Arithmetic Reasoning
Arithmetic Reasoning on the NG Navy Exam measures how well you turn a word problem into arithmetic and carry it through without a calculator. Most items are multi-step: rates, percentages, ratios, averages, unit conversions, and measurement.
Translate first
Write what is given and what is asked, with units attached. A rate needs a time unit; a percentage needs a base. Convert mixed units before computing: 45 minutes is 0.75 hour, not 45.
Core relationships
- Distance = rate × time; work rates add when people or machines work together.
- Percent: part = percent × whole. Percent change = (new − old) ÷ old.
- Average = sum ÷ count. For a weighted average, multiply each group by its weight, add, then divide by total weight.
- Ratios: set up a proportion and cross-multiply, keeping like units in the same positions.
Worked example
A tank is 2/3 full. The crew uses 1/4 of the tank's capacity, then adds 7 gallons, filling it exactly. Find the capacity. Start: 2/3 C. Used: 1/4 C. Remainder: 2/3 − 1/4 = 8/12 − 3/12 = 5/12 C. The 7 gallons fills the missing 7/12 C, so 7/12 C = 7, and C = 12 gallons. Check: 8 − 3 + 7 = 12.
Traps
Do not average two speeds by adding and dividing by 2; average speed is total distance ÷ total time. Read whether a percent is of the original or more than it. Keep gallons with gallons and hours with hours. In how-much-remains items, subtract from the whole, not from the amount used.