Arithmetic Reasoning
The Arithmetic Reasoning domain tests whether you can turn a dense word problem into an equation before the clock runs out. The mathematics is deliberately modest - fractions, percentages, ratios, averages, rates, unit conversion, and simple geometry - but the wording is packed with detail, the numbers usually reward estimating over long division, and the answer choices include the results of the most common misreadings.
Build the equation before you calculate
Underline the quantity being asked for and give it a letter. Translate each sentence into an operation, confirming that units agree. Convert everything to one unit (minutes to hours, cents to dollars) before computing; unit mismatch is the largest single source of wrong answers. When the algebra looks slow, back-solve: plug the middle answer choice into the problem and adjust up or down.
Formulas worth memorizing
- Percent change = (new − old) ÷ old × 100. A 20% increase followed by a 20% decrease leaves 96% of the original, not 100%.
- Part = whole × rate. A 15% hold rate on 480 crates is 72 crates.
- Work rate: total work = (rate per worker per hour) × workers × hours.
- Average = sum ÷ count, so sum = average × count - the way to recover a missing value.
- Distance = rate × time; rates add for objects moving apart and subtract in same-direction pursuit.
- A ratio a:b scales by a multiplier k, giving ak and bk; total = (a + b)k.
Worked example
Five officers process 1,200 declarations in 8 hours. At that rate, how many do seven officers process in 6 hours?
First find the per-officer hourly rate: 1,200 ÷ (5 × 8) = 30 declarations per officer-hour. Then apply the new staffing and shift: 30 × 7 × 6 = 1,260 declarations. Note the trap: scaling only for the extra officers (1,200 × 7/5 = 1,680) ignores that the shift is two hours shorter, and 1,680 will be offered as a choice.
Traps that cost marks
- Percentage points versus percent: a rate moving from 4% to 5% rises one point but 25%.
- "Of" versus "more than": 30% of 80 is 24; 30% more than 80 is 104.
- Averaging two group averages directly instead of weighting by group size.
- Stopping at an intermediate value; circle the quantity actually requested.
- "Remaining" problems: subtract first, then apply the next percentage to what is left.