Learning Strand II – Problem Solving & Critical Thinking
A. MATHEMATICS
1. Mang Tony needs 124 plants in a row. If there are 15 rows and each plant costs Php85.00, how much will he spend in all for the plants?
A. Php 18,600.00
B. Php 85,000.00
C. Php 136,000.00
D. Php 158,100.00
Answer: D. Php 158,100.00
124 x 15 x 85 = 158,100.00
For item 2. Below is the list of the menu in a school canteen:
Rice Php8.00
Pancit Php15.00
Spaghetti Php20.00
Menudo Php40.00
Sinigang Php40.00
Pakbet Php30.00
Softdrinks Php10.00
Water Php15.00
2. Ana and her friend Lucy went to the canteen and ordered 2 cups of rice, one serving each of menudo and pakbet and 2 bottles of water. If Lucy gave Php150.00 to the cashier, how much change did he receive?
A. Php16.00
B. Php20.00
C. Php34.00
D. Php40.00
Answer: C. Php34.00
Total order:
Rice: 2x8 = Php16.00
Menudo: 1 x 40.00 = Php40.00
Pakbet: 1 x 30.00 = Php30.00
Water: 2 x 15 = Php30.00
Total: 16+40+30+30 = 116
Change: 150 – 116 = Php34.00
3. Mang Andy has a poultry in his backyard. He bought 10 ducklings at Php8.00 each. He spends Php200.00 each week for the feeds. In 6 weeks, the ducks can be sold already. How much is his total expenses before the ducks can be sold?
A. Php800.00
B. Php820.00
C. Php1,200.00
D. Php1,280.00
Answer: D. Php1,280.00
Total Expenses:
Ducklings: 10 x 8 = Php80.00
Feeds: 200 x 6 = Php1,200.00
Total: 80 + 1,200 = Php1,280.00
4. Alvin ordered two hamburgers and a soda for lunch. A hamburger costs Php25.00 while a soda costs Php20.00. How much did he pay for lunch?
A. Php45.00
B.Php50.00
C. Php65.00
D. Php70.00
Answer: D. Php70.00
Total cost:
Hamburger: 2 x 25.00 = Php 50.00
Soda: 1 x 20.00 = Php20.00
Total: 50 + 20 = Php70.00
5. There were 6,452 enrollees at Buhay High School last year and 4,956 this year. Of these data, 3,600 are first year students. Which of the following can tell us the number n of students who are NOT in first year?
A. (6,452 + 4,956) – 3,600 = n
B. (6,452 – 4,956) + 3,600 = n
C. (6,452 + 4,956) + 3,600 = n
D. (6,452 – 4,956) – 3,600 = n
Answer: A. (6,452 + 4,956) – 3,600 = n
Kahit medyo malabo ang problema at tanong, letter A is the best choice.
6. Last weekend, Dan earned Php75.00 for selling newspaper on Saturday and Php60.00 for selling Sampaguita on Sunday. He spent Php80.00 for his school needs. To find the amount left from his earnings (E), which of the following equations is correct?
A. E = (75 + 60) – 80
B. E = (75 – 60) – 80
C. E = 80 + (75 – 60)
D. E = 80 – (75 + 60)
Answer: A. E = (75 + 60) – 80
7. Ella weighs 2 ¼ times more than his son. If her son weighs 30 ½ kg, about how many kilograms does Ella weigh?
A. 32 ½ kg
B. 32 ¾ kg
C. 60 1/8 kg
D. 68 5/8 kg
Answer: D. 68 5/8 kg
Son’s weight: 30 ½ kg
Ella’s weight: 2 ¼ times more than his son
x = 2 ¼ (30 ½) = 9/4(61/2) = 549/8 = 68 5/8 kg
Medyo may mali sa problem pero letter D ang pinaka-best sa lahat.
Ang dapat na sagot ay: 68 5/8 + 30 1/2 = 99 1/8
dahil ang tamang equation ay:
y = 2 1/4x + x , where y = Ella's age, x = her son's age
8. Janice answered 100 questions in Mathematics and Science. If 2/5 of the questions involve Mathematics, how many are Science questions?
A. 20
B. 35
C. 40
D. 60
Answer: D. 60
Mathematics: 2/5 x 100 = 200/5 = 40
Science: 3/5 x 100 = 300/5 = 60
9. Gina bought the following items from the mini store:
pad paper Php16.50
notebook Php8.75
folder Php7.25
bond paper Php36.25
colored paper Php105.50
How much change did she get if she gave a Php200.00 bill to the store owner?
A. Php15.50
B. Php20.75
C. Php25.75
D. Php32.25
Answer: C. Php25.75
Total expenses:
16.50 + 8.75 + 7.25 + 36.25 + 105.50 = Php 174.25
Change: 200 – 174.25 = Php25.75
10. Aling Ester bought 4,125 bananas and distributed it equally to 5 different stores. If each banana cost Php7.50, how much did each store pay?
