Numerical Ability: Core Formulas, Percentage Shortcuts & Word Problems
Essential algebraic formulas for ratio and proportion, percentage increases/discounts, work rate equations, and number sequences without a calculator.
Mental Math for Percentages, Discounts & Markups
Because calculators are strictly barred on exam day, master base-10 decomposition: (1) To find 10%, shift decimal left by 1 digit; (2) To find 5%, take half of 10%; (3) To find 1%, shift decimal left by 2 digits; (4) For successive discounts (e.g., 20% followed by 10%), apply multiplicatively, not additively (a 20% discount leaves 80%; 10% off 80% is 8%; total discount is 28%, NOT 30%). Formula for percentage change: ((New Value - Old Value) / Old Value) * 100%.
- Percentage Change = (Difference / Original Value) * 100%.
- Never simply sum multiple percentage discounts—compute each successively on the remaining balance.
An office desk originally priced at ₱5,000 is marked down by 20%. During a clearance sale, an additional 10% discount is applied to the discounted price. What is the final sale price?
Work Rate Formula (The Inverted Rate Rule)
If Person A completes a job in 'a' hours, their 1-hour work rate is 1/a. If Person B completes it in 'b' hours, their rate is 1/b. Working together, their combined hourly rate is (1/a + 1/b). The time 'T' to finish the entire job together is T = (a * b) / (a + b).
- Combined Work Time = (Product of individual times) / (Sum of individual times).
- If worker A takes 6 hours and worker B takes 3 hours: T = (6 * 3) / (6 + 3) = 18 / 9 = 2 hours.
Official Syllabus References & Legal Authorities
- Civil Service Commission Examination Announcement: Test Scope & Guidelines (Numerical Ability)(Civil Service Commission (CSC))
Apply what you learned
Practice specific Numerical Ability questions in timed examination conditions.