Quantitative Reasoning
Quantitative Reasoning checks whether you can set up and solve arithmetic quickly without a calculator: number series, fractions and percentages, ratios, and short word problems drawn from everyday situations.
Core rules
- Order of operations: parentheses, exponents, multiply/divide, then add/subtract.
- Percentages: "of" means multiply; percent change = (new − old) ÷ old × 100.
- Number series: test differences first, then ratios, then alternating or square/prime patterns.
- Ratios and proportions: keep units consistent and scale both parts by the same factor.
- Word problems: distance = rate × time; work = rate × time; average = sum ÷ count.
- Geometry: rectangle and triangle areas, circle circumference, Pythagorean triples such as 3-4-5 and 5-12-13.
Worked example
A jacket sells for P1,200 after a 25% discount. What was the original price? Let the original price be x. After a 25% discount the price is 75% of x, so 0.75x = 1,200 → x = 1,200 ÷ 0.75 = P1,600. The trap answer is P1,500, obtained by adding 25% of 1,200. A discount is taken from the original price, not from the sale price, so you divide rather than multiply.
Traps that cost marks
- Percent increase and decrease are not symmetric: 25% off then 25% on does not restore the original price.
- Mixing units (minutes with hours, centimeters with meters) in rate problems.
- Answering the wrong quantity - remaining instead of used, total instead of difference.
- Rounding too early in multi-step items and drifting off the choices.