Basic Math

Percentages

Calculating percentage change and understanding percentage points as an absolute measure.

Questions are set in government and office contexts. Expect budget allocations, salary changes, tax rates, and CPI calculations.

What the exam tests

Percentage Change (Relative Change)

Calculate the relative percent increase or decrease based on an original amount (e.g., a discount from $30 to $24).

Percentage Points (Absolute Change)

Find the absolute difference between two percentages, New % minus Old %. This is distinct from a relative percentage change.

Reverse Percentages

Find the original amount before a known percentage increase or decrease was applied.

Percentage Difference

Calculate change when neither value is clearly the original. Use the average of the two numbers as the denominator.

Financial Applications

Markup/markdown, ROI, inflation/CPI, and compound interest using P × (1 + i)^n.

Applied Word Problems

Isolate relevant data to find a percentage (e.g., 300 out of 400 files = 75%) or calculate budget allocations from tables.

›Percentage change (relative): (New − Old) ÷ Old × 100. Always divide by the original value.
›Percentage points (absolute): simply New % − Old %. There is no division involved: it is a raw numerical difference between two percent figures.
›Percentage difference (no clear original): (|A − B|) ÷ average of A and B × 100.

!Confusing percentage change with percentage points is the most common error. 'From 10% to 15%' is 5 percentage points but a 50% relative increase.

›Part over Whole: % = (Value ÷ Total) × 100.
›Decimal multiplier: for a 1% decrease, multiply by 0.99; for a 20% increase, multiply by 1.20.
›Compound interest: P × (1 + i)^n. For fluctuating rates, multiply the principal by each successive factor year by year.
›Reverse percentage: divide the known amount by (1 + rate) to find the original pre-change value.

!For compound interest with fluctuating rates, do not average the rates. Multiply each year's factor sequentially.

›Use mental rounding to check reasonableness before committing to an answer (e.g., 15% of $1,250 ≈ $190).
›Cross-check by applying the inverse operation: multiply back to verify a percentage result.
›In word problems, identify and ignore irrelevant data (dates, names, unrelated figures) before setting up the calculation.

Convert the fraction 3/4 into its decimal equivalent.

A.0.34

B.0.43

C.0.75

D.0.073

3 ÷ 4 = 0.75. Benchmark to memorize: 3/4 = 0.75 = 75%. Options A and B transpose the digits of the numerator and denominator.

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