,16,25,36,49,64,81,100.
10
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
b. Solution:
Cheking
2
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Each row of the triangle has one more ball than the previous one. In a triangle with 8 rows, row 1 has 1
ball, row 2 has 2 balls, row 3 has 3 balls, row 4 has 4 balls, row 5 has 5 balls, row 6 has 6 balls, row 7 has
7 balls, row 8 has 8 balls. When we add these we get: 1+2+3+4+5+6+7+8=36 balls
3
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
a. Solution:
15 + 6 = 21
21 + 7 = 28
28 + 8 = 36
36 + 9 = 45
4
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
When a problem contains information that has more than one characteristic, an effective strategy is
to set out that information in a table. A table helps to organize the information so that it can be easily
understood and so that relationships between one set of numbers and another become clear.
A table makes it easy to see what information is there, and what information is missing. When a table
is drawn up, the information often shows a pattern, or part of a solution, which can then be completed.
Students will usually have to create some of the information in order to complete the table and so solve
the problem. Using a table can help reduce the possibility of mistakes or repetitions.
Problem No. 1
You save $3 on Monday. Each day after that you save twice as
much as you saved the day before. If this pattern continues, how much
would you save on Friday?
5
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 2
b. Solution:
Team member Distance in meters
1st 300
2nd 250
3rd 200
4th 150
5th 100
50 Meters was the last team member swim in the relay race.
6
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 3
b. Solution:
Hour 1 2 3 4 5 6 7
Slow car 55 110 165 220 275 330 385
Fast car 0 65 130 195 260 325 390
7
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 4
Louise is on her way to school with her car. Unfortunately, she was
stuck in traffic. At exactly 6:30 a.m., the red or stop light appears and at
6:35 am it appears orange and finally at 6:36 am, it goes Green or Go light.
Unfortunately, Louise did not able to pass the traffic light after it goes red
or stops at 6:40 am. She estimated that only 30 cars passed before the light
become red. What time did Louise can able to pass the Traffic light if she
estimated that she was the 145th car?
b. Solution:
Red light Orange light Green light total # of cars
passed
1st 6:30 am 6:35 6:36 30
2nd 6:40 6:45 6:46 60
3rd 6:50 6:55 6:56 90
4th 7:00 am 7:05 7:06 120
5th 7:10am 7:15 am 7:16am 150
At 7:16am, she can able to passed the traffic light and continue to drive on her way to school.
Checking:
(1st Go) 30 + (2nd Go) 30 + (3rd Go) 30 + ( 4th Go) 30 + (5th Go) 30 = 150 cars and she was the 145th car
so she can passed and continue to drive on her way to school.
8
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
9
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
b. Solution:
13-gon = n(n-3)/2
= 13 ( 13 -3) / 2
= 65 diagonals
10
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
b. Solution:
1 10 60
2 12 72
3 14 84
4 16 96
5 18 108
6 20 120
Josie starts at 60 minutes per week and she increases by 12 minutes per week for five weeks.
That means the total jogging time is 60+125=120 minutes.
Checking:
Josie increases her jogging time by two minutes per day. She jogs six days per week. This means that
she increases her jogging time by 12 minutes per week.
Josie starts at 60 minutes per week and she increases by 12 minutes per week for five weeks.
11
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
12
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
Yuan save $100 on week 1. Each week after that you save
twice as much as you saved the week before. If this
pattern continues, how much would you save at end of
the month?
b. Solution:
13
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
Two dice are rolled. You are to guess the sum of the two
numbers. What is the sum that you should guess so that
you have the highest chance of guessing it right?
14
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
volume?
The box of greatest volume is made if we cut out squares with a side length of three inches.
15
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 1
b. Solution:
4 (cookies left on the plate)
12 (cookies given to neighbor)
3 ( cookies ate by Sams dad)
+ 2 (cookies ate by Sam)
______________________________________
21 cookies did Sams mother make altogether
16
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 2
b. Solution:
Fathers age = 4 x nadias age + 16
36 = 4 (X) + 16
X = 5 ; Nadias Age
Checking:
17
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 3
b. Solution:
Rose 21 yrs old
Tine 8 + 21 = 29
Tine is 29 years old
Yanna 2 * 29 = 58
Yanna is 58 years old
Mary 58 19 = 31
Therefore, Mary is 31 years old
Checking:
Mary is 31 yrs old, Yanna is 58, Tine is 29 years old and Rose is 21 years old.
