Basic operations for the NAPOLCOM exam: arithmetic, fractions, decimals and percentages, done fast by hand.
The quantitative reasoning area is arithmetic first, and arithmetic done by hand under a clock is a different skill from arithmetic done with a calculator at leisure. The items use round numbers and clean fractions for that reason, and the examinee who knows the shortcuts finishes them in seconds. This page covers the operations the area draws on, the shortcuts that matter, and the habit of estimating before computing that eliminates options for free.
- Last reviewed
- Worked examples
- 3
- Subtest
- NAPOLCOM Exam Basic Operations Reviewer: Arithmetic, Fractions and Percentages
Or drill napolcom exam basic operations reviewer: arithmetic, fractions and percentages (included with a paid plan).
Quick facts
- Covers
- Whole numbers, fractions, decimals, percent, ratio
- Calculator
- None; everything by hand
- Main trap
- Doing the operation right and the question wrong
- Method
- Estimate first; use fraction shortcuts for percent
- Payoff
- Speed here buys time for word problems
Primary keyword: napolcom exam basic operations reviewer
What the area draws on
The four operations on whole numbers with the correct order of operations; addition, subtraction, multiplication and division of fractions and decimals, and converting among fractions, decimals and percentages; percent of a number, percent change and successive percentages; ratios and proportions; and simple exponents and square roots. Nothing beyond secondary-school mathematics, and nothing that needs a formula you cannot derive in a line.
The shortcuts that save the clock
Percentages as fractions: 50% is a half, 25% a quarter, 20% a fifth, 12.5% an eighth, 33⅓% a third. '12.5% of 32,000' is 32,000 ÷ 8, done in your head. Splitting: 15% is 10% plus 5%, and 10% of anything is the decimal point moved once. Successive percentages multiply what is left: 20% off then 10% off is 0.8 × 0.9 = 0.72, so 28% off, never 30%. Fraction-to-decimal by memory for eighths and thirds. And for division by 5, double and divide by 10.
| Percent | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33⅓% | 1/3 | 0.333… |
| 37.5% | 3/8 | 0.375 |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |
Estimate before you compute
Round each number, get a rough answer, and look at the options. On a large share of items that alone eliminates two or three choices, and on some it answers the item outright. It also catches the error the exam is fishing for: a decimal point in the wrong place, a percentage applied to the wrong base. An answer that is ten times too big is obvious once you have an estimate and invisible if you have not.
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
What is 12.5% of 2,400?
- A250
- B300Correct
- C320
- D360
Explanation. 12.5% is one eighth; 2,400 ÷ 8 = 300. Multiplying 2,400 × 0.125 by hand also works but takes four times as long. The wrong options are what you get from an eighth of 2,000, 2,560 or 2,880.Item 02
A ₱1,500 item is discounted 20%, then a further 10% off the reduced price. What is the final price?
- A₱1,050
- B₱1,080Correct
- C₱1,200
- D₱1,350
Explanation. Multiply what is left: 1,500 × 0.8 = 1,200, then × 0.9 = 1,080. A is the trap for adding the discounts to 30%. C is after the first discount only.Item 03
Simplify: 3/4 + 5/8 − 1/2.
- A7/8Correct
- B1
- C9/8
- D5/4
Explanation. Over eighths: 6/8 + 5/8 − 4/8 = 7/8. Estimation first: 0.75 + 0.625 − 0.5 is about 0.875, which is A. The estimate alone rules out C and D.
Want twenty more like these, under a clock?
The napolcom exam basic operations reviewer: arithmetic, fractions and percentages drill runs ten or twenty items with full explanations and tracks which traps you fall for most often. Included with a paid plan.
Study tactics that actually move the score
- 01
Memorise the percent-fraction table above. It converts most percentage items into a single division.
- 02
Round and estimate before every computation; check the options against the estimate first.
- 03
Successive percentages multiply what is left. Never add them.
- 04
Twenty items by hand every day. Speed is a habit, and it is the habit this area tests.
Frequently asked questions
Can I use a calculator on the NAPOLCOM exam?
No. Calculators are on NAPOLCOM's list of prohibited items. Practise every computation by hand from the first week.
How advanced is the math?
Secondary-school arithmetic and basic algebra. The difficulty is speed and accuracy by hand, not the concepts.
What is the most common mistake?
Answering the wrong quantity: the discount instead of the final price, the part instead of the whole. Read what is asked before you compute.
Stop reading. Find your floor.
Forty questions across all four subtests, forty minutes, and a per-subject breakdown against the 80.00 pass mark.