Quantitative Reasoning
Quantitative Reasoning on the NGAT checks whether you can translate a short problem into arithmetic and then compute accurately under time. Topics include percentages, ratios, averages, number properties, algebra, and table or chart interpretation. Most items are solvable without a calculator; the challenge is choosing the right base and avoiding premature rounding.
Core rules
- Percent change = (new − old) ÷ old × 100. State the original amount before computing.
- Successive percentage changes multiply factors: a 20% fall then a 10% fall is 0.8 × 0.9 = 0.72, a 28% total fall, not 30%.
- Ratios scale by a common multiplier. If A:B = 3:5, write A = 3k and B = 5k.
- Average = total ÷ count, so total = average × count. Use this for missing-value questions.
- In data interpretation, read the axis labels and units first; distinguish “percentage points” from “percent”.
- For rate problems, keep units consistent and use time = distance ÷ speed.
Worked example
A jacket costs $80. Its price is reduced by 20%, and the sale price is then reduced by 10%. What is the final price? A 20% reduction leaves 80% of $80 = $64. The second reduction is 10% of $64, not of $80: 0.9 × $64 = $57.60. Total reduction is $22.40, or 28%. Answer: $57.60. Choosing $56 (30% off $80) is the trap.
Traps that cost marks
Adding successive percentages is the most frequent error. A related trap is taking a percentage of the wrong base-e.g., a 25% increase followed by a 20% decrease returns to the original, not a 5% change. Average-speed questions cannot be solved by averaging the two speeds unless the times are equal; use total distance ÷ total time. In ratio questions, do not assume the total is 100. Finally, check whether the question asks for a value, a percentage, or a percentage-point difference; those answers differ.