31 yrs + 19 = 58 ,that is the age of Yanna. Then, 58 /2 = 29; age of Tine. And finally, 29 8 is equals to
21, which is the age of Rose
18
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 4
A man died and left the following instructions for his fortune, half to
his wife; 1/7 of what was left went to his son; 2/3 of what was left went
to his butler; the mans pet pig got the remaining $ 2000. How much
money did the man leave behind altogether?
che
b. Solution:
Pig = $2000
1/3 X = 2000
X = 6000
6/7 X = 6000
X = 7000
X = 7000
X = 14 000
19
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
Suppose I am handing out candy. I give Susan 8 pieces, but she says she
doesn't need that many, so she gives me 3 pieces back. I give Mandy 7
pieces, and lastly, I give you 5 pieces. After doing this, I have 4 pieces of
candy left for myself. Based on all of this information, can you tell me how
many pieces of candy I started out with?
b. Solution:
Checking:
Right before I had 4 pieces left for me, I gave you 5 pieces. To undo this, I would add 5 pieces to
my 4, so now I have 4 + 5 = 9 pieces of candy. The next thing to undo is giving Mandy 7 pieces.
To do this, I add those 7 pieces to my 9 pieces, giving me 7 + 9 = 16 pieces of candy. Before
this, I gave Susan 8 pieces of candy, but she gave me 3 pieces back, so this one is a little trickier
to undo. There's a couple ways to think of this, but ultimately, we gave Susan 8 - 3 = 5 pieces of
candy since she gave 3 of the 8 back. Thus, to undo this step, we add 5 pieces of candy to my
running total, giving me 16 + 5 = 21. This tells us that I had 21 pieces of candy to start with.
20
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
We need to find the money in Annes bank account at the beginning of the day on Friday.
She took out $24.50 and $80 and put in $235.
She ended up with $451.25 at the end of the day.
b. Solution:
451.25235+80+24.50=320.75
Anne had $320.75 in her account at the beginning of the day on Friday.
Checking:
21
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
b. Solution:
Subtract: 1 hour 25 minutes. This is the time it took to get from Santa Clara to Los Altos..
22
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
Mr. and Mrs. Atkins had friends from Canada come to visit them. They
decided to take their friends to their favorite restaurant for dinner. In
addition to the cost of the dinner, Mr. Atkins had to pay some extra
expenses. He paid $12 for parking, $18 for tax, and he left a tip of $30 for the
waiters. When they got home, Mrs. Akins asked Mr. Atkins how much the
dinner had cost. Well, he said, looking in his wallet. I know I started with
$300, and now I have $15.
What will he tell Mrs. Atkins? How much was the dinner?
b. Solution:
23
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
b. Solution:
Average = 95%
5 x 95 = 475
Ave(3) = 92%
3 x 92 = 276
475 276 = 199
199 / 2 = 99.5
Therefore on the next two test she needs 99.5% to get an A.
24
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 1
b. Solution:
First Guess:
Amy = 8 tickets
Judy = 4 tickets
Check
8 + 4 = 12
8 - 4 = 4 ( Amy sold 4 more tickets)
These numbers do not work!
Second Guess:
Amy = 7 tickets
Judy = 5 tickets
Check
7 + 5 = 12
7- 5 = 2 ( Amy sold 2 more tickets)
These numbers do work!
25
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 2
b. Solution:
Mykel James
12 4
13 5
14 6
15 7
16 8
26
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 3
b. Solution:
27
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 4
b. Solution:
Therefore, there were 13 girls and 15 boys in Ms. Dela Cruz class.
Checking:
13 * 15 = 195
28
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 5
b. Solution:
(6 + 3)(6 - 2) = 36
(5 + 3)(5 - 2) = 29
(4 + 3)(4 - 2) = 14
29
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
b. Solution:
15 + 17 = 32. It does not work. Since 32 is smaller than 44, pick higher numbers
21 + 23 = 44
30
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
b. Solution:
Pretend that 3 children tickets were sold. Then, 17 adult tickets were sold
Total cost = 3 5 + 17 12 = 15 + 204 = 219
The total is too high. Pretend that 14 children tickets were sold. Then, 6 adult tickets were sold
Total cost = 14 5 + 6 12 = 70 + 72 = 142
The total is a little too low now. Pretend that 12 children tickets were sold. Then, 8 adult tickets were
sold
Total cost = 12 5 + 8 12 = 60 + 96 = 156
As you can see, it is going higher again and it is getting closer to 163. May be 11 tickets for children
and 9 tickets for adults will work
Total cost = 11 5 + 9 12 = 55 + 108 = 163
31
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
b. Solution:
He gave $10 -2
$5 3
$1 5
A total of 10 bills and paid $40 in all.
32
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
33
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 1
Larrys pet cricket jumps 2 inches in day one and 3 inches the next
day. How many days will it take for Larrys pet to jump 12 inches?
b. Solution:
Figure 1
34
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 2
Starting from his house, Zack cycled the following path: 2 km North, 3 km East, 3
km North, 8 km West, 1 km North, 6 km West, 10 km South, 7 km East, and finally 4 km
North. How far was Zack from his house when he completed the above journey?
