Mathematics and Numerical Reasoning
Mathematics and Numerical Reasoning
This domain tests arithmetic fluency under time pressure: fractions, decimals and percent, ratio and proportion, averages, number series, elementary algebra and geometry, and the translation of word problems into equations.
Core rules
- Percent. part = rate × base. A 20% increase followed by a 20% decrease does not return to the original value; it ends at 96%.
- Fractions. Use a common denominator to add or subtract; the word of signals multiplication.
- Ratio and proportion. For a ratio a : b, the total is a + b parts. Set up cross-products for proportion problems.
- Averages. Average = sum ÷ count, so sum = average × count. To combine groups of different sizes, weight by group size.
- Number series. Test differences first, then ratios, then alternating or interleaved patterns (odd positions, even positions).
- Rates. Distance = rate × time; work done = rate × time.
- Geometry. Area of a rectangle = length × width; triangle = ½ base × height; circle = πr²; perimeter formulas follow the same definitions.
Worked example
A sailor receives ₱12,000 a month. He spends 35% on food and one-fourth on lodging, and saves the rest. How much does he save?
Convert: one-fourth = 25%. Total spent = 35% + 25% = 60%. Savings rate = 100% − 60% = 40%. Savings = 0.40 × 12,000 = ₱4,800.
Traps that cost marks
- Confusing a percentage increase with percentage points.
- Mixing units - minutes with hours, centimeters with meters - before computing.
- Solving for the wrong quantity, especially when the question asks for the remainder.
- Averaging two averages of unequal groups without weighting.
- Missing interleaved series that jump by 3, 5, 7 in the odd slots and double in the even slots.
- Rushing the arithmetic when the method is already correct.