Numerical Ability Overview: Civil Service Exam Guide

Numerical Ability is one of the core components of the Civil Service Exam (CSE), measuring how well test-takers can analyze numerical information, solve quantitative problems, and apply mathematical concepts efficiently. Although the questions are typically not advanced, time pressure and multi-step calculations often make this section challenging for many examinees.

This comprehensive guide explains all major topics, provides essential strategies, and outlines what you must master to confidently pass the Numerical Ability portion of the CSE.

What Is Numerical Ability in the Civil Service Exam?

Numerical Ability in the CSE evaluates your capacity to work with numbers, equations, and data in logical and practical contexts. The exam focuses on everyday math skills rather than advanced theories, making it highly accessible with proper preparation.

Typical skills tested include:

• Solving arithmetic word problems

• Understanding percentages, ratios, and proportions

• Applying algebraic reasoning

• Reading and interpreting data from tables, graphs, and charts

• Handling basic geometry and measurement problems

The questions are designed to assess both accuracy and speed, making time management critical.

Why Numerical Ability Matters in the CSE

A strong performance in Numerical Ability demonstrates:

• Analytical thinking

• Decision-making skills

• The ability to process numerical information effectively

Government positions often require reviewing reports, handling budgets, interpreting statistical information, or making decisions based on quantitative data. Thus, this section is essential for evaluating an applicant’s readiness for civil service responsibilities.

Main Coverage Areas of the Numerical Ability Section

Below are the major topics you will likely encounter on the CSE. Understanding each of them increases your chance of achieving a high score.

Basic Arithmetic Operations

Arithmetic forms the foundation of most questions. It includes simple but essential operations you must perform quickly and accurately.

Key concepts:

• Addition, subtraction, multiplication, division

• Order of operations (PEMDAS/BODMAS)

• Estimation and rounding

• Fractions and mixed numbers

• Decimals

• Factors and multiples (LCM, GCF)

Many arithmetic questions appear as word problems, requiring the ability to translate a scenario into a mathematical expression.

Example:
A department has 245 employees. If 18 retire and 25 new hires arrive, how many employees are there now?
This tests both arithmetic and reading comprehension.

Fractions, Decimals, and Percentages

Conversions between these forms are heavily tested.

Important Skills

• Converting:

  • Fraction ↔ Decimal

  • Decimal ↔ Percentage

• Calculating percentage increase or decrease

• Applying percentages in real-life contexts
  (discounts, taxes, interest, population change)

Common Types of Questions

1. Finding a percentage of a number

2. Solving for the whole when the percentage and part are known

3. Percent change calculations

These concepts appear throughout the exam, especially in business-related scenarios.

Ratio and Proportion

Ratios compare quantities, while proportions help solve problems involving scale, rates, and distribution.

Topics Covered

• Simplifying ratios

• Solving proportional equations

• Direct and inverse proportion

• Dividing quantities in a given ratio

Common Problem Themes

• Recipe adjustments

• Workforce distribution

• Speed and distance

• Working together problems

A strong grasp of ratio and proportion greatly simplifies many multi-step word problems.

Algebraic Expressions and Simple Equations

Although the exam does not require advanced algebra, you must be comfortable with:

• Translating verbal statements into algebraic expressions

• Solving linear equations

• Identifying simple patterns

• Understanding variables

Types of Questions

• Solving for x in equations

• Applying formulas

• Recognizing number sequences

• Using substitution to evaluate expressions (e.g., $3a+2b$)

Learning basic algebra reduces the difficulty of many word problems.

Number Series and Patterns

Number series test logical reasoning and pattern recognition. Examinees must identify what rule governs the sequence.

Common Patterns

• Arithmetic sequence

• Geometric sequence

• Alternating patterns

• Increasing or decreasing differences

• Square or cube patterns

Strong familiarity with these patterns helps in answering quickly under time constraints.

