Arithmetic Reasoning
What this section measures
Arithmetic reasoning items are word problems: percentages, fractions, ratios and proportions, averages, rates, unit conversions, simple interest, and basic mixtures. The arithmetic is easy; the difficulty is translation and unit discipline.
Percentages. Distinguish percent of from percent change. A 25% increase multiplies by 1.25; a 20% decrease multiplies by 0.80. Successive changes compound - they do not add - so a 25% rise followed by a 20% fall yields exactly the original value (1.25 x 0.80 = 1.00). Percent change is always the difference divided by the original amount.
Ratios and proportions. Set up a proportion with matching units in matching positions, then cross-multiply.
Averages. Total equals average times count. To find a missing value, reconstruct the total first. Never average two averages unless the groups are the same size.
Rates. Distance equals rate times time; work problems add rates (1/a + 1/b), they do not add times.
Traps that appear
- Mixing minutes and hours, or cents and dollars, in one calculation.
- Computing the percent and stopping before applying it, or applying it to the wrong base.
- Rounding midway; carry exact values until the final step.
- Answering the intermediate value rather than the quantity requested.
Rule of thumb
Write the units next to every number. If the units do not cancel to the units the question asks for, the setup is wrong. If stuck, back-solve from the answer choices.
Worked example. A $80 jacket is marked down 25%, then the sale price is taxed at 8%. Final cost: 80 x 0.75 = $60; 60 x 1.08 = $64.80. Applying the tax to $80 is the classic error and gives $86.40.