Arithmetic Reasoning
What the questions test
Arithmetic Reasoning is not a calculation contest; it is a translation contest. Most items describe a situation and ask for a quantity. Identify the unknown, assign it a variable or a blank, and write an equation or a sequence of operations before computing. Core topics include rates and unit prices, proportions and scaling, percent increase and decrease, weighted averages, distance-rate-time, work rates, simple interest, and perimeter, area, and volume of rectangles, triangles, and circles.
Traps
- Percent change is multiplicative. A 25% increase followed by a 20% decrease is not a 5% change: 1.25 x 0.80 = 1.00, so the net change is 0%.
- "Less than" reverses order. "7 less than 3 times a number" is 3x - 7, not 7 - 3x.
- Units must match. Convert minutes to hours or cents to dollars before combining.
- Averages hide sums. If the average of 5 scores is 82, the sum is 410; do not average the averages.
- Extra information is common. Some numbers are distractors.
Worked example
A jacket is discounted 20% and then taxed 8% on the sale price. If the final charge is $86.40, what was the original price? Let p be the original price. After the discount the price is 0.80p; after tax it is 1.08(0.80p) = 0.864p. Set 0.864p = 86.40, so p = 100. The original price was $100. Check: $100 becomes $80, then $86.40.
Rule of thumb
Write the units beside every number. If the units do not cancel to the unit of the answer, your setup is wrong.