Word Problems and Practical Mathematics

This is one of the most challenging areas because it requires multiple skills:

• Reading comprehension

• Setting up equations

• Logical reasoning

• Mathematical accuracy

Topics Included

• Work problems

• Distance, rate, and time

• Mixture problems

• Simple and compound interest

• Profit and loss

• Age problems

These often require identifying relevant information and ignoring unnecessary details.

Measurement and Geometry

Geometry questions assess basic spatial understanding and formula usage.

Topics

• Perimeter and area of squares, rectangles, triangles, circles

• Volume of common solids (box, cylinder, prism)

• Units of measurement (metric conversions)

• Real-life applications (fencing, flooring, water tanks, etc.)

No advanced geometry appears, but you must memorize essential formulas.

Data Interpretation (Tables, Graphs, Charts)

A major part of the Numerical Ability section involves interpreting data.

Types of Data

• Bar graphs

• Line graphs

• Pie charts

• Frequency tables

Skills Required

• Extracting relevant numerical data

• Comparing values

• Calculating totals, averages, or percentages

• Identifying trends and differences

Questions can be tricky due to multi-step reasoning and time pressure.

Logical Quantitative Reasoning

Some numerical questions require logical thinking beyond simple calculations.

Examples:

• Deductive reasoning with numbers

• Choosing the best estimate

• Identifying which equation correctly represents a scenario

These questions test your understanding rather than your computational ability.

Essential Formulas to Memorize

Arithmetic

• Percentage:

  Percentage=PartWhole×100\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100Percentage=WholePart​×100

• Profit/Loss:

  $$\text{Profit}=\text{Selling Price}-\text{Cost Price}$$

Geometry

• Area of rectangle: $A=lw$

• Area of triangle: A=12bhA = \frac{1}{2}bhA=21​bh

• Area of circle: A=πr2A = \pi r^2A=πr2

• Circumference: $C=2\pi r$

• Volume of cube: V=s3V = s^3V=s3

• Volume of rectangular prism: $V=lwh$

Distance

$$\text{Distance}=\text{Rate}\times \text{Time}$$

Simple Interest

$$I=PRT$$

Memorizing these formulas saves precious time.

Test-Taking Strategies for Numerical Ability

1. Master Mental Math

Quick calculations help you answer more questions within the time limit.

2. Analyze Word Problems Carefully

Look for keywords such as:

• More than

• Less than

• Increased by

• Total

• Ratio

Rewrite the problem in your own words if necessary.

3. Eliminate Wrong Answers

Multiple-choice format allows intelligent guessing:

• Remove impossible values

• Estimate if needed

4. Watch Out for Trick Questions

Many CSE questions use:

• Extra information

• Misleading wording

• Reversed logic

Double-check what the question is actually asking.

5. Manage Your Time

If a problem takes longer than 1 minute, skip it and return later.

6. Use Approximation

Especially useful for:

• Percentages

• Large numbers

• Data interpretation

You can often find the correct answer without full computation.

Common Mistakes to Avoid

1. Rushing through arithmetic → leads to careless errors

2. Not converting units (e.g., meters to centimeters)

3. Misreading charts or tables

4. Forgetting formulas

5. Getting stuck on one hard question

Recognizing these mistakes ahead of time helps you avoid them.

How to Prepare Effectively

1. Review the Basics

Master basic operations before tackling complex word problems.

2. Practice Consistently

The more problems you solve, the faster you become.

3. Take Timed Mock Tests

Simulates real exam pressure.

4. Analyze Your Mistakes

Identify patterns in your errors.

5. Use CSE-focused Review Materials

They mirror the exam style more closely.

Conclusion

Numerical Ability in the Civil Service Exam is highly manageable with proper preparation. While the topics are not advanced, the combination of speed, accuracy, and comprehension makes this section challenging for many examinees. By understanding the key topics, practicing regularly, and applying effective test-taking strategies, you can significantly improve your score and move closer to passing the CSE.

Problem Set: Numerical Ability (Civil Service Exam Style)

Instructions

• Work without a calculator (CSE style).

