Numerical Reasoning Reviewer for CSE 2026 (Complete Guide Philippines)

Numerical Reasoning is one of the most consistently tested and most feared subjects on the Civil Service Exam. Approximately 25 to 30 items out of 170 (Professional) or 165 (Subprofessional) test your math skills under tight time pressure with no calculator allowed.

This deep dive reviewer covers every major topic, the shortcut techniques that save time, and the question patterns that appear in every CSE cycle.

What Numerical Reasoning Tests

The CSE Numerical Reasoning section assesses your ability to solve mathematical problems quickly and accurately using only mental computation and pen-and-paper work.

Key constraint: Calculators and electronic devices are strictly prohibited. You must master mental math and shortcut techniques.

Topics covered:

• Basic arithmetic operations
• Order of operations (PEMDAS)
• Fractions, decimals, percentages
• Ratio and proportion
• Word problems (age, time, distance, work, money)
• Number sequences and patterns
• Averages and weighted averages

Topic 1: Basic Arithmetic Operations

Master these foundations because they appear in every other topic.

Addition and Subtraction Shortcuts

Round and adjust: When adding 47 + 38, round to 50 + 40 = 90, then subtract the rounding error: 90 - 3 - 2 = 85.

Left to right addition: For 234 + 567, add hundreds first (200 + 500 = 700), then tens (30 + 60 = 90), then ones (4 + 7 = 11). Total: 800 + 1 = 801.

Multiplication Shortcuts

Multiply by 5: Multiply by 10, then divide by 2. Example: 84 x 5 = 840 / 2 = 420.

Multiply by 11: For 2-digit numbers, add the digits and place between them. Example: 36 x 11 = 3 (3+6=9) 6 = 396.

Multiply by 25: Multiply by 100, then divide by 4. Example: 32 x 25 = 3,200 / 4 = 800.

Multiply by 9: Multiply by 10, then subtract the original. Example: 47 x 9 = 470 - 47 = 423.

Division Shortcuts

Divide by 5: Multiply by 2, then divide by 10. Example: 240 / 5 = 480 / 10 = 48.

Divide by 25: Multiply by 4, then divide by 100. Example: 800 / 25 = 3,200 / 100 = 32.

Topic 2: Order of Operations (PEMDAS)

PEMDAS dictates the sequence of operations in a math expression.

P - Parentheses

E - Exponents

MD - Multiplication and Division (left to right)

AS - Addition and Subtraction (left to right)

Example: 8 + 6 x (4 - 2) squared divided by 3

Step 1 (Parentheses): 8 + 6 x 4 / 3

Step 2 (Exponents): 8 + 6 x 4 / 3

Step 3 (Multiplication, left to right): 8 + 24 / 3

Step 4 (Division): 8 + 8

Step 5 (Addition): 16

Common mistake: Doing multiplication before division when division comes first reading left to right.

Topic 3: Fractions, Decimals, Percentages

These three forms represent the same value and questions often require converting between them.

Conversion Reference

|----------|---------|------------|

Memorize this table. It will save 30 to 60 seconds on multiple questions.

Fraction Operations

Adding/Subtracting Fractions: Find common denominator first.

1/3 + 1/4 = 4/12 + 3/12 = 7/12

Multiplying Fractions: Multiply numerators, multiply denominators.

2/3 x 3/4 = 6/12 = 1/2

Dividing Fractions: Flip the second fraction, then multiply.

2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 2/3

Percentage Shortcuts

10 percent of any number: Move decimal one place left. 10% of 250 = 25.

1 percent of any number: Move decimal two places left. 1% of 250 = 2.5.

5 percent: Half of 10%. 5% of 250 = 12.5.

15 percent: 10% + 5%. 15% of 200 = 20 + 10 = 30.

20 percent: Double 10%. 20% of 250 = 50.

25 percent: Divide by 4. 25% of 200 = 50.

50 percent: Divide by 2. 50% of 84 = 42.

Topic 4: Ratio and Proportion

A ratio compares two quantities. A proportion is two equal ratios.

Ratio Basics

Reading a ratio: 3:5 reads as "3 is to 5" or "3 to 5".

Simplifying ratios: Like simplifying fractions. 12:18 simplifies to 2:3 (divide both by 6).

Total parts: In ratio 3:5, total parts = 3 + 5 = 8.

Solving Ratio Problems

Example: Two siblings share PHP 1,200 in the ratio 3:5. How much does each receive?

