Word problems for the NAPOLCOM exam: the six types, and the setup that turns a paragraph into one line of arithmetic.
Word problems are where the quantitative area is won or lost, because they combine reading with arithmetic under a clock. They are also more predictable than they look: a handful of types recur, and each has a setup that turns the paragraph into a single line. This page names the types, gives the setup for each, and shows the one habit that prevents the most common miss, which is solving correctly for the wrong thing.
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Quick facts
- Types
- Rate, percent, ratio, average, age, work
- First move
- Read the last sentence; name the type
- Main trap
- Solving the wrong quantity
- Tool
- One line of arithmetic per type
- Share
- The largest block of quantitative marks
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Read the question first
Read the last sentence before the rest. It tells you what is being asked and in what unit, and naming that before you read the numbers means every number you then meet is sorted as you go. Underline the target. Then read the problem, name its type, and write the one line of arithmetic the type calls for. The examinee who reads top to bottom and starts computing at the first number is the one who finds the discount when the question asked for the price.
The six types and their setups
Most NAPOLCOM word problems are one of six shapes. Recognising the shape is most of the work.
| Type | The one line | The trap |
|---|---|---|
| Rate (distance, speed, time) | distance = speed × time; convert minutes to hours first | Dividing by 2.3 hours when the time is 2 hours 30 minutes (2.5) |
| Percent | part = percent × whole; change = (new − old) ÷ old | Using the new value as the base for percent change |
| Ratio and proportion | Set the ratio equal to the parts; total ÷ sum of parts = one share | Giving one share when the question asks for one party's total |
| Average | sum = average × count; the missing value is the sum minus the known | Averaging averages of groups of different sizes |
| Age | Set today's ages as x and x + d; shift both by the same years | Shifting only one person's age |
| Work | Rates add: 1/a + 1/b = 1/together | Adding the times instead of the rates |
Estimate, then check the unit
Before computing, estimate. A car at about 70 km/h for about 4 hours is about 280 km; if the options are 72, 288 and 720, the estimate has already answered. After computing, check the unit against the underlined target: kilometres, pesos, years, hours. A right number in the wrong unit is a wrong answer and is always among the options.
Worked examples
These items are written specifically for this guide. The actual practice bank pulls from a separate pool of original NAPOLCOM-style items reviewed by passers.
Item 01
A police mobile covers 180 km in 2 hours 30 minutes. At the same average speed, how far will it travel in 4 hours?
- A252 km
- B270 km
- C288 kmCorrect
- D313 km
Explanation. Rate type. 2 hours 30 minutes is 2.5 hours; 180 ÷ 2.5 = 72 km/h; 72 × 4 = 288. D is what dividing by 2.3 gives; A and B come from other mis-conversions. Convert time to hours before anything else.Item 02
Three recruits share ₱4,500 in the ratio 2 : 3 : 4. How much does the recruit with the largest share receive?
- A₱500
- B₱1,000
- C₱1,500
- D₱2,000Correct
Explanation. Ratio type. Parts total 9; one share is 4,500 ÷ 9 = 500; the largest share is 4 × 500 = 2,000. A is one share, the trap for stopping early.Item 03
Ana's average on four tests is 82. What must she score on the fifth to average 85 across all five?
- A88
- B91
- C94
- D97Correct
Explanation. Average type. Needed sum: 85 × 5 = 425. Current sum: 82 × 4 = 328. Fifth score: 425 − 328 = 97. Working in sums, not averages, is the whole method.
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Study tactics that actually move the score
- 01
Read the last sentence first and underline the target quantity and its unit.
- 02
Name the type before touching a number; each type has exactly one setup.
- 03
Convert every time to hours and every percent to a fraction or decimal before computing.
- 04
Estimate first and check the options; on many items the estimate is the answer.
Frequently asked questions
Which word problem types come up most?
Rate, percent and ratio items are the most common in the reviewers we checked, with average, age and work problems appearing regularly. All six have a one-line setup.
How long should a word problem take?
Under two minutes, and under one for rate and percent items once the setups are automatic. Anything longer is a sign to estimate, choose and move on.
Do I need algebra?
Only the simplest kind: a single unknown in a linear equation, as in age problems. Nothing beyond that appears.
Stop reading. Find your floor.
Forty questions across all four subtests, forty minutes, and a per-subject breakdown against the 80.00 pass mark.