Skip to content
Back to Civil Service Notes
Lesson 250 min read

Numerical Ability

Percentages, Ratio, Word Problems & Number Series (30% of exam)

Essential Formulas

Percentage

Percentage = (Part / Whole) × 100

Part = (Percentage × Whole) / 100

Whole = (Part × 100) / Percentage

Ratio & Proportion

a : b = c : d means a/b = c/d

Cross multiply: a × d = b × c

Distance, Speed, Time

Distance = Speed × Time

Speed = Distance / Time

Time = Distance / Speed

Simple Interest

I = P × R × T

P = Principal, R = Rate (decimal), T = Time

Discount & Markup

Discount = Original Price × Rate

Sale Price = Original - Discount

Average

Average = Sum of all values / Count

Sum = Average × Count

Number Series Patterns

Arithmetic Sequence (Add/Subtract constant)

2, 5, 8, 11, 14, 17 (adding 3)

Geometric Sequence (Multiply/Divide constant)

2, 6, 18, 54, 162 (multiply by 3)

Fibonacci-like (Add previous two)

1, 1, 2, 3, 5, 8, 13

Alternating Patterns

2, 5, 4, 7, 6, 9, 8 (two sequences: 2,4,6,8 and 5,7,9)

Square Numbers

1, 4, 9, 16, 25, 36 (1², 2², 3², 4², 5², 6²)

Increasing Difference

2, 3, 5, 8, 12, 17 (differences: +1, +2, +3, +4, +5)

Word Problem Examples

Percentage Problem

A shirt originally costs ₱500. It is on sale at 20% off. What is the sale price?

Discount = ₱500 × 0.20 = ₱100

Sale Price = ₱500 - ₱100 = ₱400

Ratio Problem

If 3 pencils cost ₱15, how much do 7 pencils cost?

3 : 15 = 7 : x

3x = 15 × 7 = 105

x = 105 / 3 = ₱35

Distance Problem

A car travels 120 km in 2 hours. What is its speed?

Speed = Distance / Time = 120 / 2 = 60 km/hr

Age Problem

Maria is twice as old as Juan. In 5 years, Maria will be 25. How old is Juan now?

Maria now = 25 - 5 = 20 years

Juan = 20 / 2 = 10 years old

Problem-Solving Strategy

  1. 1
    Read carefully - Identify what's being asked
  2. 2
    List the given - Write down all numbers and relationships
  3. 3
    Choose the formula - Match the problem type to the appropriate formula
  4. 4
    Solve step by step - Show your work and check each step
  5. 5
    Check your answer - Does it make sense? Plug it back in.