CSE Numerical Ability: Practice Guide & Sample Questions
CSE Numerical Ability covers 45 of the 170 items on the Professional-level exam — the second-largest category after Verbal Ability. It tests three broad skills: basic arithmetic operations (fractions, percentages, ratios), word problems (translating a real-world scenario into an equation), and data interpretation (reading and reasoning from tables and graphs). Unlike a pure math test, most items are word problems rather than bare computation, so the real skill being tested is translating language into the correct arithmetic operation — a large share of wrong answers come from setting up the wrong equation, not from arithmetic mistakes.
This page walks through the three sub-skills, the setup mistakes that account for most wrong answers, and gives worked sample questions with full step-by-step explanations. Below the study material, a full practice quiz pulls Numerical Ability questions from Pasa's question bank so you can drill the category specifically, with instant scoring and explanations for every attempt.
Pasa is an independent study aid, not affiliated with the CSC or AFP.
What's tested
Basic operations items test fractions, decimals, percentages, and ratios directly — converting between them, comparing them, and combining them. Word problems dominate the category: age problems (relating two people's ages at different points in time), work problems (how long two people take to finish a task together), mixture problems (combining quantities at different rates or concentrations), and distance/rate/time problems all appear regularly. Data interpretation items present a table, bar graph, line graph, or pie chart and ask a question that requires reading a specific value, calculating a difference or percentage change between two values, or identifying a trend — these items reward careful reading of axis labels and legends over raw computation speed.
| Sub-skill | What it looks like |
|---|---|
| Basic operations | Fractions, decimals, percentages, ratios |
| Word problems | Age, work, mixture, distance/rate/time scenarios |
| Data interpretation | Reading and reasoning from tables/graphs/charts |
No calculator is allowed on the actual exam, so every technique you practice with needs to work by hand — estimation and simplification (canceling common factors before multiplying, for instance) save significant time over brute-force calculation, especially on percentage and ratio items where the numbers are often chosen to simplify cleanly if you spot the shortcut.
Sample Questions
1. A local government unit's budget for a school-building project is ₱2,400,000. If 35% of the budget has already been disbursed, how much remains?
- A. ₱840,000
- B. ₱1,560,000
- C. ₱1,440,000
- D. ₱960,000
Correct answer: B — ₱1,560,000
35% of ₱2,400,000 is ₱840,000 (the disbursed amount), so the remaining balance is ₱2,400,000 − ₱840,000 = ₱1,560,000. A common mistake is stopping after computing the 35% figure (₱840,000) and forgetting the question asks for what's LEFT, not what was spent.
2. In a batch of 240 applicants, the ratio of male to female applicants is 5:7. How many female applicants are there?
- A. 100
- B. 120
- C. 140
- D. 105
Correct answer: C — 140
The ratio 5:7 has 12 total parts, and 240 applicants divided by 12 parts gives 20 applicants per part. Female applicants make up 7 of those parts: 7 × 20 = 140. A common mistake is dividing 240 by 5 or 7 directly instead of by the SUM of the parts (12).
3. Worker A can finish a task alone in 6 hours, and Worker B can finish the same task alone in 12 hours. Working together, how long will they take to finish the task?
- A. 3 hours
- B. 4 hours
- C. 9 hours
- D. 18 hours
Correct answer: B — 4 hours
Worker A completes 1/6 of the task per hour, and Worker B completes 1/12 per hour. Combined, they complete 1/6 + 1/12 = 3/12 = 1/4 of the task per hour, so the full task takes 4 hours. A common mistake is averaging the two individual times directly ((6+12)/2 = 9 hours) — combined work rates add, but completion times don't average that way.
4. Two buses leave the same terminal at the same time, traveling in opposite directions. Bus A travels at 60 km/h and Bus B travels at 45 km/h. After how many hours will they be 315 kilometers apart?
- A. 2 hours
- B. 2.5 hours
- C. 3 hours
- D. 3.5 hours
Correct answer: C — 3 hours
Since the buses travel in opposite directions, their separation grows at the SUM of their speeds: 60 + 45 = 105 km/h. Dividing the total distance by this combined speed gives 315 ÷ 105 = 3 hours. A common mistake is using only one bus's speed or averaging the two speeds instead of adding them.
5. How many liters of a 40% alcohol solution must be mixed with 10 liters of a 10% alcohol solution to produce a 25% alcohol solution?
- A. 8 liters
- B. 10 liters
- C. 12 liters
- D. 15 liters
Correct answer: B — 10 liters
Setting up the alcohol-content balance: 0.40x + 0.10(10) = 0.25(x + 10). Expanding gives 0.40x + 1 = 0.25x + 2.5, so 0.15x = 1.5, and x = 10 liters. A common mistake is averaging the two percentages directly ((40%+10%)/2 = 25%) and assuming the two volumes must be equal — that shortcut only happens to work here because the target is exactly the midpoint.
