Arithmetic Reasoning
Core skills
Most Arithmetic Reasoning items are dressed-up versions of a few templates: percent change, rates (distance = rate times time), proportions, averages, work rates, simple interest, and unit conversions. Translate each sentence into an equation before computing, and label every number with its unit.
Traps
- Percent of versus percent more than. A 20 percent increase multiplies by 1.20; a 20 percent decrease multiplies by 0.80. They do not cancel out.
- Average speed is total distance divided by total time, not the average of the two speeds.
- Mixed units: minutes paired with hours, or cents paired with dollars.
- Chained fractions. After spending one third, two thirds remain; spending one quarter of that remainder leaves three quarters of two thirds, not one half of the original.
- Work problems add rates, not times. If one pipe fills a tank in 3 hours and another in 6 hours, together they fill 1/3 + 1/6 = 1/2 tank per hour, so 2 hours total.
- Of versus more than and part-to-part versus part-to-whole ratios.
Worked example
A car travels 120 miles outbound at 60 mph and returns at 40 mph. Total distance is 240 miles. Time outbound is 2 hours and time back is 3 hours, so total time is 5 hours. Average speed = 240 divided by 5 = 48 mph, not 50. Whenever a problem gives two speeds over equal distances, expect the answer to be lower than the simple average.