A. Php5,830.45
B. Php6,187.50
C. Php9,625.00
D. Php30,937.50
Answer: B. Php6,187.50
How many bananas each store got: 4125/5 = 825 bananas
Payment by each store: 825 x 7.50 = Php6,187.50
11. Cloe brought 40 cookies to school for her birthday. Five students wanted two cookies each. A new student came and wanted three cookies. Then, two of the kids gave their two cookies back. How many cookies did Cloe had left to pass out?
A. 20
B. 23
C. 30
D. 32
Answer: C. 30
Malabo ang tanong na ito at wala rin ang tamang sagot sa pagpipilian. MDAS example problem ang nais ipahiwatig ng tanong subalit may mali yata sa sagot.
Heto ang equation na magagawa kung uunawain ang tanong:
Five students wanted 2 cookies each: - (5 x 2)
New student wanted 3 cookies: -3
Two kids returned their 2 cookies: + (2 x 2)
Solution :
40 – (5x2) – 3 + 2 x 2 = 40 – 10 – 3 + 4 = 30 – 3 + 4 = 27 + 4 = 31
Since 30 is the nearest to 31, I chose C. 30 because 32 is doubtful.
12. Ana is saving money to buy a new bag. On Monday, she saved Php60.00 and doubled that amount on Tuesday and Wednesday. Her teacher gave a project which costs her Php30.00. On Friday she saved Php40.00. But unfortunately, she lost her wallet on Saturday with Php25.00 in it. How much is her total savings?
A. Php145.00
B. Php165.00
C. Php215.00
D. Php250.00
Answer: B. Php165.00
Savings:
Monday: Php60.00
Tuesday: 2 x 60 = Php120.00
Wednesday: 2 x 60 = Php120.00
Friday: Php40.00
Total Savings: Php340.00
Loss/Deduction:
Project: Php30.00
Lost wallet: Php25.00
Total loss: 55
Assuming that all the amounts are related, the equation should be:
340 – 55 = Php285.00===> not in the choices
Probably the maker of the test forgot the amount on Wednesday. If this was the case, the equation should be:
340 – 120 – 55 = Php165.00
I chose C. Php165.00 as answer although it is not the correct answer.
13. Irish had Php7 500.00 in her savings account. Last Monday, she deposited Php2 500.00. On Tuesday, she withdrew Php1 200.00 to pay for her bills. How much is her current balance?
A. Php6,200.00
B. Php8,800.00
C. Php 11,200.00
D. Php 10,000.00
Answer: B. Php8,800.00
Beginning balance: Php 7 500.00
Monday deposit: Php 2 500.00
Balance on Monday: 7 500 + 2 500 = Php10 000
Tuesday withdrawal: P 1 200.00
Balance on Tuesday: 10 000 – 1 200 = Php8 800.00
14. From their house, Rona walked 3 km east while Ben walked 4 km south. How many kilometers are they apart?
A. 5
B. 7
C. 12
D. 19
Answer: A. 5
This is a case of Pythagorean theorem when the figure form is a right triangle. The formula for the Pythagorean theorem is c^2 = a^2 + b^2, where c is the hypotenuse, a and b is the opposite side and adjacent side respectively.
c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
c = sqrt 25
c = 5 km
15. Daisy is interested in finding the circumference of the given circle below. How will she compute for its value?
A. C = 2 x 27.1 cm
B. C = 2 x 54.2 cm
C. C= 3.14 x 54.2 cm
D. C = 3.14 x 27.1 cm
Answer: C. C= 3.14 x 54.2 cm
The circumference is the perimeter of the circle. The circumference of a circle is found using this formula:
C=Ï€⋅d ==> where Ï€ is the pi which is approximately equal to 3.14; d is the diameter which is 2r, where r is the radius.
C=2Ï€⋅r
Finding the circumference using
A. C=Ï€⋅d
C = 3.14 x 54.2 cm
B. C=2Ï€⋅r
C = 2 x 3.14 x 27.10 cm = 3.14 x 54.2 cm
16. A rectangular table with length 250 dm and width 150 dm needs to be painted. What is the area of the table to be painted?
A. 400 dm^2
B. 800 dm^2
C. 28 500 dm^2
D. 37 500 dm^2
Answer:
The formula for finding the area of a rectangular is length times width of l x w:
length: l = 250 dm
width: w: = 150 dm
Area: l x w = 250 x 150 = 37 500 dm^2
Reminder: Make sure that the units of the length and the width are the SAME before multiplying.
