Basic Math

Ratios & Proportions

Determining relative values and solving for unknown parts in a ratio.

Questions appear in government staffing, budget allocation, and business analytics contexts.

What the exam tests

Part-to-Whole Ratio Problems

Find the number of specific items within a group based on a given ratio and total (e.g., red marbles in a jar of 70 where red:blue = 3:4).

Rate Problems (Three-Variable)

Relate two quantities in different units (typically speed/distance/time or work/time/workers) and solve for the missing variable.

Proportional Staffing/Workload Scenarios

Determine how many employees are needed to complete a task in a specific number of days, assuming uniform work rate.

Unit Rate Calculations

Calculate a value 'per' unit, such as job applications per opening or how many items a fixed budget can buy at a given rate.

Financial and Partnership Proportions

Profit sharing where partners receive percentages based on the proportion of their capital contributions.

Mathematical Financial Ratios

Apply specific business formulas such as Inventory Turnover Ratio (cost of sales ÷ average inventory) or P/E Ratio.

Map and Scale Problems

Determine actual distances based on a map scale (e.g., ¼ cm on a map = 20 km in reality).

›Part-to-whole: Number of a items = (a ÷ (a + b)) × Total.
›Speed: Distance = Velocity × Time. Rearrange to solve for any missing variable.
›Work: Work = Power × Time. Use to find workers needed or time required.
›Unit rate: divide the total quantity by the total units to get the per-unit value.

!Rate problems with multiple workers: double the workers and you halve the time. This is an inverse relationship, not a direct one.

›Isolate the unknown (X) using cross-multiplication in a proportional statement: a/b = c/X → X = (b × c) ÷ a.
›Convert all time or quantity units to the same standard (yearly, hourly) before applying rate formulas.
›A fraction can represent the relative probability or 'odds' of an event. Treat it the same as a ratio.

›Identify and ignore irrelevant information (names, dates, unrelated figures) before setting up the ratio.
›Use mental estimation to confirm your answer is in the right ballpark and to eliminate illogical multiple-choice options.

!Map/scale problems: confirm which direction the scale goes (map → reality or reality → map) before multiplying or dividing.

A jar contains red and blue marbles in a ratio of 3:4. If there are 70 marbles in total, how many are red?

A.20

B.25

C.30

D.40

Part = (component ÷ total parts) × whole. Red = 3 ÷ (3+4) × 70 = 3/7 × 70 = 30. Option D (40) is the blue count, not red.

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