Ratios are a high-frequency topic on the GRE Quant section, testing your ability to work flexibly with relationships. This guided path will teach you the core skills and the strategic shortcuts needed to solve these questions quickly and accurately.
Start with the core definition and walk through a step-by-step example of how to simplify ratios to their lowest terms.
A ratio compares values. Always express it in simplest form (like a fraction).
Car Zippy: $37,500
Car Giffy: $32,500
Ratio Z : G?
Divide by 100:
$$ 375 : 325 $$Both end in 5. Divide by 25:
$$ 375 \div 25 = 15 $$
$$ 325 \div 25 = 13 $$
Final Ratio: 15 : 13
Learn the fundamental method for solving word problems by representing unknown values with a common multiplier 'x'.
Multiply a ratio by a constant. The value remains the same.
Master the methods for distributing a total amount into a given ratio and for working backwards to find the total from a single part.
Master the crucial technique for combining two separate ratios (e.g., a:b and b:c) into a single, continuous ratio (a:b:c).
Walk through a real-world application of ratios in partnership problems, where both investment and time must be considered.
When investment periods differ, profit is shared in the Compound Ratio of (Capital × Time).
A invests \$10k for 4 months.
B invests \$20k for 6 months.
C invests \$30k for 12 months.
Profit: \$7800.
Ratio: $$ 2:6:18 \rightarrow 1:3:9 $$
Total Parts: $$ 1+3+9 = 13 $$
1 Part = $$ 7800/13 = \$600 $$
A: \$600 | B: \$1800 | C: \$5400
Learn how to convert statements of multiples (e.g., 3A = 4B) into the correct A:B ratio, a common trap in advanced problems.
If 3A = 4B, what is A:B?
Rule: Inverse the coefficients.
$$ A:B = 4:3 $$If 2A = 3B = 4C, find A:B:C.
Step 1: Invert coefficients: $$ \frac{1}{2} : \frac{1}{3} : \frac{1}{4} $$
LCM of denominators (2, 3, 4) is 12.
Multiply each fraction by 12.
A: $$ \frac{1}{2} \times 12 = 6 $$
B: $$ \frac{1}{3} \times 12 = 4 $$
C: $$ \frac{1}{4} \times 12 = 3 $$
A:B:C = 6 : 4 : 3
Test your ability to solve for the "fourth proportional," a key skill for solving a wide variety of ratio problems.
Two ratios are equal.
$$ a:b = c:d \implies \frac{a}{b} = \frac{c}{d} $$a, b, c are linked.
$$ a:b = b:c \implies b^2 = ac $$Learn the fastest way to solve QC ratio problems by using strategic substitution instead of slow, formal algebra.
Given: $$ \frac{x}{y} = \frac{3}{5} $$
Put your understanding of GRE Ratio & Proportion: A Guide to Efficient Problem Solving to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
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