Time saving estimation techniques and shortcut strategies for the GRE quantitative reasoning section.
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- When estimating a square root, how can you quickly check if it falls between two integers?
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Test the squares of nearby integers. For example, to estimate sqrt(50), note that 7^2=49 and 8^2=64, so sqrt(50) is slightly above 7.- What is the fastest way to compare two fractions without finding a common denominator?
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Cross-multiply. If comparing a/b and c/d, compute a*d and b*c. The larger product corresponds to the larger fraction.- What shortcut can you use for percent increase calculations under time pressure?
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Use the multiplier formula: new = old * (1 + percent/100). For a 20% increase, multiply by 1.2. This avoids two separate steps.- When should you recognize a quadratic as a difference of squares to save time?
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When you see x^2 minus a perfect square. For example, x^2 - 9 factors instantly to (x-3)(x+3) without using the quadratic formula.- How do you quickly estimate 1 / 0.098 without a calculator?
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Recognize 0.098 is close to 0.1. So 1/0.098 is slightly more than 1/0.1 = 10.- What is the mental shortcut for comparing products of numbers equidistant from a middle value?
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If comparing (n-d)(n+d) to n^2, note that (n-d)(n+d) = n^2 - d^2, which is always smaller than n^2.- How do you quickly identify if a three-digit number is divisible by 3?
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Add the digits. If the sum is divisible by 3, the number is. For example, 459: 4+5+9=18, which is divisible by 3.- What is the fastest approach to solving a proportion like x/20 = 3/5 mentally?
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Cross-multiply once: 5x = 60, so x = 12. This is faster than finding a common denominator.- When comparing sqrt(2) and 1.4, how can you avoid computing the full square root?
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Square both sides to compare: 2 vs 1.96. Since 2 > 1.96, sqrt(2) > 1.4.- What is a quick check for whether a large number is divisible by 9?
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Sum the digits repeatedly until you get a single digit. If it equals 9, the original is divisible by 9.- How do you quickly compute a discount like 'take 15% off 60'?
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Decompose: 10% of 60 is 6, and 5% is 3. So 15% is 9, and the result is 60 - 9 = 51.- What shortcut applies when comparing values with exponents or logarithms in an inequality?
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If the base is greater than 1, the exponential/log function is increasing. If 0 < base < 1, it is decreasing. Use monotonicity to compare without computing.- How do you recognize when two algebraic expressions are equal without full algebra?
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Plug in simple test values like 0, 1, -1, or 2 and check if both sides match. If they differ at any test value, the expressions are not equivalent.- What is the fastest way to compute 25 * 36?
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Recognize that 25 * 4 = 100. Rewrite as 25 * 36 = 25 * 4 * 9 = 100 * 9 = 900.- When you see a percent problem involving change, how do you avoid confusion?
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Percent increase: new = old(1 + r). Percent of: new = old * p. Always define which operation applies based on the problem's wording.
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