Zack cycled the following path: 2 km North, 3 km East, 3 km North, 8 km West, 1 km North, 6
km West, 10 km South, 7 km East, and finally 4 km North.
How far was Zack from his house when he completed the above journey?
b. Solution:
35
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 3
Marah is putting up a tent for a family reunion. The tent is 16 feet by 5 feet.
Each 4-foot section of tent needs a post except the sides that are 5 feet. How many
posts will she need?
b. Solution:
I drew a rectangle where each long side is 16 feet, and there is 1 post every 4 feet. I drew a circle for each
post. I remembered to draw a post at each end. There are 10 posts total.
Checking:
36
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 4
June 4 , start of rainy season, Ralph placed an empty 1.5 liter bottle. Every rain, the
bottle filled 0.2 litter of rain water. If only every other day heavy rain falls, on what
nth day thus the bottle completely filled by water?
b. Solution:
It started on June 4 and it filled 0.2 L. The next day, June 5, it doesnt rain. The next rain is June 6, the
container filled an additional 0.2 L so it contains a total of 0.4 L. and finally, on June 18, the 1.5 L was totally
filled of rain water.
Checking:
Day Filled water
( add 0.2)
June 4 0.2
June 6 0.4
June 8 0.6
June 10 0.8
June 12 1.0
June 14 1.2
June 16 1.4
June 18 1.6
th
On the 18 of June was completely filled the container by water rain.
37
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
b. Solution:
Divide one rectangle into 20 equal-sized sections. Then shade 1320 of the diagram.
The diagram is 11320 shaded. So, Shannon jogged a total of 11320 miles on those two days.
To find out how many miles she jogged all together, add 1320+12.
The fractional part of the mixed number has a different denominator than 12.
Find the least common multiple (LCM) of both denominators. The least common multiple of 20 and
2 is 20.
Next, we rename the problems.
12=1020
Now we can add the two together.
38
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
Laura has 3 green chips, 4 blue chips and 1 red chip in her bag.
What fractional part of the bag of chips is green?
1320+1020=11320
b. Solution:
Draw 8 chips.
39
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
Murat has decided to plant grapes in the garden behind his house. His neighbor Volkan has
grown grapes successfully for a long time and has given Murat advice about how to plant vines.
Volkan told him to plant them three meters apart in rows that are three meters apart. He also told
him to leave at least three meters between each vine and the edge of the garden. Murat has
measured the size of his garden and learned that its a rectangle with sides of 25 meters and 35
meters. How many vines should Murat buy?
40
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
Handan wants to make soup. The recipe says she should use one liter of water, but
she does not have a one-liter container. She has a five-liter container and a three-liter
container. How can she use these two containers to measure one liter of water?
b. Solution:
41
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
Each of the small boxes in the figure at the right is a square. What is the total
number of different squares that can be traced using the segments of the figure?
b. Solution:
1x1 21
2x2 12
3x3 5
42
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
b. Solution:
First Second Third
43
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 2
a. Understand the problem:
Find the median of the What is the median?
following test scores: 73,
65, 82, 78, and 93.
b. Solution:
44
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 3
a. Understand the problem:
Sarah is on vacation Sarah is on vacation.
and brought 3 pairs of pants She brought 3 pairs of pants
(blue, black, and white) and 3 and 3 shirts.
shirts (pink, yellow and green). How many different outfit
combinations can she make?
How many different outfit
combinations can she make?
b. Solution:
45
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
b. Solution:
Checking:
Simply, if it starts with 1, there were combinations. If it starts with 12, there were combinations. If it
starts with 3, there were combinations. And if it starts with 4, there were combinations.
46
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 5
b. Solution:
F1T1 F1T2 F1T3 F1T4
47
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 6
Solution:
48
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
a. Understand the problem:
Judy is taking pictures of You need to know that
Jim, Karen and Mike. She any of the students can be first, second or
asks them, " How many third.
different ways could you
three children stand in a
line?"
b. Solution:
So, there are 6 ways that the children could stand in line.
49
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
Melike and Funda are good friends. When Melike got the flu, her doctor wrote a prescription
for twenty 30mg pills, and told her to take two a day, one after breakfast and one after dinner.
Three days later, Funda also got the flu. Her doctor prescribed thirty 20mg pills, and told her
to take a pill every four hours between 9:00 and 21:00. Whose medicine was finished first?
50
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
The game of dominoes is played with black and white tiles. Each tile is divided into two
halves and on each half a number from 0-6 is represented in the form of dots. Each tile
contains a pair of numbers and each pair appears only once in a complete set. How many
tiles are there in a complete set of tiles?
b. Solution:
51
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
b. Solution:
If n =104, then (n + 2) = (104 +2) = 106, and (n + 4) = (104 + 4) = 108. Therefore, the three consecutive
even numbers are 104, 106, and 108.
