AFPSAT Numerical Reasoning: Practice Guide & Sample Questions
AFPSAT Numerical Reasoning covers 35 of the 150 items, with 35 minutes to complete them — exactly one minute per item on average, more breathing room than Verbal or Abstract Reasoning. It tests basic arithmetic operations and word problems, done entirely without a calculator, similar in spirit to the CSE's Numerical Ability category. Because no calculator is allowed, the real skill being built is fast, accurate mental and by-hand computation, not just knowing the right method.
This page walks through the sub-skills tested, the setup mistakes that account for most wrong answers, and worked sample questions with full step-by-step explanations. Below the study material, a full practice quiz pulls Numerical Reasoning questions from Pasa's question bank.
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, similar to the CSE's Numerical Ability category. Word problems are the bulk of the section: distance/rate/time problems, age problems, work problems, and basic financial calculations (simple interest, discounts) all appear. Because the section is separately timed with a full minute per item on average — more time per item than either of the other two AFPSAT sections — accuracy is realistically achievable if your underlying arithmetic is solid.
| Sub-skill | What it looks like |
|---|---|
| Basic operations | Fractions, decimals, percentages, ratios |
| Word problems | Distance/rate/time, age, work, basic financial calculations |
Since no calculator is allowed, practicing mental shortcuts — like recognizing that dividing by 5 is the same as multiplying by 2 and dividing by 10, or that 15% of a number is 10% plus half of that 10% — pays off more here than in almost any other section.
Sample Questions
1. A patrol vehicle leaves a base traveling at 40 km/h. Thirty minutes later, a second vehicle leaves the same base traveling the same route at 60 km/h. How long after the SECOND vehicle departs will it catch up to the first?
- A. 1 hour
- B. 1.5 hours
- C. 1 hour 15 minutes
- D. 45 minutes
Correct answer: A — 1 hour
When the second vehicle departs, the first is already 40 × 0.5 = 20 km ahead. Since the second vehicle gains ground at the DIFFERENCE of their speeds (60 − 40 = 20 km/h, because they move in the same direction), it takes 20 ÷ 20 = 1 hour to close the gap. A common mistake is adding the speeds (as for objects moving toward each other) instead of subtracting them.
2. A uniform originally priced at ₱1,200 is sold at a 15% discount. What is the sale price?
- A. ₱1,020
- B. ₱180
- C. ₱1,050
- D. ₱1,100
Correct answer: A — ₱1,020
15% of ₱1,200 is ₱180 (the discount amount), so the sale price is ₱1,200 − ₱180 = ₱1,020. A common mistake is stopping after computing the discount amount itself (₱180) instead of subtracting it from the original price.
3. Five years ago, a father was four times as old as his daughter. Now, he is three times as old as her. How old is the daughter now?
- A. 10
- B. 15
- C. 20
- D. 25
Correct answer: B — 15
Let the daughter's age five years ago be x, so the father's was 4x. Now their ages are x+5 and 4x+5, and the father is three times the daughter's current age: 4x + 5 = 3(x + 5). Solving: 4x + 5 = 3x + 15, so x = 10, meaning the daughter is now x + 5 = 15. A common mistake is applying "three times as old" to their ages FIVE YEARS AGO instead of their current ages.
4. A water tank can be filled by Pipe A alone in 4 hours. A drain can empty the full tank in 6 hours. If both the pipe and the drain are open at the same time, how long will it take to fill the empty tank?
- A. 10 hours
- B. 8 hours
- C. 12 hours
- D. 5 hours
Correct answer: C — 12 hours
The pipe fills at 1/4 of the tank per hour, while the drain empties at 1/6 per hour. Since they work in opposite directions, the net fill rate is 1/4 − 1/6 = 1/12 of the tank per hour, so filling the tank takes 12 hours. A common mistake is adding the two rates as if both were filling (giving 2.4 hours) instead of subtracting, since the drain works against the pipe.
5. A recruit answered 80% of the items correctly on a 50-item practice test. Of the items answered correctly, 25% were in the Numerical Reasoning section. How many correctly-answered items were in Numerical Reasoning?
