Introduction to Numerical Ability (Sub-Professional)

The Numerical Ability section for the Sub-Professional level tests your ability to perform basic mathematical calculations and solve practical, everyday problems. The questions are straightforward and focus on accuracy and speed.

Exam Tip: You are not allowed to use a calculator. Practice solving problems manually to improve your speed. Use the provided scratch paper for your calculations.

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Part 1: The Four Basic Operations (MDAS)

Mastering addition, subtraction, multiplication, and division is essential. The order of operations is also important. Remember MDAS: Multiplication and Division are performed first (from left to right) before Addition and Subtraction (from left to right).

• Example: Solve 20 + 5 * 4 - 10 / 2
  1. Multiplication/Division:
     • 5 * 4 = 20
     • 10 / 2 = 5
  2. The equation becomes: 20 + 20 - 5
  3. Addition/Subtraction:
     • 20 + 20 = 40
     • 40 - 5 = 35
  • Answer: 35

Practice Questions (MDAS)

1. What is 50 - 15 + 10? a) 25 b) 45 c) 55 d) 35

2. Calculate: 100 / 5 * 2 a) 10 b) 40 c) 50 d) 20

Answers: 1. (b) 45, 2. (b) 40 (100/5 = 20, then 20*2 = 40)

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Part 2: Fractions, Decimals, and Percentages

These are different ways of representing parts of a whole. You should be comfortable with basic operations involving them.

2.1 Fractions

• Adding/Subtracting: You need a common denominator.
  • Example: 1/3 + 1/4 -> 4/12 + 3/12 = 7/12
• Multiplying: Multiply the numerators and the denominators.
  • Example: 2/3 * 3/5 -> 6/15 (which simplifies to 2/5)
• Dividing: Invert the second fraction and multiply.
  • Example: 1/2 ÷ 1/4 -> 1/2 * 4/1 -> 4/2 = 2

2.2 Decimals

• Adding/Subtracting: Align the decimal points.
• Multiplying: Multiply as usual, then count the total decimal places in the numbers you multiplied to place the decimal point in the answer.
  • Example: 1.5 * 0.2 -> 15 * 2 = 30. There are two decimal places in total (one in 1.5, one in 0.2), so the answer is 0.30 or 0.3.

2.3 Percentages

"Percent" means "per hundred."

• Finding the percentage of a number: Convert the percentage to a decimal and multiply.
  • Example: What is 25% of P300?
  • 0.25 * 300 = 75. Answer: P75.
• Shortcut: For common percentages, use fractions. 25% = 1/4. So, 1/4 of 300 is 300 / 4 = 75.

Practice Question (Fractions/Percentages)

1. A store offers a 20% discount on a shirt that costs P500. How much is the discount? a) P100 b) P50 c) P20 d) P150

Answer: (a) P100. (0.20 * 500 = 100)

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Part 3: Word Problems

Word problems test your ability to understand a situation and apply the correct mathematical operation.

Strategy for Solving Word Problems

1. Read and Understand: What is the question asking for?
2. Identify the Given Information: What numbers and facts are provided?
3. Choose the Right Operation: Do you need to add, subtract, multiply, or divide?
4. Solve and Check: Perform the calculation and check if the answer makes sense.

Common Types of Word Problems

• Single-Step Problems: Require only one operation.

  • Example: You have P500. If you buy a book for P280, how much money do you have left?
  • Solution: 500 - 280 = 220. Answer: P220.

• Multi-Step Problems: Require two or more operations.

  • Example: Maria bought 3 notebooks at P45 each and 2 pens at P15 each. How much did she spend in total?
  • Solution:
    • Notebooks: 3 * 45 = 135
    • Pens: 2 * 15 = 30
    • Total: 135 + 30 = 165. Answer: P165.

• Average Problems:

  • Example: A student's scores on three quizzes are 85, 90, and 95. What is the student's average score?
  • Solution:
    • Sum of scores: 85 + 90 + 95 = 270
    • Divide by the number of quizzes: 270 / 3 = 90. Answer: 90.

Practice Question (Word Problem)

1. An employee earns P120 per hour. If he works 8 hours a day, 5 days a week, what is his total weekly earning? a) P4,800 b) P960 c) P6,000 d) P4,000

Answer: (a) P4,800.

• Daily earning: 120 * 8 = P960
• Weekly earning: 960 * 5 = P4,800