Arithmetic and Quantitative Reasoning
What the questions test
Expect fractions, decimals, and percents; percent change; ratios and proportions; unit rates; averages; order of operations; measurement and time conversions; and simple table reading. Most items are word problems, so the arithmetic is easy but the setup is where candidates lose points.
Concepts to know
Convert freely among fractions, decimals, and percents. Percent change always uses the original amount as the base: change divided by original. A part-whole percent problem asks 'what is 15% of 80,' while a percent-more problem asks 'what is 80 increased by 15%' - different equations. Averages require weighting when groups differ in size. Keep units attached to every number and convert before computing.
Traps
- Adding or subtracting percents directly instead of applying them one at a time.
- Using the new value as the base for a percent change.
- Averaging two averages when the groups have different counts.
- Mixing minutes with hours, or cents with dollars.
- Rounding mid-calculation and then choosing a nearby wrong answer.
- Distractors built from the wrong operation (adding where you should divide).
Worked example
A $60 item is marked up 20%, then discounted 20%. Many candidates answer $60. Correctly: $60 x 1.20 = $72; $72 x 0.80 = $57.60. The discount applies to the marked-up price, not the original. Rule of thumb: write the problem as an equation with units, then run percent changes sequentially on the running total. Estimate first - if your answer is far from the estimate, recheck the setup.