6. A company's quarterly sales were: Q1 – ₱180,000; Q2 – ₱225,000; Q3 – ₱210,000; Q4 – ₱270,000. What was the percentage increase in sales from Q1 to Q4?
- A. 33.3%
- B. 50%
- C. 90%
- D. 66.7%
Correct answer: B — 50%
The increase from Q1 to Q4 is ₱270,000 − ₱180,000 = ₱90,000. As a percentage of the ORIGINAL (Q1) value: 90,000 ÷ 180,000 = 0.50, or 50%. A common mistake is dividing the increase by the NEW value instead (90,000 ÷ 270,000 ≈ 33.3%) — percentage increase is always calculated relative to the starting value.
7. What is the value of (3/4 + 1/6) × 2/5?
- A. 11/30
- B. 7/15
- C. 19/60
- D. 2/5
Correct answer: A — 11/30
First add the fractions using a common denominator of 12: 3/4 = 9/12 and 1/6 = 2/12, so 9/12 + 2/12 = 11/12. Then multiply by 2/5: (11/12) × (2/5) = 22/60, which simplifies to 11/30. A common mistake is multiplying before adding, ignoring the parentheses.
8. A cooperative lends ₱15,000 at a simple interest rate of 8% per year. How much total interest will accrue after 2 years and 6 months?
- A. ₱1,200
- B. ₱2,400
- C. ₱3,000
- D. ₱3,600
Correct answer: C — ₱3,000
Simple interest is Principal × Rate × Time: ₱15,000 × 0.08 × 2.5 years = ₱3,000. A common mistake is using only whole years (15,000 × 0.08 × 2 = ₱2,400) and forgetting to convert "2 years and 6 months" into 2.5 years.
9. If 8 workers can build a fence in 15 days, how many days would it take 12 workers to build the same fence, assuming the same work rate per worker?
- A. 8 days
- B. 10 days
- C. 12 days
- D. 20 days
Correct answer: B — 10 days
The total amount of work is constant: 8 workers × 15 days = 120 "worker-days" of effort. With 12 workers doing the same total work, the time needed is 120 ÷ 12 = 10 days. A common mistake is treating this as a direct proportion (more workers = more days) instead of an inverse one — more workers should REDUCE the time needed.
10. Maria is currently three times as old as her son. In 10 years, she will be twice as old as him. How old is Maria now?
- A. 24
- B. 30
- C. 36
- D. 27
Correct answer: B — 30
Let the son's current age be x, so Maria's current age is 3x. In 10 years, the equation becomes 3x + 10 = 2(x + 10). Solving: 3x + 10 = 2x + 20, so x = 10, making Maria 3 × 10 = 30. A common mistake is applying the "twice as old" relationship to their CURRENT ages instead of their ages 10 years from now.
Common Traps
The single most common mistake in word problems is setting up the wrong equation from a rushed reading of the question — for example, confusing "A is 20% more than B" (B × 1.20 = A) with "A is 20% of B" (B × 0.20 = A). These produce very different answers, and the exam's wrong-option set is usually built around exactly this kind of misreading, so a wrong setup will almost always match one of the four choices, giving false confidence that you got it right.
In percentage problems specifically, a frequent trap is applying a percentage change to the wrong base — a 25% increase followed by a 20% decrease does NOT return you to the original number, because the decrease is calculated on the NEW, larger amount, not the original. Multiplying the factors (1.25 × 0.80 = 1.00) is the reliable way to check whether two sequential percentage changes cancel out, rather than subtracting them.
In data interpretation, the most common error is misreading which axis or column a value comes from, especially in multi-series graphs. In work-rate problems, forgetting to convert "time to complete a job" into a RATE (jobs per hour) before combining two people's rates is a common setup error — you can't average two completion TIMES directly to find a combined time.
Study Routine
Spend early sessions drilling fraction-decimal-percentage conversions until they're automatic — being able to instantly recognize that 1/8 = 12.5% or 3/4 = 75% saves real time on exam day. Then move to word problems by TYPE: dedicate a session each to age problems, work problems, mixture problems, and distance/rate/time problems, since each type has a standard setup pattern that transfers across different specific numbers once you've internalized it. Practice data interpretation using real Philippine government statistics so you're comfortable with realistic axis labels and units, not just clean textbook numbers. In your final two weeks, do timed mixed sets covering all three sub-skills together, since recognizing WHICH type of problem you're looking at quickly is itself a skill that needs practice, not just solving each type in isolation.