• Time yourself if possible.

• After finishing, check the Answer Key and explanations below.

Part 1: Basic Arithmetic and Number Sense

1. What is the value of:
$875-296+129=?$

2. Evaluate:
$48÷6\times 5=?$

3. Which of the following is the smallest number?
a) 0.503
b) 0.53
c) 0.35
d) 0.305

4. Which of the following is a factor of 84?
a) 5
b) 6
c) 7
d) 11

5. What is the least common multiple (LCM) of 6, 8, and 12?
a) 12
b) 24
c) 36
d) 48

Part 2: Fractions, Decimals, and Percentages

6. Convert 38\dfrac{3}{8}83​ to decimal.
a) 0.28
b) 0.375
c) 0.48
d) 0.58

7. What is 25% of 480?

8. A value increases from 400 to 500. What is the percentage increase?
a) 20%
b) 22.5%
c) 25%
d) 30%

9. A student answered 36 items correctly out of 45. What percentage of the items did the student answer correctly?

10. Express 0.45 as a fraction in simplest form.

Part 3: Ratio and Proportion

11. The ratio of men to women in an office is 3 : 5. If there are 40 employees, how many are women?

12. If 4 notebooks cost ₱120, how much will 10 notebooks cost, assuming the same rate?

13. A recipe uses the ratio of sugar to flour as 2 : 5. If you use 600 g of flour, how many grams of sugar are needed to maintain the ratio?

14. Three co-workers share a bonus in the ratio 2 : 3 : 5. If the total bonus is ₱40,000, how much does the person with the largest share receive?

Part 4: Algebra and Number Series

15. Solve for $x$:
$3x+7=25$

16. Solve for $x$:
$5x-12=3x+8$

17. Find the next number in the series:
4, 7, 10, 13, 16, __

18. Find the missing term:
3, 9, 27, __, 243

19. The sum of two consecutive integers is 89. What are the two integers?

Part 5: Word Problems (Work, Distance, Mixture, Money)

20. A train travels at an average speed of 60 km/h. How long will it take to travel 180 km?

21. Two workers, A and B, can finish a job in 12 days and 18 days respectively, working alone. If they work together, in how many days can they finish the job?
(Choose the closest answer.)
a) 6 days
b) 7.2 days
c) 7.5 days
d) 8 days

22. A store bought an item for ₱1,600 and sold it for ₱2,000. What is the profit percentage?

23. A solution contains 20% sugar. If there are 250 mL of solution, how many mL of sugar does it contain?

24. A person’s present age is 5 years more than twice the age of his daughter. If the daughter is 12 years old, how old is the person?

Part 6: Measurement and Geometry

25. Find the perimeter of a rectangle with length 15 m and width 8 m.

26. The area of a triangle is 60 cm² and its base is 12 cm. What is its height?

27. A circular park has a radius of 7 m. Using $\pi =3.14$, approximate the area of the park.
(Choose the closest answer.)
a) 120 m²
b) 140 m²
c) 150 m²
d) 154 m²

Part 7: Data Interpretation

Use the table below to answer Questions 28–30.

Table: Number of Applicants by Department

28. How many applicants are there in total?

29. What percentage of the applicants applied to the IT department?
(Choose the closest answer.)
a) 27%
b) 30%
c) 32%
d) 35%

30. How many more applicants are there in Admin than in HR?

Answer Key and Explanations

1. $875-296+129=579+129=708$
Answer: 708

2. Follow order of operations (left to right for division and multiplication):
$48÷6=8$; then $8\times 5=40$
Answer: 40

3. Compare decimals:
0.305 < 0.35 < 0.503 < 0.53
Answer: d) 0.305

4. 84 ÷ 6 = 14 and 84 ÷ 7 = 12, both are factors, but from the options the factors are 6 and 7. The question asks “a factor,” so any correct choice is acceptable; standard single-answer key:
Answer: b) 6 (or c) 7, depending on exam format)