Total parts = 3 + 5 = 8

Each part = 1,200 / 8 = 150

First sibling: 3 x 150 = PHP 450

Second sibling: 5 x 150 = PHP 750

Proportion (Cross Multiplication)

If a/b = c/d, then a x d = b x c

Example: If 5 workers can finish a job in 12 days, how many days will 8 workers need?

This is inverse proportion (more workers = fewer days):

5 x 12 = 8 x d

60 = 8d

d = 7.5 days

Topic 5: Word Problems by Type

Word problems are the most challenging part of CSE Numerical Reasoning. Each type follows a recognizable pattern.

Age Problems

Example: Maria is 3 times as old as her sister. In 5 years, she will be twice as old. How old is Maria now?

Let sister's current age = x

Maria's current age = 3x

In 5 years: Maria = 3x + 5, Sister = x + 5

3x + 5 = 2(x + 5)

3x + 5 = 2x + 10

x = 5

Maria is currently 3 x 5 = 15 years old.

Distance, Rate, Time Problems

Formula: Distance = Rate x Time (D = R x T)

Example: A car travels at 60 km/h for 4 hours. How far does it go?

D = 60 x 4 = 240 km

Example: Two cars start from the same point traveling in opposite directions at 50 km/h and 60 km/h. How long until they are 330 km apart?

Combined rate = 50 + 60 = 110 km/h

Time = 330 / 110 = 3 hours

Work Problems

Formula: If A finishes in x hours, A's rate = 1/x per hour.

Example: A finishes a job in 6 hours. B finishes the same job in 4 hours. How long if they work together?

A's rate = 1/6, B's rate = 1/4

Combined rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12

Time = 1 / (5/12) = 12/5 = 2.4 hours (2 hours 24 minutes)

Money Problems

Example: Ana invested PHP 10,000 at 5% simple interest per year. How much interest after 3 years?

Simple Interest = Principal x Rate x Time

SI = 10,000 x 0.05 x 3 = PHP 1,500

Mixture Problems

Example: How much water must be added to 50 mL of 40% alcohol solution to make it 25% alcohol?

Pure alcohol stays the same: 50 x 0.40 = 20 mL

Final volume x 0.25 = 20

Final volume = 80 mL

Water added = 80 - 50 = 30 mL

Topic 6: Number Sequences

Identify the pattern, predict the next number.

Common Patterns

Arithmetic sequence: Constant difference between terms.

2, 5, 8, 11, ___ (difference = 3, next = 14)

Geometric sequence: Constant ratio between terms.

3, 6, 12, 24, ___ (ratio = 2, next = 48)

Squared numbers: 1, 4, 9, 16, 25, ___ (next = 36)

Cubed numbers: 1, 8, 27, 64, ___ (next = 125)

Fibonacci-like: Each term is the sum of the two before.

1, 1, 2, 3, 5, 8, ___ (next = 13)

Alternating patterns: Two patterns interleaved.

2, 5, 4, 10, 6, 15, ___ (odd positions: +2, even positions: x2; next = 8)

Topic 7: Averages

Arithmetic Mean: Sum / Number of items.

Example: Test scores 85, 90, 78, 92, 80. Average = (85 + 90 + 78 + 92 + 80) / 5 = 425 / 5 = 85.

Weighted Average: Each value is multiplied by its weight before summing.

Example: Quiz worth 30%, Exam worth 70%. Quiz score 80, Exam score 90. Final grade?

(80 x 0.30) + (90 x 0.70) = 24 + 63 = 87

Practice Strategy for Numerical Reasoning

Daily target: 20 to 30 numerical questions per day starting 8 weeks before exam.

Time yourself: Target 60 seconds per question. If you finish faster, accuracy is more important than speed.

Track common mistakes: Keep a notebook of errors. Review weekly.

Master multiplication tables: Memorize 1x1 through 15x15. This single skill saves enormous time.

Practice without calculator: Train your brain. Calculators are not allowed on exam day.

Common Mistakes That Cost Points

Mistake 1: Misreading the question. Read every word carefully. The question may ask "how many more" not "how many total".

Mistake 2: Not converting units. Convert hours to minutes, kilometers to meters, etc., when needed.

Mistake 3: Skipping the scratch work. Use the test booklet margins to organize your work. Mental math errors cost easy points.

Mistake 4: Spending too long on one question. If a question takes more than 90 seconds, mark it and move on.

Mistake 5: Not checking answer choices. Some answer choices are obvious traps (off by one, wrong sign). Eliminate clearly wrong options first.

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