- A. 10
- B. 8
- C. 12
- D. 16
Correct answer: A — 10
80% of 50 items is 40 items answered correctly. Of those 40, 25% were Numerical Reasoning items: 25% × 40 = 10. A common mistake is calculating 25% of the original 50 items instead of 25% of the 40 correctly answered items.
6. A recipe for field rations requires rice and beans in a ratio of 3:2. If a batch uses 18 kilograms of rice, how many kilograms of beans are needed?
- A. 10 kg
- B. 12 kg
- C. 14 kg
- D. 9 kg
Correct answer: B — 12 kg
Rice corresponds to 3 parts of the ratio and equals 18 kg, so each part equals 18 ÷ 3 = 6 kg. Beans correspond to 2 parts: 2 × 6 = 12 kg. A common mistake is treating 18 kg as the total of both ingredients combined rather than just the rice portion.
7. A soldier deposits ₱20,000 in a cooperative savings account earning 6% simple interest per year. How much total interest will the deposit earn after 3 years?
- A. ₱1,200
- B. ₱3,600
- C. ₱2,400
- D. ₱6,000
Correct answer: B — ₱3,600
Simple interest is Principal × Rate × Time: ₱20,000 × 0.06 × 3 = ₱3,600. A common mistake is computing only one year's interest (₱1,200) and forgetting to multiply by the full 3-year period.
8. A convoy travels 210 kilometers at a constant speed of 70 km/h. If it departs at 6:00 AM, at what time will it arrive?
- A. 8:30 AM
- B. 9:00 AM
- C. 9:30 AM
- D. 10:00 AM
Correct answer: B — 9:00 AM
Time = distance ÷ speed = 210 ÷ 70 = 3 hours. Adding 3 hours to a 6:00 AM departure gives an arrival time of 9:00 AM. Since no calculator is allowed, double-checking a division like this by multiplying the answer back (70 × 3 = 210) is a reliable way to catch arithmetic slips.
9. Of a company of 120 soldiers, 3/8 are assigned to logistics and the rest to combat roles. How many soldiers are assigned to combat roles?
- A. 45
- B. 75
- C. 40
- D. 80
Correct answer: B — 75
3/8 of 120 soldiers is (3 × 120) ÷ 8 = 45, assigned to logistics. The remaining soldiers, assigned to combat roles, number 120 − 45 = 75. A common mistake is answering with the logistics figure itself instead of the remainder the question actually asks about.
10. A camp's food budget is increased by 20% one year, then decreased by 20% the following year. If the original budget was ₱500,000, what is the budget after both changes?
- A. ₱500,000
- B. ₱480,000
- C. ₱520,000
- D. ₱460,000
Correct answer: B — ₱480,000
After a 20% increase, the budget becomes ₱500,000 × 1.20 = ₱600,000. Applying a 20% decrease to this NEW amount gives ₱600,000 × 0.80 = ₱480,000 — less than the original, since the decrease is calculated on a larger base than the increase was. A common mistake is assuming equal-percentage increase and decrease cancel out perfectly.
Common Traps
The most common trap in word problems is the same one that affects the CSE's Numerical Ability category: setting up the wrong equation from a rushed reading, especially confusing "X% more than" with "X% of." In distance/rate/time problems specifically, a frequent error is using the wrong combined-speed formula — for objects moving in OPPOSITE directions, speeds ADD; for one object catching up to another moving in the SAME direction, you use the DIFFERENCE of their speeds.
In percentage-based word problems, forgetting to convert time units consistently before computing is a frequent source of otherwise-correct-method wrong answers. Because there's no calculator, arithmetic slips are also a bigger risk here — it's worth building in a habit of a quick sanity check on the answer's rough magnitude. Since the section has more time per item than Verbal or Abstract Reasoning, rushing through Numerical Reasoning items to "bank time" isn't necessary — this section rewards careful, correct computation more than raw speed.
Study Routine
Because this section shares its content with the CSE's Numerical Ability category, the same word-problem-by-type routine transfers directly: dedicate sessions to distance/rate/time, age, work, and basic financial problems. What's specific to AFPSAT preparation is practicing entirely without a calculator from the start, including basic operations like long division and percentage calculations by hand. Time yourself doing sets of 10-15 items at the section's actual pace (about a minute each) in your final two weeks, to confirm your accuracy holds up at speed, not just when working slowly and carefully.