5. LCM of 6, 8, 12 = 24
(6 = 2 × 3; 8 = 2³; 12 = 2² × 3 → LCM = 2³ × 3 = 24)
Answer: b) 24

6. 38=0.375\dfrac{3}{8} = 0.37583​=0.375
Answer: b) 0.375

7. 25% of 480 = $0.25\times 480=120$
Answer: 120

8. Increase from 400 to 500 = 100.
Percentage increase = 100400×100=25%\dfrac{100}{400} \times 100 = 25\%400100​×100=25%
Answer: c) 25%

9. 3645=45=0.8=80%\dfrac{36}{45} = \dfrac{4}{5} = 0.8 = 80\%4536​=54​=0.8=80%
Answer: 80%

10. 0.45 = 45/100 = 9/20 (simplify by dividing by 5)
Answer: 920\dfrac{9}{20}209​

11. Men : Women = 3 : 5, total parts = 3 + 5 = 8
Each part = 40 ÷ 8 = 5
Women = 5 parts = 5 × 5 = 25
Answer: 25 women

12. 4 notebooks → ₱120 → per notebook = 120 ÷ 4 = ₱30
10 notebooks → 10 × 30 = ₱300
Answer: ₱300

13. Sugar : Flour = 2 : 5
If flour = 600 g = 5 parts, then 1 part = 600 ÷ 5 = 120 g
Sugar = 2 parts = 2 × 120 = 240 g
Answer: 240 g

14. Total ratio = 2 + 3 + 5 = 10 parts
Total bonus = ₱40,000 → 1 part = 40,000 ÷ 10 = ₱4,000
Largest share = 5 parts = 5 × 4,000 = ₱20,000
Answer: ₱20,000

15. $3x+7=25$
$3x=25-7=18$
$x=18÷3=6$
Answer: $x=6$

16. $5x-12=3x+8$
$5x-3x=8+12$
$2x=20\Rightarrow x=10$
Answer: $x=10$

17. Pattern: +3 each step
4, 7, 10, 13, 16, 19
Answer: 19

18. Pattern: ×3 each step
3, 9, 27, 81, 243
Answer: 81

19. Let the integers be n and n + 1
$n+(n+1)=89\Rightarrow 2n+1=89\Rightarrow 2n=88\Rightarrow n=44$
Integers: 44 and 45
Answer: 44 and 45

20. Distance = Rate × Time → Time = Distance ÷ Rate
Time = 180 ÷ 60 = 3 hours
Answer: 3 hours

21. Work rates:
A: 1/12 job per day
B: 1/18 job per day
Combined rate = 1/12 + 1/18 = (3 + 2)/36 = 5/36 job per day
Time = 1 ÷ (5/36) = 36/5 = 7.2 days
Answer: b) 7.2 days

22. Profit = SP − CP = 2,000 − 1,600 = ₱400
Profit % = (400 ÷ 1,600) × 100 = 25%
Answer: 25%

23. 20% of 250 mL = 0.20 × 250 = 50 mL
Answer: 50 mL of sugar

24. Let person’s age = P, daughter’s age = 12
Given: $P=2(12)+5=24+5=29$
Answer: 29 years old

25. Perimeter of rectangle = 2(l + w)
= 2(15 + 8) = 2 × 23 = 46 m
Answer: 46 m

26. Area of triangle = ½ × base × height
60 = ½ × 12 × h → 60 = 6h → h = 10 cm
Answer: 10 cm

27. Area of circle = πr2=3.14×72=3.14×49≈153.86\pi r^2 = 3.14 \times 7^2 = 3.14 \times 49 \approx 153.86πr2=3.14×72=3.14×49≈153.86
Closest option: 154 m²
Answer: d) 154 m²

28. Total applicants = 24 + 18 + 30 + 28 = 100
Answer: 100

29. Percentage in IT = (30 ÷ 100) × 100 = 30%
Answer: b) 30%

30. Difference between Admin and HR = 28 − 18 = 10
Answer: 10 more applicants