Civil Service
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Practice Exams

Introduction to Numerical Ability

The Numerical Ability section of the Civil Service Exam tests your speed and accuracy in solving mathematical problems. For the Professional Level, this includes a range of topics from basic arithmetic to more complex word problems and data analysis. Strong foundational skills and strategic problem-solving are key to success.

Exam Tip: Don't get stuck on one problem. If a question is too difficult, make an educated guess, mark it, and move on. You can return to it later if you have time.

Part 1: Core Mathematical Concepts

A solid understanding of the fundamentals is non-negotiable. Ensure you are comfortable with these concepts.

1.1 Order of Operations (PEMDAS)

PEMDAS is the acronym for the order in which mathematical operations should be performed:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)
  • Example: Solve 10 + (3 * 2^2) - 4
    1. Parentheses/Exponents: 2^2 = 4 -> 3 * 4 = 12
    2. The equation becomes: 10 + 12 - 4
    3. Addition/Subtraction: 10 + 12 = 22 -> 22 - 4 = 18
    • Answer: 18

1.2 Fractions, Decimals, and Percentages

You must be able to convert between these three formats quickly.

Fraction Decimal Percentage
1/2 0.5 50%
3/4 0.75 75%
1/5 0.20 20%
1/100 0.01 1%

Key Formulas:

  • Percentage of a Number: What is 20% of 300? -> 0.20 * 300 = 60
  • Percentage Increase/Decrease: ((New Value - Old Value) / Old Value) * 100
    • Example: If an item's price increased from P150 to P180, what is the percentage increase?
    • ((180 - 150) / 150) * 100 = (30 / 150) * 100 = 0.20 * 100 = 20%

1.3 Ratios and Proportions

A ratio compares two quantities. A proportion states that two ratios are equal.

  • Ratio Example: If there are 10 apples and 15 oranges, the ratio of apples to oranges is 10:15, which simplifies to 2:3.
  • Proportion Problem: If 3 notebooks cost P45, how much will 7 notebooks cost?
    • Set up the proportion: 3/45 = 7/x
    • Cross-multiply: 3 * x = 45 * 7
    • 3x = 315
    • x = 315 / 3
    • x = 105. Answer: P105.

Practice Questions (Core Concepts)

  1. Calculate: 5 * (4 + 3) - 12 / 2 a) 29 b) 23.5 c) 11.5 d) 30

  2. A department has 45 employees. If 60% of them are female, how many male employees are there? a) 27 b) 18 c) 25 d) 20

Answers: 1. (a) 29, 2. (b) 18 (40% are male, 0.40 * 45 = 18)

Part 2: Word Problems

Word problems require you to translate a real-world scenario into a mathematical equation.

2.1 Age Problems

  • Strategy: Create a table to track the ages of individuals at different points in time (past, present, future).
  • Example: Ana is twice as old as Ben. Ten years ago, she was three times as old as Ben. How old is Ana now?
    • Let A be Ana's current age and B be Ben's current age.
    • Eq 1: A = 2B
    • Ten years ago: A - 10 and B - 10
    • Eq 2: A - 10 = 3(B - 10)
    • Substitute Eq 1 into Eq 2: (2B) - 10 = 3B - 30
    • 20 = B. Ben is 20 years old.
    • Since A = 2B, A = 2 * 20 = 40. Answer: Ana is 40 years old.

2.2 Work Problems

  • Formula: 1/T = 1/A + 1/B, where T is the time taken working together, A is the time for person A alone, and B is the time for person B alone.
  • Example: Painter A can finish a job in 6 hours. Painter B can finish the same job in 4 hours. How long will it take them if they work together?
    • 1/T = 1/6 + 1/4
    • Find a common denominator (12): 1/T = 2/12 + 3/12
    • 1/T = 5/12
    • T = 12/5 = 2.4 hours. Answer: 2.4 hours or 2 hours and 24 minutes.

2.3 Distance, Rate, and Time Problems

  • Formula: Distance = Rate × Time (D = R * T)
  • Example: A car travels at 60 km/h for 2 hours and then at 80 km/h for the next 3 hours. What is the total distance traveled?
    • Part 1: D1 = 60 * 2 = 120 km
    • Part 2: D2 = 80 * 3 = 240 km
    • Total Distance: 120 + 240 = 360 km. Answer: 360 km.

Part 3: Data Interpretation and Number Series

3.1 Data Interpretation

This involves analyzing data from tables, graphs (bar, line, pie), and charts.

  • Strategy:
    1. Read the title and labels of the chart/table carefully.
    2. Understand the units of measurement.
    3. Read the question and identify the specific data needed.
    4. Perform the necessary calculations (e.g., finding averages, percentages, or differences).

3.2 Number Series

You need to find the pattern in a sequence of numbers and determine the next number.

  • Common Patterns:
    • Arithmetic Sequence: A constant number is added or subtracted. (e.g., 2, 5, 8, 11, ... Pattern: +3)
    • Geometric Sequence: A constant number is multiplied or divided. (e.g., 3, 9, 27, 81, ... Pattern: *3)
    • Alternating Sequence: Two or more patterns alternate. (e.g., 2, 10, 4, 12, 6, 14, ... Pattern: +2 for 2,4,6 and +2 for 10,12,14)
    • Fibonacci-like Sequence: Each number is the sum of the two preceding ones. (e.g., 1, 1, 2, 3, 5, 8, ...)

Practice Question (Number Series)

  1. What is the next number in the series: 5, 7, 11, 17, 25, ___? a) 35 b) 33 c) 37 d) 39

Answer: 1. (a) 35 (The pattern is adding consecutive even numbers: +2, +4, +6, +8, so the next step is +10. 25 + 10 = 35)