52
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem no. 2
b. Solution:
The sum of these two numbers is twenty, so I will add them and set this equal to 14.
P/4 + 1 + P/3 1 = 14
P/4 + P/3 = 14
P/4 + P/3 = 14
12 [(3P+ 4P) /12 = 14 ]
3P + 4P = 168
7 [7P = 168 ] 7
P= 24
Paolos age is 24
Checking:
If Paolo is 24 now, then he will 28 in four years, fourth of it is 7 and she was 21, three years ago, third of
it is 7. So, 7 + 7 = 14, so the solution is correct.
53
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
b. Solution:
If x=4;
4y -2(4) = 16
4y = 16 + 8
Y = 24 /4
The value of Y = 6
54
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 4
b. Solution:
If y = 6;
2x + 4y = 30 + y
2x + 4(6) = 30 + (6)
2x = 36 24
2x = 12
X = 12 / 2
The value of X = 6
55
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
A rectangle has an area of 40 a. Understand the problem:
A rectangle has an area of 40
square meters. If the
square meters. If the perimeter of the
perimeter of the rectangle is
rectangle is
26 meters, what are the
26 meters, what are the
length and the width of the length and the width of the rectangle?
rectangle?
b. Solution:
A = L x W 40 = L x W
2W + 2L = P 2W + 2L = 26
A = L x W 40 = L x W
40 is a product of 2 and 20, 4 and 10, or 5 and 8.
2W + 2L = P 2W + 2L = 26
The numbers 5 and 8 are the two numbers that work for both formulas.
56
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
b. Solution:
2X 3 = 13
2x = 13 + 3
X = 16 / 2
X=8
57
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
b. Solution:
3( 2 + 4 + 4) = 0
3(( + 2)2 ) = 0
(( + 2)2 ) = 0
X+2 = 0
X = -2
58
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
a. Understand the problem:
A truck driver travels for 4 T = 4 hours and 30
hours and 30 minutes at a minutes =
constant speed and travels constant speed
252 miles. Find the speed of D = 252 miles
the truck in miles per hour. Find the speed of the
truck in miles per hour (R)
b. Solution:
T = 9 / 2 hrs
D = RT
252 = R (9/2)
504 = 9 R
504 / 9 = R
R = 56
59
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
a. Understand the problem:
Eight less than the product
What is the inequality to
of -3 and a number is represent this relationship?
greater than -26. What is
the inequality to represent
this relationship?
b. Solution:
60
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 1
b. Solution:
61
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 2
If there are no dancers that arent slim and no singers that arent
dancers, then which statements are always true?
b. Solution:
The tricky part is that the question is phrased negatively. This means that you first need to identify the nature
of each group, and then establish the relationship between the groups. If you draw a diagram, the relationship
between the groups becomes clearer. The only statement is that all singers are slim.
Checking:
62
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 3
Anna, Karen and Nina take turns in getting the midnight shift at
Ward 143 such that no one is assigned two nights in a row. Anna
was assigned two nights ago and is assigned again tomorrow
evening. If Karen is assigned the night immediately following
Annas duty, who can take tonights midnight shift?
1. Only Anna
2. Only Karen
3. Only Nina
b. Solution:
63
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 4
Mina, Bing, Amy, and Cel have surnames Folres, Mendez, Presez
and Reyex but not respectively. Mina is taller than Amy and Cel. Ms.
Mendez is tallest of the four. Ms. Flores is taller than Ms. Reyes but
shorter than Ms. Perez. Also, Cel is taller than Amy and Bing. What
is the full name of the second tallest person?
1. Amy Mendez
2. Cel Perez
3. Cel Flores
4. Bing Reyes
5. Mina Perez
64
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 5
Three popular courses at a local high school are geography, art,
and science. A review of the
schedules of 200 students revealed that 70 have geography, 80
have science, 60 have art, 35
have geography and science, 33 have geography and art, 31 have
science and art, and 15
have all three classes. How many of the 200 students have none of
these classes?
b. Solution:
COLLEGE OF EDUCATION
Problem No. 6
True
False
Uncertain
The correct answer is that the third statement is true. If GC > RM and LG > GC,
then LG > GC > RM. Livingwell Gate is the most expensive apartment
complex.
66
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 7
True
False
Uncertain
The correct answer is that the third statement is false. If T > E and C > T, then C
> T > E. Elena is the youngest of the three, so the statement is false.
67
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 8
1/14
1/12
The pattern is being cut in half, so the next number in the series after should be
.
68
University of Perpetual Help System JONELTA
Sto. Nio, City of Bian, Laguna, Philippines, 4024
COLLEGE OF EDUCATION
Problem No. 9
6
8
10
13
The pattern is increasing by 3, then decreasing by 2, so the next number in the series after
12 should be 10.
69