GSET: Quantitative Reasoning

The GSET Quantitative Reasoning domain tests arithmetic, algebra, geometry, number properties, ratios, percentages, rates, and elementary probability in short problems. Structure and estimation matter as much as computation, especially when answer choices are spread apart.

Core rules

• Translate the wording into an equation or a proportion before calculating.
• Track units. A rate must match the time unit in the question; convert before multiplying.
• For percent change, use (new − old) / old × 100. The original value is the base.
• When a problem gives variables in the answer choices, plug in small numbers that satisfy the conditions.
• Use divisibility, prime factorization, and LCM/GCF to avoid long arithmetic.

Worked example

A jacket is priced at $80. It is discounted 25%, then an additional 10% is taken off the sale price. What is the final price? The first discount leaves 75% of $80: 0.75 × 80 = $60. The second discount applies to $60, not $80: 0.90 × 60 = $54. The final price is $54. Adding the discounts and taking 35% off $80 gives $52, which is wrong because the second discount has a smaller base.

Traps

• Adding successive percent discounts instead of multiplying the remaining factors.
• Confusing percentage points with percent change.
• Using an unweighted average for rates, such as averaging two speeds over equal distances.
• Missing a second valid solution in absolute-value or quadratic problems.
• Forgetting that a 20% increase followed by a 20% decrease yields a net 4% decrease.