17. What is the area of the triangular figure below?
A. 6 square units
B. 7 square units
C. 12 square units
D. 15 square units
Answer: A. 6 square units
The formula for finding the area of a rectangle is:
1/2bh ===> where b is the measure of the base, and h is the measure of the height.
b = 4 units
h = 3 units
½ b h = ½ x 4 x 3 = ½ x 12 = 12/2 = 6 square units
18. A rectangular box is 5 cm long, 3 cm wide, and 4 cm high. Find its surface area.
A. 12 cm^2
B. 60 cm^2
C. 94 cm^2
D. 180 cm^2
Answer: C. 94 cm^2
To find the surface area of a rectangular box, just add ALL the area of the 6 faces of the box. Use the formula below:
S = 2[(lw + wh + lh)] ==> where l = length; w = width; h = height
l = 5 cm
w = 3 cm
h = 4 cm
S = 2[( 5 x 3) + (3 x 4) + (5 x 4)]
S = 2(15 + 12 + 20)
S = 2(47)
S = 94 cm^2
Reminder: The length, width, and height must have the SAME UNITS before multiplying.
19. A swimming pool whose dimensions are 10 m by 3 m by 6 m needs to be filled with water for the pool party. How many cubic meters of water will it need?
A. 19
B. 116
C. 180
D. 200
Answer: C. 180
This is a volume problem. In finding the volume of a rectangular shaped figure with length, width, and height, use the formula below:
V = length times width times height
V = l x w x h
V = lwh
l = 10 m
w = 3 m
h = 6 m
V = 10 x 3 x 6
V = 180 m^3 or 180 cubic meters
Reminder: Make sure the units of measure of the length, width, and height are the SAME before multiplying.
20. Cindy plans to buy a new cellphone. She already saved Php 1 040.00. If the cellphone costs Php8 000.00, what percent of the total price was her savings?
A. 13%
B. 15%
C. 25%
D. 30%
Answer: A. 13%
To express one number as a percentage of another, form a fraction using these two numbers and multiply it by 100. Note that the number that is being expressed as a percentage is placed in the numerator of the fraction.
Normally in finding the percentage, just divide the lesser value by the bigger value and then multiply by 100%.
Use this formula in finding percentages:
P = the number that is being expressed as a percentage DIVIDED BY the other number TIMES 100%
Savings: the number that is being expressed as a percentage
Cost of cellphone: the other number
P = 1 040/8 000 = 0.13 x 100% = 13%
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What is a percentage?
Percent means “for every 100” or "out of 100." The (%) symbol as a quick way to write a fraction with a denominator of 100. As an example, instead of saying "it rained 14 days out of every 100," we say "it rained 14% of the time."
Percentages can be written as decimals by moving the decimal point two places to the left:
24% = 24/100 = 0.24
Decimals can be written as a percentage by moving the decimal point two places to the right:
0.32 x 100 = 32%
21. The Health Center in Frisco listed down 1 524 patients in a month. Based on the data from the City Hall, this is 30% of the total patients in the whole district. How many patients were there in the district within the month?
A. 1 554
B. 5 080
C. 26 430
D. 45 720
Answer: B. 5 080
Given: 1 524 is only 30% of the total patients in the whole district.
As a formula, this can be written as:
1 524 = 30% of x
1 524 = 0.30x
x = 1 524/ 0.30
x = 5 080
This can also be computed as follows:
Since 1 524 is 30%; then 1524 x 3 = 4 572 is 90%.
Then we only need 10%.
Since 1 524 is 30%, its 10% is 1 524/ 3 = 508
The 100% is 4 572 + 508 = 5 080
For items 22 – 24. The budget allotted by the government to Barangay Laging Handa is Php2 000 000.00 for one year as presented in the graph below:
22. Which item in the budget is allotted the least?
A. Salary
B. Projects
C. Expenses
D. Contingency
Answer: D. Contingency
The LEAST budget = the SMALLEST budget or allocation : Contingency = only 5%
23. What percent of the budget is allotted for projects?
A. 5%
B. 20%
C. 25%
D. 50%
Answer: 25%
See the illustration: Projects = 25%
24. How much is allotted for salary?
A. Php1 000 000.00
B. Php500 000.00
C. Php400 000.00
D. Php100 000.00
Answer: A. Php1 000 000.00
The total budget = Php2 000 000.00
Budget for salary = 50%
2 000 000 x 50% = 2 000 000 x 0.50 = Php1 000 000.00
25. In a map that used a scale of 1 cm : 20 km, what is the distance in centimeter between Manila and Cavite if Manila is 180 km away from Cavite?
A. 6 cm
B. 9 cm
C. 200 cm
D. 360 cm
Answer: B. 9 cm
The scale is 1 cm : 20 km. This means that 20 km is equivalent to 1 cm in the map.
The distance of Manila to Cavite = 180 km
This is equivalent to: 180/20 = 9 cm in the map
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